REFERENCE STATEMENT FROM EDEXCEL ......REFERENCE STATEMENT FROM EDEXCEL SPECIFICATION FOR GCSE (9-1)...

REFERENCE STATEMENT FROM EDEXCEL SPECIFICATION FOR GCSE (9-1) MATHEMATICSHigher tier students will be assessed on all content.Foundation tier students will be assessed on content identified by the standard and underlined type.

N1 order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, > , ≤, ≥N2 apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and

improper), and mixed numbers – all both positive and negative; understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)

N3 recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions); use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

N4 use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem

N5 apply systematic listing strategies, including use of the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways)

N6 use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5; estimate powers and roots of any given positive number

N7 calculate with roots, and with integer and fractional indicesN8 calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares (e.g. √12 = √(4 × 3) =

√4 × √3 = 2√3) and rationalise denominatorsN9 calculate with and interpret standard form A × 10n, where 1 ≤ A < 10 and n is an integer

N10 work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8); change recurring decimals into their corresponding fractions and vice versa

N11 identify and work with fractions in ratio problemsN12 interpret fractions and percentages as operatorsN13 use standard units of mass, length, time, money and other measures (including standard compound measures) using

decimal quantities where appropriateN14 estimate answers; check calculations using approximation and estimation, including answers obtained using technology

N15 round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding

N16 apply and interpret limits of accuracy, including upper and lower boundsA1 use and interpret algebraic manipulation, including:

● ab in place of a × b● 3y in place of y + y + y and 3 × y● a2 in place of a × a, a3 in place of a × a × a, a2b in place of a × a × b● a/b in place of a ÷ b● coefficients written as fractions rather than as decimals● brackets

A2 substitute numerical values into formulae and expressions, including scientific formulaeA3 understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and

factorsA4 simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:

● collecting like terms● multiplying a single term over a bracket● taking out common factors● expanding products of two or more binomials● factorising quadratic expressions of the form x2 + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax2 + bx + c● simplifying expressions involving sums, products and powers, includingthe laws of indices

A5 understand and use standard mathematical formulae; rearrange formulae to change the subjectA6 know the difference between an equation and an identity; argue mathematically to show algebraic expressions are

equivalent, and use algebra to support and construct arguments and proofsA7 where appropriate, interpret simple expressions as functions with inputs and outputs; ; interpret the reverse process as

the ‘inverse function’; interpret the succession of two functions as a ‘composite function’ (the use of formal function notation is expected)

A8 work with coordinates in all four quadrantsA9 plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify

parallel and perpendicular lines; find the equation of the line through two given points or through one point with a given gradient

A10 identify and interpret gradients and intercepts of linear functions graphically and algebraically

A11 identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square

A12 recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, exponential functions y = kx for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size

A13 sketch translations and reflections of a given functionA14 plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real

contexts to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

A15 calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts (this does not include calculus)

A16 recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point

A17 solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph

A18 solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph

A19 solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph

A20 find approximate solutions to equations numerically using iterationA21 translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous

equations), solve the equation(s) and interpret the solutionA22 solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on

a number line, using set notation and on a graphA23 generate terms of a sequence from either a term-to-term or a position-to-term ruleA24 recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type

sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer, and r is a rational number > 0 or a surd) and other sequences

A25 deduce expressions to calculate the nth term of linear and quadratic sequencesR1 change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g.

speed, rates of pay, prices, density, pressure) in numerical and algebraic contextsR2 use scale factors, scale diagrams and mapsR3 express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1R4 use ratio notation, including reduction to simplest formR5 divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two

parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

R6 express a multiplicative relationship betweeb two quantities as a ratio or a fractionR7 understand and use proportion as equality of ratiosR8 relate ratios to fractions and to linear functionsR9 define percentage as `number of parts per hundred¿; interpret percentages and percentage changes as a fraction or a

decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics

R10 solve problems involving direct and inverse proportion, including graphical and algebraic representationsR11 use compound units such as speed, rates of pay, unit pricing, density and pressureR12 compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale

factorsR13 understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; construct and interpret equations

that describe direct and inverse proportionR14 interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and

inverse proportionR15 interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and

instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts (this does not include calculus)

R16 set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes

G1 use conventional terms and notation: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries; use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description

G2 use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line

G3 apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

G4 derive and apply the properties and definitions of special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language

G5 use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)G6 apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about

angles and sides, including Pythagoras' theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs

G7 identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors)

G8 describe the changes and invariance achieved by combinations of rotations, reflections and translationsG9 identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc,

sector and segmentG10 apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove

related resultsG11 solve geometrical problems on coordinate axesG12 identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and

spheresG13 construct and interpret plans and elevations of 3D shapesG14 use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)

G15 measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

G16 know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

G17 know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr²; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids

G18 calculate arc lengths, angles and areas of sectors of circlesG19 apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar

figuresG20 know the formulae for: Pythagoras' theorem a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ =

adjacent/hypotenuse and tan θ = opposite/adjacent apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

G21 know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°

G22 know and apply the sine rule a/sin A = b/sin B = c/sin C , and cosine rule a² = b² + c² – 2bc cos A, to find unknown lengths and angles

G23 know and apply Area = 1/2 ab sin C to calculate the area, sides or angles of any triangleG24 describe translations as 2D vectorsG25 apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column

representations of vectors; use vectors to construct geometric arguments and proofsP1 record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees

P2 apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments

P3 relate relative expected frequencies to theoretical probability, using appropriate language and the 0-1 probability scale

P4 apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one

P5 understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

P6 enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams

P7 construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

P8 calculate the probability of independent and ependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

P9 calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

S1 infer properties of populations or distributions from a sample, while knowing the limitations of samplingS2 interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for

categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data and know their appropriate use

S3 construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use

S4 interpret, analyse and compare the distributions of data sets from univariate empirical distributions through:● appropriate graphical representation involving discrete, continuous and grouped data, including box plots● appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)

S5 apply statistics to describe a populationS6 use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw

estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends while knowing the dangers of so doing

Maths Progress Second Edition: Core Curriculum Scheme of Work

Year 7 Year 8 Year 9Core curriculum Core curriculum Core curriculumUnit 1 Analysing and displaying data Unit 1 Number Unit 1 Indices and standard formUnit 2 Number skills Unit 2 Area and volume Unit 2 Expressions and formulae

Unit 3 Expressions, functions and formulae Unit 3 Statistics, graphs and charts Unit 3 Dealing with data

Unit 4 Decimals and measures Unit 4 Expressions and equations Unit 4 Multiplicative reasoning

Unit 5 Fractions Unit 5 Real-life graphs; Unit 9 Straight-line graphs Unit 5 Constructions

Unit 6 Probability Unit 6 Decimals and ratio Unit 6 Sequences, inequalities, equations and proportion

Unit 7 Ratio and proportion Unit 7 Lines and angles Unit 7 Circles, Pythagoras and prismsUnit 8 Lines and angles Unit 8 Calculating with fractions Unit 8 GraphsUnit 9 Sequences and graphs Unit 9 Straight-line graphs Unit 9 Probability

Unit 10 Transformations Unit 10 Percentages, decimals and fractions Unit10 Comparing shapes

The Support, Core and Depth strands all follow the same Core Curriculum. The Objectives and Key Concepts covered in each lesson can be found in the following tabs. End of Unit, End of Term and End of Year Assessments are included as part of ActiveLearn Service or ActiveLearn Progress & Assess.

7 KS3 Maths Progress TERM UNIT / LESSON HOURS CORE OBJECTIVES SUPPORT OBJECTIVES DEPTH KEY CONCEPTSAUTUMN 1 Analysing and displaying

data10

1.1 Mode, median and range

1 Find the mode of a set of data, numerical and non-numerical.

Find the mode of a set of data, numerical and non-numerical.

Understand what an average is a measure of, and what it does and doesn’t represent.

Find the median of a set of data (odd and even number of values).

Find the median of a set of data (odd and even number of values).

Find the range of a set of data. Find the range of a set of data.1.2 Displaying data 2 Read and draw pictograms, bar charts

and bar-line charts.Read pictograms, read and draw bar charts.

Understand how to choose the best representation for different sets of data.

Read and construct tally charts and frequency tables.

Read and construct tally charts and frequency tables.

Find the mode and range from a chart or table.

Find the mode from a chart or table.

1.3 Grouping data 2 Read and construct grouped tally charts and frequency tables.

Read and construct grouped tally charts and frequency tables.

Understand different averages and what they represent.

Read and construct grouped bar charts for discrete and continuous data.

Read and construct grouped bar charts for discrete and continuous data.

Find the modal class from a bar chart or frequency table.

Find the modal class from a frequency table.

1.4 Averages and comparing data

1 Calculate the mode, median, mean and range of a set of values.

Calculate the mode, median, mean and range of a set of values.

Understand averages and what they represent.

Compare two sets of data using an average and the range.

Compare two sets of data using an average and the range.

Understand how to use the range to compare data.Understand which average is most appropriate.

1.5 Line graphs and more bar charts

1 Read and draw a line graph. Read and draw a line graph. Understand how to choose the best representation for different types of data.

Read and draw a dual bar chart. Read and draw a dual bar chart.Read and draw a compound bar chart. Read and draw a compound bar chart.

Unit 1 Check, Stengthen & Extend

2

Unit 1 Test 1AUTUMN 2 Number skills 11

2.1 Mental maths 1 Know and use the priority of operations, including brackets.

Use multiplication facts up to 10 × 10 up to 10 x 10 and the laws of arithmetic to do mental multiplication and division.

Understand how multiplying by 10, 100, 1000, etc relates to our place value system and why this means we have a decimal system.

Recall and use multiplication facts up to 10 × 10 and the laws of arithmetic to do mental multiplication and division.

Multiply and divide by 10, 100 and 1000

Multiply by multiples of 10, 100, 1000. Use the priority of operations

2.2 Addition and subtraction

1 Round whole numbers to the nearest 10000, 100000, 1000000.

Use a written method to add and subtract whole numbers.

Understand inverse operations (addition and subtraction).

Use estimation and inverse operations to check answers.

Round whole numbers to the nearest 10, 100 and 1000.

Add and subtract whole numbers using written methods.

2.3 Multiplication 1 Multiply whole numbers using a written method.

Use a written method to multiply whole numbers.

Know what it means to multiply - e.g. by comparing grid method and long multiplication and explaining why they are the same.

Use estimation to check an answer to a multiplication.

2.4 Division 1 Divide whole numbers using a written method.

Use a written method to divide numbers. Know what it means if a division calculation has a remainder.

Use inverse operations to check answers. Understand inverse operations (multiplication and division).

2.5 Money and time 1 Round money to the nearest pound or penny.

Round money to the nearest whole pound or penny.

Understand how multiplying by 10, 100, 1000 etc relates to our place value system and why this means that we have a decimal system. (NOTE: For this lesson this should be specifically in the context of money )

Interpret a calculator display in different contexts.

Use a calculator to solve problems involving money and time.

Solve problems involving money and time using a calculator.

2.6 Negative numbers 1 Order positive and negative numbers. Order positive and negative numbers. Understand what negative numbers are and how they behave: where they fit into the ordering of the number line and how they multiply.

Add and subtract positive and negative numbers.

Add and subtract positive and negative numbers.

Begin to multiply with negative numbers.2.7 Factors, multiples and primes

1 Find all the factor pairs for any whole number.

Work out multiples and find the lowest common multiple.

Connect remainders to factors and multiples

Identify common factors, the highest common factor and the lowest common multiple.

Find all factor pairs of a number and highest common factor of two numbers.

Recognise prime numbers. Recognise prime numbers.2.8 Square numbers 1 Recognise square numbers. Recognise square numbers. Most square roots give decimal answers

(Do not stray into surds!) Use a calculator to find squares and square roots.

Use a calculator to find squares and square roots.

Use the priority of operations including powers.

Use the priority of operations including powers.

Use index form for powers.Do mental calculations with squares and square roots.


2

Unit 2 Test 1

AUTUMN 3 Expressions, functions and formulae

10

3.1 Functions 1 Find outputs of simple functions written in words and using symbols.

Find outputs of simple functions written in words and using symbols.

Understand that a function is a relationship that maps one set of numbers on to another, with each input mapping to exactly one output, and with the maths they know so far, it can use any of the four operations, and the order of the operations is important. (eg x 3 + 1 is not usually the same as + 1 x 3).

Describe simple functions in words.3.2 Simplifying expressions 1

1 Simplify linear algebraic expressions by collecting like terms.

Simplify linear algebraic expressions by collecting like terms.

Know what an unknown is, how you can use any letter to represent an unknown number or quantity, and that as they represent numbers, you can add, subtract them in the same way as you do numbers

Use letters to represent unknowns in algebraic expressions.

3.3 Simplifying expressions 2

1 Use brackets with numbers and letters. Multiply and divide algebraic terms. Extend the understanding from 3.2 to include multiplying and dividing.

Multiply and divide algebraic terms. Use brackets with numbers and letters. Understand that algebra uses the same arithmetic rules as number.

3.4 Writing expressions 2 Write expressions from word descriptions using addition, subtraction, multiplication and division.

Write expressions from word descriptions using addition, subtraction and multiplication.

Begin to understand that an algebraic expression can represent a rule, and that writing an algebraic expression may be easier than explaining a rule in words, and easier for the reader to understand.

Write expressions to represent function machines.

Write expressions to represent function machines.

3.5 Substituting into formulae

1 Substitute positive integers into simple formulae written in words.

Substitute positive integers into simple formulae written in words.

Understand that the letters are called variables because they can change or vary, but the relationship between them given by the formula will always remain the same.

Substitute positive integers into formulae written with letters.

Substitute positive integers into formulae written with letters.

3.6 Writing formulae 1 Write simple formulae in words. Write simple formulae in words. Understand that a formula can be seen as a rule that tells you how to do a calculation (eg length x width) or how to work out the number of people when you know the number of tables, and writing it in algebra can save time drawing diagrams or writing out in words

Write simple formulae using letter symbols.

Write simple formulae using letter symbols.

Identify formulae and functions.Identify the unknowns in a formula and a function.


2

Unit 3 Test 1AUTUMN 4 Decimals and measures 12

4.1 Decimals and rounding 1 Measure and draw lines to the nearest millimetre.

Measure and draw lines to the nearest millimetre.

Understand how to choose suitable numbers to round to when estimating an answer to a calculation (and this is not always rounding up or down to the nearest whole number).

Write decimals in order of size. Write decimals in order of size.Round decimals to the nearest whole number and to one decimal place.

Round decimals to the nearest whole number.

Round decimals to make estimates and approximations of calculations.

HALF TERM

4.2 Length, mass and capacity

2 Multiply and divide by 10, 100 and 1000. Multiply and divide whole numbers and decimals by 10, 100 and 1000.

Understand how all units in the metric system are multiples/divisors of a 'base' unit (metres, grams, litres, etc), and explore the relationships between units not adjacent in size (e.g. mm and m, rather than only cm and m and mm and cm)

Compare measurements by converting them into the same units.

Convert between metric units of length, mass and capacity.

Understand how decimal parts relate to each other, e.g. how tenths relate to hundredths; how hundredths relate to thousandths; how tenths relate to thousandths

Solve simple problems involving units of measurement in the context of length, mass and capacity.Convert between metric units of length, mass and capacity.

4.3 Scales and measures 1 Use scale diagrams. Read scales. Understand how different scales enable different levels of accuracy.

Read scales on a range of measuring equipment.

Use scale diagrams. Understand why reading decimal fractions of metric measures on a calculator is easier than decimal fractions of measures of time.

Write decimal measures as two related units of measures.Interpret metric measures displayed on a calculator.

4.4 Working with decimals mentally

1 Multiply decimals by multiples of 10, 100 and 1000.

Multiply decimals by multiples of 10 and 100.

Explore patterns in place value multiplication decimal calculations.

Multiply decimals mentally. Multiply decimals mentally. Understand the inverse operations of multiplication and division in relation to place value decimal calculations.

Check a result by considering whether it is of the right order of magnitude.

Understand where to position the decimal point by considering equivalent calculations.

Understand where to position the decimal point by considering equivalent calculations.

4.5 Working with decimals 1 Add and subtract decimals. Add and subtract decimals. Understand when a mental method may be better than a written method (and vice versa).

Multiply and divide decimals by single-digit whole numbers.

Multiply and divide decimals.

Divide numbers that give decimal answers.

4.6 Perimeter 1 Work out the perimeters of composite shapes and polygons.

Work out the perimeter of squares, rectangles and regular polygons.

Understand how to deduce formulae for perimeters of different shapes.

Solve perimeter problems. Calculate the perimeter of shapes made from rectangles.

4.7 Area 1 Find areas of irregular shapes by counting squares.

Find areas of shapes by counting squares. Understand that shapes can have the same area, but different perimeters; and shapes can have the same perimeter but different areas.

Calculate the areas of shapes made from rectangles.

Find the area of rectangles and squares. Know why area is measured in square units, and length (perimeter) is measured in linear units.

Solve problems involving area. Calculate the area of shapes made from rectangles.

4.8 More units of measure 1 Choose suitable units to estimate length and area.

Choose suitable units to measure area. Understand that to compare measures in different units, they must all be converted to the same unit.

Use units of measurement to solve problems.

Use units of measure to solve problems. Understand how to make choices about which unit to convert measures to.

Use metric and imperial units. Use metric and imperial units.Unit 4 Check, Stengthen & Extend

2

Unit 4 Test 1END OF TERM TEST 1SPRING 5 Fractions and

percentages10

5.1 Comparing fractions 1 Use fraction notation to describe parts of a shape.

Use fraction notation to describe parts of a shape.

Know that, for unit fractions, the larger the denominator, the smaller the value of the fraction.

Compare simple fractions. Compare simple fractions.Use a diagram to compare two or more simple fractions.Order fractions

5.2 Simplifying fractions 1 Change an improper fraction to a mixed number.

Change an improper fraction to a mixed number.

Understand that simplifying fractions can make them easier to visualise.

Identify equivalent fractions. Identify equivalent fractions.Simplify fractions by dividing numerator and denominator by common factors.

Simplify fractions by dividing numerator and denominator by common factors.

5.3 Working with fractions 2 Add and subtract simple fractions. Add and subtract fractions. Understand inverse operations relating to fractions.

Calculate simple fractions of quantities. Calculate fractions of a quantity.

5.4 Fractions and decimals 1 Work with equivalent fractions and decimals.

Work with equivalent fractions and decimals.

Understand that all 1, 2 and 3 place decimals are also fractions.

Write one quantity as a fraction of another.

Write one number as a fraction of another.

5.5 Understanding percentages

1 Understand percentage as ‘the number of parts per 100’.

Understand percentage as ‘the number of parts per 100’.

Understand when it is easier to compare proportions when using fractions, decimals or percentages, e.g. comparing marks in a test.

Convert a percentage to a fraction or decimal.

Convert a percentage to a fraction or decimal.

Working with fractions and percentages that are >1 and what this means (laying ground work for percentage increase).

Work with equivalent percentages, fractions and decimals.

5.6 Percentages of amounts

1 Use different strategies to calculate with percentages.

Calculate percentages. Working with fractions and percentages that are >1 and what this means (laying ground work for percentage increase).

Express one quantity as a percentage of another.

When is it possible to have 110%? (what are realistic contexts? (revenue, exam marks, effort)


2

Unit 5 Test 1SPRING 6 Probability 9

6.1 The language of probability

1 Use the language of probability. Use the language of probability. “Unlikely" and "Likely" have more precise meanings in probability than everyday language.

Use a probability scale with words. Use a probability scale with words. Assigning numerical values to probabilities can help us compare them more accurately.

Understand the probability scale from 0 to 1.

Understand the probability scale from 0 to 1.

6.2 Calculating probability 1 Identify outcomes and equally likely outcomes.

Identify outcomes of an event. Know that probability can be represented as a fraction, decimal or a percentage (and how you choose which to use for a given question).

Calculate probability based on equally likely outcomes.

Calculate probabilities. There may only be n outcomes, but the probability of each is only 1/n if the outcomes are equally likely.

Use a probability scale from 0 to 1.6.3 More probability calculations

1 Calculate more complex probabilities. Use probability notation. Understand that when there are outcomes A, B and C, P(A or B) = P(A) + P(B), and that P(A) + P(B) + P(C) =1, so P(C) = 1 - P(A or B)

Calculate the probability of an event not happening.

Calculate the probability of an event not happening.

6.4 Experimental probability

2 Record data from a simple experiment. Estimate probability based on experimental data.

Understand that experimental probability is always an estimate, and for some contexts you can only use experimental probability as it is not possible to calculate a theoretical probability

Estimate probability based on experimental data.

Understand why more trials lead to better estimate of probability.

Make conclusions based on the results of an experiment.

6.5 Expected outcomes 1 Use probability to estimate the expected number of times an outcome will occur.

Use probability to estimate the expected number of outcomes.

Understand that if an event has probability ⅓ then we expect it to happen 1 in 3 times, but that doesn’t mean that it will happen 1 in 3 times.

Apply probabilities from experimental data in simple situations.

Apply probabilities from simple experimental data in simple situations.


2

Unit 6 Test 1

SPRING 7 Ratio and proportion 107.1 Direct proportion 2 Use direct proportion in simple contexts. Use direct proportion in simple contexts. Understand when

scaling/doubling/halving may be more or less efficient than the unitary method, to solve direct proportion problems.

Solve simple problems involving direct proportion.

Solve simple problems involving direct proportion.

Understand that when two quantities are in direct proportion, when one increases the other increases at the same rate.

Use the unitary method to solve simple word problems involving direct proportion.

7.2 Writing ratios 1 Use ratio notation. Use ratio notation. Understand how to use ratios to make comparisons.

Reduce a ratio to its simplest form. Reduce a ratio to its simplest form.

HALF TERM

Reduce a three-part ratio to its simplest form by cancelling.

7.3 Using ratios 2 Find equivalent ratios. Find equivalent ratios. Understand the multiplicative nature of ratio.

Divide a quantity into two parts in a given ratio.

Divide a quantity into two parts in a given ratio.

Know the relationship between km, metres (cm) and mm, litres and ml, kg and g, and understand how all units in the metric system are multiples/divisors of a 'base' unit (metres, grams, litres, etc).

Solve word problems involving ratio. Solve word problems involving ratios.

Use ratios and measures.7.4 Ratios, proportions and fractions

1 Use fractions to describe and compare proportions.

Use fractions to describe proportions. Understand the relationship between ratio and proportion (what is the same; what is different).

Understand and use the relationship between fractions, ratio and proportion.

Understand the relationship between ratio and proportion.

Understand that a ratio is simply another way of comparing parts - and how this relates to comparing parts written in fraction form.

7.5 Proportions and percentages

1 Use percentages to describe proportions. Use percentages to describe proportions. Understand that a ratio is simply another way of comparing parts - and how this relates to comparing parts written in percentage form.

Use percentages to compare simple proportions.

Use percentages to compare simple proportions.

Understand how to decide when it is better/more efficient to use ratios or proportion to make comparisons.

Understand and use the relationship between percentages, ratio and proportion.

Understand the relationship between ratio and proportion.


2

Unit 7 Test 1END OF TERM TEST 1SUMMER 8 Lines and angles 11

8.1 Measuring and drawing angles

2 Use a protractor to measure and draw angles.

Use a protractor to measure and draw angles.

When do you need to measure and when can you just estimate angles (eg in the prize wheel question).

Recognise acute, obtuse and reflex angles.

Understand the possible types of angles on a straight line, round a point, and in shapes.Know and understand why a protractor has two scales, and which to use to measure a given angle.

8.2 Lines, angles and triangles

1 Estimate the size of angles. Name and label lines, angles and triangles.

Understand how to draw a diagram from written instructions.

Describe and label lines, angles and triangles.

Estimate the size of angles. Classify triangles using more than one name, eg right angled scalene, and right angled isosceles.

Identify angle and side properties of triangles.

8.3 Drawing triangles accurately

2 Use a ruler and protractor to draw triangles accurately.

Use a ruler and protractor to draw triangles accurately.

Understand that you can draw more than one triangle with the same angles and different side lengths (leads into enlargement in unit 10).Given one side and two angles, understand that you can only draw one triangle (but it may be in different orientations).

8.4 Calculating angles 1 Use the rules for angles on a straight line, angles around a point and vertically opposite angles.

Find missing angles on a straight line and around a point.

Understand relationship between angles on a straight line and round a point. Eg two straight lines back to back make angles round a point. Two right angles make a straight line, 4 make a full point.

Solve problems involving angles. Use vertically opposite angles. Understand that there is no limit to the number of angles around a point. You could have eg 180 angles around a point.

8.5 Angles in a triangle 1 Use the rule for the sum of angles in a triangle.

Work out the size of unknown angles in triangles.

Use angles in triangles to solve problems involving other shapes made up of triangles.

Calculate interior and exterior angles. Explore the relationship between exterior and interior angles of a triangle.

Solve angle problems involving triangles.

8.6 Quadrilaterals 1 Identify and name types of quadrilaterals.

Identify and name types of quadrilaterals.

Know that the order in which you find angles can make solving a problem more or less efficient.

Use the rule for the sum of angles in a quadrilateral.

Use the rule for the sum of angles in a quadrilateral.

Use angles in quadrilaterals to solve problems involving other shapes made up of quadrilaterals.

Solve angle problems involving quadrilaterals.

Solve angle problems involving quadrilaterals.

Unit 8 Check, Strengthen & Extend

2

Unit 8 Test 1SUMMER 9 Sequences and graphs 10

9.1 Sequences 1 Recognise, describe and continue number sequences.

Recognise, describe and continue number sequences.

Know that the first term and term-to-term rule together define a sequence. With just one of these, there is (an infinite) number of sequences that could be generated.

Generate terms of a sequence using a one-step term-to-term rule.

Generate terms of a sequence using a one-step term-to-term rule.

Understand that an infinite sequence doesn't necessarily tend to +/- infinity. e.g. 1/2, 1/4, 1/8.

Find missing terms in a sequence. Find missing terms in a sequence.9.2 Pattern sequences 1 Find patterns and rules in sequences. Find patterns and rules in sequences. Understand that the first pattern gives

the first term, and what is added each time is the term to term rule (for simple pattern sequences, and for more complex ones that 'grow' in two dimensions, such as Q8 and the Challenge )

Describe how a pattern sequence grows. Describe how a pattern sequence grows.

Write and use number sequences to model real-life problems.

9.3 Coordinates and midpoints

1 Generate and plot coordinates from a rule.

Read and plot coordinates. Recognise that the negative coordinate axes are extensions of the number line in two directions.

Solve problems and spot patterns in coordinates.

Generate and plot coordinates from a rule.

Know and understand that the midpoint is (mean of x coordinates, mean of y coordinates), just as midpoint of a two numbers is the mean of the two numbers.

Find the midpoint of a line segment. Find the midpoint of a line segment.9.4 Extending sequences 1 Continue and describe special sequences. Use the term-to-term rule to work out

terms in a sequence.Understand that when you plot an arithmetic sequence, it will always give a straight line. Relate this to 'going up or down in equal size steps' - and this is why we sometimes call them linear sequences

Use the term-to-term rule to work out more terms in a sequence.

Recognise an arithmetic sequence.

Recognise an arithmetic sequence and a geometric sequence.

Recognise a geometric sequence.

9.5 Straight-line graphs 2 Recognise, name and plot straight line graphs parallel to the x- or y-axis.

Recognise, name and plot graphs parallel to the axes.

Understand that the equation of a straight line is a function that generates a y value for every x value, and when you input x = 1, 2, 3, (consecutive terms) into the function, the y values form an arithmetic sequence

Recognise, name and plot the graphs of y = x and y = –x.

Recognise, name and plot the graph of y = x.

Plot straight line graphs using a table of values.

Plot straight line graphs using a table of values.

Draw graphs to represent relationships.

9.6 Position-to-term rules 1 Generate terms of a sequence using a position-to-term rule.

Generate terms of a sequence using a position-to-term rule.

Understand the connection between: nth term, term-to-term rule or common difference and first term (arithmetic sequences only).


2

Unit 9 Test 1

SUMMER 10 Transformations 1410.1 Congruency and enlargements

2 Identify congruent shapes. Identify congruent shapes. Understand the language of 'scale factor' - scale relating to scaling up/down and multiplicativity; factor relating to one measure being divisible by another (also about multiplicativity).

Use the language of enlargement. Enlarge shapes using given scale factors. Understand how ratio and enlargement relate to each other (including side lengths and perimeter and area).

Enlarge shapes using given scale factors. Work out the scale factor given an object and its image.

Know that in enlargements, angles in shapes remain unchanged.

Work out the scale factor given an object and its image.

10.2 Symmetry 1 Recognise line and rotational symmetry in 2D shapes.

Recognise line and rotational symmetry in 2D shapes.

Understand the symmetries of 3D solids and the shapes of their planes of symmetry.

Solve problems using line symmetry. Identify all the symmetries of 2D shapes. Understand the relationship between rotational and line symmetry in regular polygons.

Identify all the symmetries of 2D shapes. Identify reflection symmetry in 3D shapes.

HALF TERM

Identify reflection symmetry in 3D shapes.

10.3 Reflection 2 Recognise and carry out reflections in a mirror line.

Recognise and carry out reflections in a mirror line.

Identify patterns/rules in coordinates of vertices when a shape is reflected in different straight lines on a coordinate grid.

Reflect a shape on a coordinate grid. Reflect a shape on a coordinate grid.Describe a reflection on a coordinate grid.

Find the mirror line for a reflection on a coordinate grid.

10.4 Rotation 1 Describe and carry out rotations on a coordinate grid.

Draw and describe rotations. Identify patterns/rules in coordinates of vertices when a shape is rotated by different angles and in different directions on a coordinate grid.

10.5 Translations and combined transformations

2 Translate 2D shapes. Translate 2D shapes. Know that in translation, rotation, reflection the image is congruent to the object.

Transform 2D shapes by combinations of rotations, reflections and translations.

Transform 2D shapes by combinations of translations.

Understand that combined transformations can be equivalent to a single transformation.


2

Unit 10 Test 1END OF TERM TEST 1END OF YEAR TEST 1

8 KS3 Maths Progress TERM UNIT / LESSON HOURS CORE OBJECTIVES SUPPORT OBJECTIVES DEPTH KEY CONCEPTSAUTUMN 1 Number 15

1.1 Calculations 2 Use written methods to add and subtract more than two numbers (including decimals).

Use written methods to add and subtract more than two numbers (including decimals).

Understand, choose and use a range of strategies for mental calculations by developing an understanding of relationships between numbers.

Use mental calculation for multiplication.

Use mental calculation for multiplication.

Estimate answers to calculations.

Estimate answers to calculations.

1.2 Divisibility and division

2 Know and use divisibility rules.

Know and use divisibility rules. Understand why divisibility rules work.

Use a written method to divide decimal numbers by integers.

Use a written method to divide decimal numbers by integers.

Understand the relationships between divisibility rules and relate to factors and multiples.

1.3 Calculating with negative integers

2 Add, subtract, multiply and divide positive and negative numbers, including larger numbers and decimals.

Add, subtract, multiply and divide positive and negative numbers.

Extend the 'rules' for calculations with negative numbers to very large numbers and decimal numbers.

Distinguish between the negative sign and subtract operation.

1.4 Powers and roots 2 Calculate using squares, square roots, cubes and cube roots.

Calculate using squares, square roots, cubes and cube roots.

Know when the negative square root is an appropriate solution to a problem.

Give integers that a square root lies between.

Give integers that a square root lies between.

1.5 Powers, roots and brackets

2 Calculate combinations of squares, square roots, cubes, cube roots and brackets.

Calculate combinations of squares, square roots, cubes, cube roots and brackets.

Understand how to write complex calculations with a given answer.

Use a calculator to check answers.

1.6 Multiples and factors 2 Use index notation. Use index notation. Understand that prime numbers are the building blocks for the natural numbers - ie that all numbers can be written as a product of prime factors.

Write a number as a product of its prime factors.

Write a number as a product of its prime factors.

Understand when to use HCF and LCM to find the answer to a word problem.

Use prime factor decomposition to find the HCF and LCM.

Use prime factor decomposition to find the HCF and LCM.


2

Unit 1 Test 1AUTUMN 2 Area and volume 13

2.1 Area of a triangle 1 Derive and use the formula for the area of a triangle.

Derive and use the formula for the area of a triangle.

When calculating area of triangle it doesn't matter which measurements you choose for the base and height, as long as they are perpendicular to each other.

Calculate the area of compound shapes made from rectangles and triangles.

Calculate the area of compound shapes made from rectangles and triangles.

Every triangle's area is half of the area of a rectangle of the same base and height.

Understand that there are many triangles with the same area (but only one square with a given area).

2.2 Area of a parallelogram and trapezium

1 Derive and use the formula for the area of a parallelogram.

Derive and use the formula for the area of a parallelogram.

When calculating area of parallelogram or trapezium it doesn't matter which measurements you choose for the base (or top and base in trapezium) and height, as long as they are perpendicular to each other. Generalise understanding that all areas are product of perpendicular lengths.

Use the formula for the area of a trapezium.

Use the formula for the area of a trapezium.

Understand that composite areas can be calculated by 'subtracting' a shape, as well as by splitting into two different shapes.

2.3 Volume of cubes and cuboids

2 Calculate the volume of cubes and cuboids.

Calculate the volume of cubes and cuboids.

Understand why volume is measured in cube units.

Calculate the volume of 3D solids made from cuboids.

Understand that composite volumes can be calculated by 'subtracting' a shape, as well as by splitting into two different shapes.

Solve volume problems.2.4 2D representations of 3D solids

2 Sketch nets of 3D solids. Sketch nets of 3D solids. Understand that different representations of a 3D shape convey different information about the faces and edges of the shape, and move between different representations.

Draw 3D solids on isometric paper.

Draw 3D solids on isometric paper.

Draw plans and elevations of 3D solids.

Draw plans and elevations of 3D solids.

2.5 Surface area of cubes and cuboids

2 Calculate the surface area of cubes and cuboids.

Calculate the surface area of cubes and cuboids.

Know that two cuboids can have the same volume but different surface area, but all cubes with the same volume have the same surface area.

2.6 Measures 2 Solve problems in everyday contexts involving measures.

Solve problems in everyday contexts involving measures.

Know the relationship between km, metres (cm) and mm, litres and ml, kg and g, and understand how all units in the metric system are multiples/divisors of a 'base' unit (metres, grams, litres, etc) - extend to tonnes, hectares etc.

Convert between different measures for area, volume and capacity.

Convert between cm³ and litres. 1 cm = 10 mm, so 1 cm2 = 102 mm2 and 1m = 100 cm, so 1 m2 = 1002 cm2

Use tonnes and hectares. Know rough metric equivalents of imperial measures.

Know rough metric equivalents of imperial measures.


2

Unit 2 Test 1

AUTUMN 3 Statistics, graphs and charts

11

3.1 Pie charts 1 Interpret pie charts. Interpret simple pie charts. Understand that pie charts show the proportions of data, and when a pie chart is a suitable diagram to represent data.

Calculate angles and draw pie charts.

Calculate angles and draw pie charts.

3.2 Using tables 2 Use two-way tables. Calculate the mean from a frequency table.

Understand that a table presents data from lists or that could be represented in other types of diagram. Move between tables and other representations.

Calculate the mean from a frequency table.

Use two-way tables. Understand that the method for calculating mean from a frequency table is the same as the method for calculating the mean from a list, but more efficient.

Use tables for grouped data, find modal class and estimate range.

Use tables for grouped data. Understand which average is appropriate/inappropriate/more appropriate to represent a set of data.

3.3 Stem and leaf diagrams

1 Draw and interpret stem and leaf diagrams with different stem values.

Draw and interpret stem and leaf diagrams.

Understand the similarities and differences between stem and leaf diagrams and bar charts, including back to back bar charts and stem and leaf diagrams

Find mode, median and range from stem and leaf diagrams.

Find the median and mode from stem and leaf diagrams.

3.4 Comparing data 2 Compare two sets of data using averages and range.

Compare two sets of data using statistics or the shape of the graph.

Understand how to make comparisons between data.

Compare two sets of data using the shape of a line graph or pie charts.

Choose the most appropriate average to use.

Draw line graphs to compare two sets of data.

HALF TERM

Choose the most appropriate average to use.

3.5 Scatter graphs 1 Draw scatter graphs. Draw scatter graphs. Deepen understanding of correlation by considering examples where there is weak or no correlation, as well as examples where there is correlation that you might not expect (between two seemingly random quantities)

Describe types of correlation.

Describe types of correlation.

Draw a line of best fit on a scatter graph.

Draw a line of best fit on a scatter graph.

3.6 Misleading graphs 1 Interpret graphs and charts.

Interpret graphs and charts. Understand when a statistical diagram is appropriate/inappropriate to represent a set of data. Eg when to use a bar chart/stem and leaf and when to use a pie chart.

Explain why a graph or chart could be misleading.

Explain why a graph or chart could be misleading.


2

Unit 3 Test 1AUTUMN 4 Expressions and

equations11

4.1 Algebraic powers 1 Understand and simplify algebraic powers.

Understand and simplify algebraic powers.

Understand that powers of variables are written in the same way as powers of numbers, and that ab2 means a x b2 and not (ab)2

Write and use expressions involving powers.

Write and use expressions involving powers.

Understand that an algebraic expression is the generalisation of a rule or relationship.Understand the meaning of 'variable' and that the choice of letter is not important when writing an expression.

4.2 Expressions and brackets

2 Expand brackets. Expand brackets. Understand when to use brackets when writing an expression, and when the brackets are not needed.

Write and simplify algebraic expressions and formulae using brackets and division.

Write and simplify algebraic expressions using brackets and division.

Understand that in an expression like (u − 10)/3, you treat the expression in the numerator as if it were written in brackets, when following the order of operationsUnderstand that an algebraic expression is the generalisation of a rule or relationship.Understand the meaning of 'variable' and that the choice of letter is not important when writing an expression.

4.3 Factorising expressions

1 Factorise expressions. Factorise expressions. Understand the significance of multiplying by both terms in a bracket - the expression in the bracket is one factor, the term in front of the bracket is another factor - and that factorisation is the inverse of this.

4.4 One-step equations 2 Find the inverse of a simple function.

Find the inverse of a simple function. The difference between expressions, formulae and equations.

Write and solve one-step equations using function machines.

Write and solve one-step equations using function machines.

Understand that while you can solve most one step equations 'in your head', you are doing this by identifying and using inverse operations (informally).

4.5 Two-step equations 1 Solve two-step equations using function machines.

Solve two-step equations using function machines.

Understand that writing and solving an equation is a powerful and efficient method for solving many problems involving an unknown quantity - 'using x for the unknown' is a useful problem solving strategy

Solve problems using equations.

Solve problems using equations. Know that solutions to equations can be positive and negative integers, and (simple) decimals and fractions.

4.6 The balancing method

1 Solve equations using the balancing method.

Solve equations using the balancing method.

Understand that algebraic operations follow the same rules as number operations.Know and use priority of operations to decide on order of inverse operations when using the balancing method.


2

Unit 4 Test 1END OF TERM TEST 1SPRING 5 Real-life graphs 10

5.1 Conversion graphs 1 Use and interpret conversion graphs.

Use and interpret conversion graphs. Understand why a conversion graph between currencies or units of length, mass and volume will always be a straight line through the origin.

Plot conversion graphs from a table of data.

Plot conversion graphs from a table of data.

5.2 Distance-time graphs 1 Interpret distance-time graphs.

Interpret a distance-time graph. Understand that a distance time graph can represent journeys using different units of distance and time, such as metres per second.

Plot distance-time graphs from descriptive text.

Plot simple distance-time graphs from descriptive text.

Understand that on a distance time graph showing a journey of 60 miles in 1 hour by a straight line, the car's speed may have varied slightly from minute to minute, but the graph does not show this

Draw and use graphs to solve distance-time problems.

5.3 Line graphs 1 Plot line graphs from tables of data.

Plot line graphs from tables of data. On a line graph, intermediate points are only estimates and not actual values. Begin to understand that is more reliable to predict intermediate values within the data (interpolate) than to assume a trend will continue and predict future values (extrapolate).

Interpret line graphs. Interpret line graphs.5.4 More line graphs 1 Draw and interpret line

graphs and identify trends.Draw and interpret line graphs and identify trends.

Understand that a graph may show seasonal or other variations, but still show an upward or downward trend.

5.5 Real-life graphs 2 Draw and interpret non-linear graphs from a range of sources.

Draw and interpret linear and non-linear graphs from a range of sources.

You can use graphs to solve problems, by finding patterns in data, or predicting midpoints or identifying trends, or times when rate of change is slower or faster - easier than from data.

5.6 Curved graphs 1 Draw and interpret curved graphs from a range of sources.

Draw and interpret curved graphs from a range of sources.

Understand that for some graphs it is more realistic to join data points with a curve than with straight lines, as a curve better represents the data.


2

Unit 5 Test 1SPRING 6 Decimals and ratio 11

6.1 Ordering decimals and rounding

2 Round decimals to two or three decimal places.

Round decimals to one, two or three decimal places.

Understand when it is more appropriate (and more accurate) to round to decimal places than significant figures (or vice versa).

Round numbers to a given number of significant figures.

Round numbers to a given number of significant figures.

Understand the impact of rounding.

Round numbers to an appropriate degree of accuracy.

Order decimals of any size, including positive and negative decimals.

Order decimals of any size, including positive and negative decimals.

6.2 Place-value calculations

2 Multiply larger numbers. Multiply any number by 0.1 and 0.01. Apply the inverse relationship of multiplication and division to decimal calculations.

Multiply decimals with up to and including two decimal places.

Multiply larger numbers.

Multiply any number by 0.1 and 0.01.

Multiply decimals with up to and including two decimal places.

6.3 Calculations with decimals

2 Divide by 0.1 and 0.01. Divide by 0.1 and 0.01. Understand the relative sizes of answers to related decimal calculations.

Multiply and divide by decimals.

Multiply and divide by decimals.

Solve problems involving decimals and all four operations.

Solve problems involving decimals and all four operations.

6.4 Ratio and proportion with decimals

2 Divide a quantity into three or more parts in a given ratio.

Divide a quantity into three or more parts in a given ratio.

Understand how to use unit ratios to make comparison.

Use ratios involving decimals.

Use ratios involving decimals. Deepen understanding of decimal, ratio and proportion calculations by working out problems in real life contexts and relating to previously learnt multiplicative concepts

Solve ratio and proportion problems involving decimals.

Solve ratio and proportion problems. Understand the same ‘rule’ applies to simplifying ratios involving fractions as ratios involving decimals’.

Use unit ratios. Use unit ratios.Unit 6 Check, Strengthen & Extend

2

Unit 6 Test 1

SPRING 7 Lines and angles 87.1 Quadrilaterals 1 Classify quadrilaterals by

their geometric properties.Classify quadrilaterals by their geometric properties.

Understand that the properties of a quadrilateral allow you to name the quadrilateral, and conversely knowing the name of a quadrilateral means you know its side, angle and symmetry properties, and can use them to find missing lengths and angles in quadrilaterals

Solve geometric problems using side and angle properties of special quadrilaterals.

Solve geometric problems using side and angle properties of special quadrilaterals.

7.2 Alternate angles and proof

1 Identify alternate angles on a diagram

Identify alternate angles on a diagram. Understand the difference between demonstration (that a theory works for some values) and proof (where it works for all values).

Understand proofs of angle facts.

Understand proof of angle facts.

7.3 Angles in parallel lines

1 Identify corresponding angles.

Identify corresponding angles. Understand that missing angles in parallel lines can be found using angle facts in different combinations, that often there is more than one way of solving the angle problem, and you may need to find angles that are not labelled on the diagram in order to work out the size of the angles you want.

Solve problems using properties of angles in parallel and intersecting lines.

Solve problems using properties of angles in parallel and intersecting lines.

Understand that angles in parallel lines prove the angle properties of trapezium, rhombus, parallelogram (eg opposite angles equal) and extend to co-interior angles in these shapes.

7.4 Exterior and interior angles

1 Calculate the sum of the interior and exterior angles of a polygon.

Calculate the sum of the interior and exterior angles of a polygon.

All 2D shapes have sum of exterior angles 360 (eg because if you walked around the outside of a polygon you would end up back where you started), but only quadrilaterals have sum of interior angles 360. The interior sum has to be a multiple of 180 because n (number of sides) has to be an integer.

Work out the sizes of interior and exterior angles of a polygon.

Work out the sizes of interior and exterior angles of a polygon.

7.5 Solving geometric problems

1 Solve geometrical problems showing reasoning.

Solve geometrical problems showing reasoning.

Solving geometric problems may involve using angles in parallel lines, properties of triangles, quadrilaterals and polygons, and that there is often more than one way of solving a problem.

HALF TERM

Solve problems involving angles by setting up equations.

Solve problems involving angles by writing and solving equations.

Understand when it is helpful/appropriate to write and solve an equation to solve angle problems (and when it is not).


2

Unit 7 Test 1END OF TERM TEST 1SUMMER 8 Calculating with

fractions8

8.1 Ordering fractions 1 Identify fractions more than ½ or less than ½.

Identify fractions more than ½ or less than ½.

Understand how to use a fraction benchmark when ordering fractions.

Order fractions. Order fractions.8.2 Adding and subtracting fractions

1 Add and subtract fractions with any size denominator.

Add and subtract fractions with any size denominator.

Understand the addition and subtraction of fractions with any size denominator, where one or more fraction is negative, or the answer is a negative fraction.

8.3 Multiplying fractions 1 Multiply integers and fractions by a fraction.

Multiply integers and fractions by a fraction.

Understand the multiplication of fractions, with any size denominator, where one or more fraction is negative, or the answer is a negative fraction.

Use appropriate methods for multiplying fractions.

Use appropriate methods for multiplying fractions.

Apply BIDMAS to fraction calculations, involving the multiplication of fractions.

8.4 Dividing fractions 1 Divide integers and fractions by a fraction.

Divide integers and fractions by a fraction.

Apply the inverse relationship of multiplication and division to fraction calculations.

Use strategies for dividing fractions.

Use strategies for dividing fractions. Apply BIDMAS to fraction calculations, involving the division of fractions.

Find the reciprocal of a number.

Find the reciprocal of a number.

8.5 Calculating with mixed numbers

1 Write a mixed number as an improper fraction.

Write a mixed number as an improper fraction.

Understand the four operations with mixed numbers, where one or more mixed number is negative, or the answer is a negative mixed number.

Use the four operations with mixed numbers.

Use the four operations with mixed numbers.

Apply inverse relationships to mixed number calculations.Apply BIDMAS to mixed number calculations.


2

Unit 8 Test 1SUMMER 9 Straight-line graphs 9

9.1 Direct proportion on graphs

2 Recognise when values are in direct proportion with or without a graph.

Recognise when values are in direct proportion with or without a graph.

Understand when one (or more) part of a graph shows quantities in direct proportion, but another part does not.

Plot graphs and reading values to solve problems.

Plot graphs and read values to solve problems.

Understand when quantities may sometimes be in direct proportion and sometimes not.

9.2 Gradients 2 Plot a straight-line graph and work out its gradient.

Plot a straight-line graph and work out its gradient.

Understand the relationship between two quantities in direct proportion (increasing or decreasing at the same rate) and the gradient of the graph when the quantities are plotted against each other

9.3 Equations of straight lines

2 Plot the graphs of linear functions.

Write the equations of straight line graphs in the form y = mx + c.

Identify reflective symmetry between related graphs with different equations.

Write the equations of straight line graphs in the form y = mx + c.


2

Unit 9 Test 1

SUMMER 10 Percentages, decimals and fractions

10

10.1 Fractions and decimals

1 Recall equivalent fractions and decimals.

Recall equivalent fractions and decimals. Understand what is the same and what is different about a terminating decimal with repeating numbers and a recurring decimal with the same repeating numbers

HALF TERM

Recognise recurring and terminating decimals.

Recognise recurring and terminating decimals.

Recognise where fractions of time and other measures result in a recurring decimal.

Order fractions by converting them to decimals or equivalent fractions.

Order fractions by converting them to decimals or equivalent fractions.

Change time to decimal hours.

Change time to decimal hours.

10.2 Equivalent proportions

2 Recall equivalent fractions, decimals and percentages.

Recall equivalent fractions, decimals and percentages.

Understand proportions involving large numbers.

Use different methods to find equivalent fractions, decimals and percentages.

Use different methods to find equivalent fractions, decimals and percentages.

Know how to deal with proportions that involve decimals.

Use the equivalence of fractions, decimals and percentages to compare two proportions.

Use the equivalence of fractions, decimals and percentages to compare two proportions.

Compare and interpret more than two proportions.

10.3 Writing percentages 2 Express one number as a percentage of another when the units are different.

Express one number as a percentage of another when the units are different.

Understand how to express one measure as a percentage of another where the proportion involves large measures (e.g. the proportion of pence out of 1000s of pounds) and the units are not adjacent (e.g. the proportion of a measure given in mm out of a metre measure).

Work out an amount increased or decreased by a percentage.

Work out a number increased or decreased by a percentage.

Investigate mental strategies for solving problems involving decimal percentages, and make decisions about most efficient method to use for different problems.

Use mental strategies to solve percentage problems.

Use mental strategies to solve percentage problems.

10.4 Percentages of amounts

2 Use a multiplier to calculate amounts increased or decreased by a percentage.

Use a multiplier to calculate amounts increased or decreased by a percentage.

Understand how to use a repeated multiplier to work out an amount that has undergone more than one percentage change.

Use the unitary method to solve percentage problems.

Use the unitary method to solve percentage problems.

Understand how to use the unitary method to work out an original amount where there has been more than one percentage change (e.g. a decrease of a given percentage and then an increase of a given percentage; or a decrease of a given percentage and then another decrease of a given percentage).


2

Unit 10 Test 1END OF TERM TEST 1END OF YEAR TEST 1

YEAR 9 KS3 Maths Progress TERM UNIT / LESSON HOURS GCSE (9-1) SPEC

REFERENCECORE OBJECTIVES SUPPORT OBJECTIVES DEPTH KEY CONCEPTS

AUTUMN 1 Indices and standard form 8 N3 N6 N7 N91.1 Indices 1 Calculate combinations of indices and brackets, including square

brackets.Calculate combinations of indices, fractions and brackets. Understand how the sign of a power of a negative

number changes the sign of the answer (ie even number powers of a negative number give a positive answer; odd number powers of a negative number give a negative answer)

Use index laws to simplify expressions. Use index laws to simplify expressions. Understand when to insert square brackets and when to insert round brackets in a calculation.

1.2 Calculations and estimates 2 Calculate combinations of powers, roots, fractions and brackets. Estimate answers to calculations. Understand that the relationship between squares and square roots, cubes and cube roots extends to powers of 4, and 4th root etc. for integers and fractions (positive and negative)

Estimate answers to calculations.1.3 More indices 1 Understand numbers written in index form that are raised to a

power.Understand numbers written in index form that are raised to a power.

Understand how the rules of indices can be extended to negative powers of products.

Understand negative and zero indices. Understand negative and zero indices.Use powers of 10 and their prefixes. Use powers of 10.

1.4 Standard form 1 Write large and small numbers using standard form. Write large and small numbers using standard form. Understand how to calculate numbers in standard form, e.g. add or subtract two numbers in standard form, or multiply or divide two numbers in standard form

Enter and read standard form numbers on a calculator.Order numbers written in standard form.

Unit 1 Check, Strengthen & Extend 2Unit 1 Test 1

AUTUMN 2 Expressions and formulae 9 A2 A3 A4 A5 A172.1 Solving equations 1 Write and solve equations with fractions. Write and solve equations with fractions. For solutions to equations that are fractions,

understand when to give the solution as a fraction or as a decimal (and when it does not matter).

Write and solve equations with the unknown on both sides. Write and solve equations with the unknown on both sides For equations with the unknown on one side, understand that it does not matter which side you 'move' the unknowns too, but if you subtract the smaller term from each side this may often be easier (fewer negatives)

2.2 Substituting into expressions 1 Use the priority of operations when substituting into algebraic expressions.

Use the priority of operations when substituting into algebraic expressions

In priority or operations, values under a square (or cube) root are treated as if in a bracket. In particular square root of (a + b) is not equal to square root a + square root b (and similarly for subtraction, and for cube roots)

Substitute values into expressions involving powers and roots. Substitute values into expressions involving powers and roots

2.3 Writing and using formulae 1 Write and use formulae. Write and use formulae. For a real life (linear) graph, understand the relationship between the formula connecting the variables and the equation of the line, and interpret the gradient in a real life context

2.4 Using and rearranging formulae 1 Substitute into formulae and then solve equations to find unknown values.

Substitute into formulae and then solve equations to find unknown values.

Understand that changing the subject of a formula uses the same process as solving an equation using the balance method.

Change the subject of a formula. Change the subject of a formula. Understand that changing the subject of a formula may be more efficient for repeated calculations than substituting into a formula and solving an equation.

2.5 Index laws and brackets 1 Use the rules for indices for multiplying and dividing. Use the rules for indices for multiplying and dividing. x to the power -n =1/x to the power n.

Simplify expressions involving brackets. Simplify expressions involving brackets. Any number or letter to a negative power can be written as a reciprocal but if the original number is '–1< x< 1 then the final answer is not a fraction.

Factorise an expression by taking out an algebraic common factor. Factorise an expression by taking out an algebraic common factor.

When you raise a number in index form to a power, you multiply the powers.

2.6 Expanding double brackets 1 Multiply out double brackets and collect like terms. Multiply out double brackets and collect like terms. A quadratic expression has a squared term as its highest power.You can show that two expressions are equivalent by expanding and simplifying both sides.

You can extend the approach of 'multiply everything in the bracket by everything outside the bracket) to multiplying three binomial expressions.


AUTUMN 3 Dealing with data 11 S1 S2 S4 S5 S63.1 Planning a survey 1 Identify sources of primary and secondary data. Identify sources of primary and secondary data. Understand that the larger the sample size the more

reliable your results, but testing can be time consuming and expensive (or may destroy the product, eg firework testing), so a 10% sample is not always appropriate

Choose a suitable sample size and what data to collect. Choose a suitable sample size and what data to collect.

Identify factors that may affect data collection and plan to reduce bias.

Identify factors that may affect data collection and plan to reduce bias.

3.2 Collecting data 2 Design and use data collection sheets and tables. Design and use data collection sheets and tables. Understand that 'closed' questions eg with tick boxes make questionnaires easier for people to complete, and that reducing options to eg age groups rather than just asking 'age', provides data that is already grouped, and so saves time recording and organising data

Design a good questionnaire. Design a good questionnaire. Understand that there is not a 'best' type of data collection sheet, but that data collection sheets have to be designed to match each individual questionnaire/survey

3.3 Calculating averages 1 Find the median from a frequency table. Find the median from a frequency table. Understand the effect on the mean of adding a constant to each value in a data set.

Estimate the mean form a large set of grouped data. Estimate the mean form a large set of grouped data. Calculate a mean using an assumed mean - and understand when this is more efficient.

3.4 Displaying and analysing data 2 Construct and use a line of best fit to estimate missing values. Construct and use a line of best fit to estimate missing values.

Understand that it is best to draw a line of best fit to predict values from a scatter diagram, and that the closer the points on a scatter diagram are to the line of best fit (ie the stronger the correlation), the more accurate the predictions will be.

Identify and suggest reasons for outliers in data. Identify and suggest reasons for outliers in data.Identify further lines of enquiry. Identify further lines of enquiry.Draw line graphs to represent grouped data. Draw line graphs to represent grouped data.

3.5 Presenting and comparing data 2 Draw back-to-back stem and leaf diagrams. Draw back-to-back stem and leaf diagrams. Understand how for a given set of data, different types of graph (scatter diagram, pie chart, dual bar chart, line graph, stem and leaf including back to back) or different types of table may highlight different features of the data or may better facilitate comparison of data, i.e. begin to choose appropriate graphs to represent data

Write a report to show survey results. Write a report to show survey results.Unit 3 Check, Strengthen & Extend 2Unit 3 Test 1

AUTUMN 4 Multiplicative reasoning 10 N15 R9 R10 R11 R12 G7

4.1 Enlargement 2 Enlarge 2D shapes using a positive whole number scale factors and centre of enlargement.

Enlarge 2D shapes using a positive whole number scale factors and centre of enlargement.

Understand that scale factors for enlargement are not always integer values, and centres of enlargement do not always have integer coordinates.

Find the centre of enlargement by drawing lines on a grid. Find the centre of enlargement by drawing lines on a grid.

Understand that the scale factor is the ratio ofcorresponding lengths.

Understand that the scale factor is the ratio ofcorresponding lengths.

4.2 Negative and fractional scale factors 2 Enlarge 2D shapes using a negative whole number scale factors. Enlarge 2D shapes using a negative whole number scale factor.

Describe enlargements that involve negative and fractional scale factors (by finding the centre of enlargement)

HALF TERM

Enlarge 2D shapes using a fractional scale factor. Enlarge 2D shapes using a fractional scale factor. Understand that a combined enlargement, involving positive and/or negative integers and/or fractional scale factors (like a combined transformation), can be described as a single enlargement or single transformation

4.3 Percentage change 1 Find an original value using inverse operations. Find an original value using inverse operations. Understand there is more than one method for finding an original amount, given a final amount and the percentage increase or decrease (ie inverse operations, or unitary method). Make decisions about the most efficient method to use.

Calculate percentage change. Calculate percentage change. Understand how to interpret a scenario that requires the use of percentage change, where it is not a straightforward 'Work out the percentage loss/profits/increase/decrease' question.

4.4 Compound measures 1 Solve problems using compound measures. Solve problems using compound measures. Understand that solving problems involving the comparison of compound measures or constant rates may require changing units.

Solve problems using constant rates and related formulae. Solve problems using constant rates and related formulae. Understand why a speed given (or calculated) may (or may not) be an average speed.

4.5 Direct and inverse proportion 1 Solve best-buy problems. Solve best-buy problems. Understand how to distinguish between situations where quantities are in direct, inverse or not proportional at all

Solve problems involving inverse proportion. Solve problems involving inverse proportion. Apply understanding of inverse proportion to compound measures.


END OF TERM TEST 1SPRING 5 Constructions 10 R2 G2 G3 G15

5.1 Using scales 1 Use scales on maps and diagrams. Use scales on maps and diagrams. In a map scale given as a ratio, eg 1:50 000, the units are not given because the ratio applies to any units. Eg 1 cm represents 50 000cm is equivalent to 1 m represents 50 000 m

Draw diagrams to scale. Draw diagrams to scale.5.2 Basic constructions 2 Make accurate constructions using drawing equipment. Use a ruler and compasses to bisect a line segment. Understand why the construction methods for

perpendicular and angle bisectors work, by considering properties of intersecting circles and rhombus, and that a circle is the locus of all points equidistant from a fixed point (without using the term locus)

Use a ruler and compasses to bisect an angle.5.3 Constructing triangles 2 Construct accurate triangles. Construct accurate triangles. Construct accurate angles of 45, 30, 60 based on

known constructions of perpendicular bisector, angle bisector and equilateral triangle.

Construct accurate nets of solids involving triangles. Construct accurate nets of solids involving triangles.5.4 Using accurate scale diagrams 2 Construct and draw accurate scale diagrams. Construct and draw accurate scale diagrams. Constructing accurate scale diagrams (including

triangles) is a strategy for solving problems involving finding sizes of angles and unknown lengths.

Use scale diagrams to solve problems. Use scale diagrams to solve problems. Plus, building on understanding that shortest distance to a line is perpendicular distance, use Core 3 lesson 5.4 Q9 to discover that points on the angle bisector are equidistant from both arms of the angle.


SPRING 6 Sequences, inequalities, equations and proportion

9 A3 A17 A21 A22 A23 A24 A25 R10 R13

6.1 nth term of arithmetic sequences 1 Use the nth term to generate an arithmetic sequence. Use the nth term to generate an arithmetic sequence. A sequence may contain more than one sequence. For example in a fractions sequence the numerators may follow one sequence and the denominators another. Or in a pattern sequence, black dots may follow one sequence and white dots another. You can find the nth terms for each sequence and combine them

Find and use the nth term of an arithmetic sequence. Find and use the nth term of an arithmetic sequence.6.2 Non-linear sequences 1 Recognise and continue geometric sequences. Recognise and continue geometric sequences. Discover/understand the relationship between the

2nd difference of a quadratic sequence and the coefficient of n squared in the nth term. Use this to find the nth term of sequences of the form n squared + b and an squared plus b

Recognise and continue quadratic sequences. Recognise and continue quadratic sequences.6.3 Inequalities 1 Represent inequalities on a number line. Represent inequalities on a number line. You can solve linear inequalities by doing the same to

both sides, but if you multiply or divide both sides by a negative number, this changes the direction of the inequality sign

Find integer values that satisfy an inequality. Find integer values that satisfy an inequality.6.4 Solving equations 1 Construct and solve equations including fractions or powers. Construct and solve equations including fractions or

powers.You can use trial and improvement to solve an equation if you do not have an algebraic method.

6.5 Proportion 2 Write formulae connecting variables in direct or inverseproportion.

Write formulae connecting variables in direct or inverse proportion.

A quantity can be directly proportional to the square or cube of another quantity. Try to relate direct proportion (linear, square and cubic) to relationships and formulae they have already met in mathematics. NB circles not covered till next chapter.

Use algebra to solve problems involving direct or inverse proportion. Use algebra to solve problems involving direct or inverse proportion.


SPRING 7 Circles, Pythagoras and prisms 9 G6 G9 G16 G17 G18 G20 N15 N16 R1

7.1 Circumference of a circle 2 Calculate the circumference of a circle. Calculate the circumference of a circle. Understand that pi is not a number - it is a ratio of the circumference to the diameter for any circle. - Understand that pi is an irrational number - it will not give an exact value

Estimate calculations involving pi (π). Estimate calculations involving pi (π). Solve problems involving arcs of circles.Solve problems involving the circumference of a circle. Solve problems involving the circumference of a circle.

7.2 Area of a circle 1 Calculate the area of a circle. Calculate the area of a circle. Understand the effect of estimating pi (including to nearest integer, 1.d.p. and as a fraction 22/7).

Solve problems involving the area of a circle. Solve problems involving the area of a circle. Solve problems involving sectors of circles.7.3 Pythagoras' theorem 1 Find the length of an unknown side of a right-angled triangle. Find the length of an unknown side of a right-angled

triangle.Understand how to use Pythagoras's Theorem to show that a triangle is NOT a right angled triangle.

Solve problems involving right-angled triangles. Solve problems involving right-angled triangles. Understand the advantages/disadvantages of using scale drawing OR Pythagoras' Theorem to find missing lengths on right angled triangles.

7.4 Prisms and cylinders 1 Calculate the volume and surface area of a right prism. Calculate the volume and surface area of a right prism. Understand that a cylinder is not a prism, but has similarities.

Calculate the volume and surface area of a cylinder. Calculate the volume and surface area of a cylinder. Understand that as you increase the number of sides of a polygon that is the cross section of a prism, then you approach a cylinder

Convert between m³, cm³ and mm³.7.5 Errors and bounds 1 Find the lower and upper bounds for a measurement. Find the lower and upper bounds for a measurement. Understand when a decimal value is not appropriate

for an error bound or interval, and how this can change the inequality signs.

Calculate percentage error intervals. Calculate percentage error intervals.Unit 7 Check, Strengthen & Extend 2Unit 7 Test 1

END OF TERM TEST 1SUMMER 8 Graphs 10 A5 A9 A10 A11 A12

A14 A18 A198.1 Using y = mx + c 1 Draw a graph from its equation, without working out points. Draw a graph from its equation, without working out

points.Write the equation of a line perpendicular to another line.

Write the equation of a line parallel to another line. Write the equation of a line parallel to another line. Understand the relationship between the gradients of perpendicular lines.

Compare graph lines using their equations. Compare graph lines using their equations.8.2 More straight-line graphs 1 Draw graphs with equations like ax + by = c. Draw graphs with equations like ax + by = c. You can plot any linear graph by substituting x = 0 and

y = 0 into its equation, to find the x and y intercepts.

HALF TERM

Rearrange equations of graphs into y = mx + c. Rearrange equations of graphs into y = mx + c. Find the equation of a line between two points.8.3 Simultaneous equations 2 Rearrange equations of graphs into y = mx + c. Rearrange equations of graphs into y = mx + c. Understand that a pair of linear simultaneous

equations has either no solutions, one solution or infinitely many solutions

Solve problems using simultaneous equations. Solve problems using simultaneous equations.8.4 Graphs of quadratic functions 2 Draw graphs with quadratic equations in the form y = x². Draw graphs with quadratic equations in the form y = x². Understand that simultaneous equations may not

both be linear, eg could be linear/quadratic, and therefore could have more than one solution.

Interpret graphs of quadratic functions. Interpret graphs of quadratic functions.8.5 More non-linear graphs 1 Draw and interpret graphs showing inverse proportion. Draw and interpret graphs showing inverse proportion. Draw cubic graphs, recognise their features and

distinguish between them and linear or quadratic graphs

Draw and interpret non-linear graphs. Draw and interpret non-linear graphs.Unit 8 Check, Strengthen & Extend 2Unit 8 Test 1

SUMMER 9 Probability 10 P1 P2 P3 P4 P5 P6 P7 P8 P9

9.1 Mutually exclusive events 2 Identify mutually exclusive outcomes and events. Identify mutually exclusive outcomes and events. Understand that 'A' and 'not A' are mutually exclusive and so P(A) + P(not A) = 1, which leads to P(not A) = 1 - P(A)

Work out the probabilities of mutually exclusive outcomes and events.

Work out the probabilities of mutually exclusive outcomes and events.

Understand the importance of knowing whether events are mutually exclusive before attempting to work out P(A or B) .

9.2 Experimental and theoretical probability

2 Calculate estimates of probability from experiments. Calculate estimates of probability from experiments. Understand that a 'fair' dice, spinner, etc will not have exactly the same experimental probability as theoretical probability. Consider when experimental outcomes and theoretical expected outcomes are close enough, eg for a dice, expected number of 6s in 200 throws is 33.33... so if you get 30 6s is it likely to be fair? What if you get 28, or 41?

Decide whether a dice or spinner is unbiased. Decide whether a dice or spinner is unbiased.9.3 Sample space diagrams 1 List all the possible outcomes of one or two events in a sample space

diagram.List all the possible outcomes of one or two events in a sample space diagram.

Understand by seeing patterns in a sample space that you do not always need to fill in all the possible outcomes in a sample space diagram in order to work out the probability,. Eg for two 6 - sided dice there will be 6 x6 possible outcomes, and the 'doubles' will be on the diagonal. Or for two 4 sided dice 1-4, to find P(sum <5) you only need to fill in part of the sample space grid.

Decide if a game is fair Decide if a game is fair9.4 Two-way tables 1 Show all the possible outcomes of two events in a two-way table. Show all the possible outcomes of two events in a two-way

table.Understand that you can calculate theoretical probabilities from a two way table of possible outcomes, which is equivalent to a sample space diagram, and that you can calculate estimates of probabilities (Experimental probabilities) from two-way tables of survey or experimental results.

Calculate probabilities from two-way tables. Calculate probabilities from two-way tables.9.5 Venn diagrams 1 Draw Venn diagrams. Draw Venn diagrams. Understand that Venn diagrams represent sets of

data that are not mutually exclusive, and allow us to calculate probability of P(A and B) when A and B are not mutually exclusive. Begin to understand that when A and B are not mutually exclusive, P(A ) + P(B) counts the intersection of A and B twice.

Calculate probabilities from Venn diagrams. Calculate probabilities from Venn diagrams.Unit 9 Check, Strengthen & Extend 2Unit 9 Test 1

SUMMER 10 Comparing shapes 14 G5 G6 G7 G19 G20 G21 G24 G25

10.1 Congruent and similar shapes 1 Use congruent shapes to solve problems about triangles and other polygons.

Use congruent shapes to solve problems about triangles and other polygons.

Use congruent shapes to solve problems about shapes other than triangles and quadrilaterals.

Work out whether shapes are similar, congruent or neither. Work out whether shapes are similar, congruent or neither.

Identify where shapes are similar, congruent or neither, when descriptions only (NO DIAGRAMS) are given

10.2 Ratios in triangles 2 Solve problems involving similar triangles. Solve problems involving similar triangles. Solve problems involving similar shapes, other than triangles.

10.3 The tangent ratio 2 Use conventions for naming the sides of a right-angled triangle. Use conventions for naming the sides of a right-angled triangle.

Understand how to use the tangent ratio and Pythagoras to find lengths of all sides of a right angled triangle

Work out the tangent ratio of any angle. Work out the tangent ratio of any angle.Use the tangent ratio to work out an unknown side of a right-angled triangle.

Use the tangent ratio to work out an unknown side of a right-angled triangle.

10.4 The sine ratio 2 Work out the sine ratio of any angle. Work out the sine ratio of any angle. Understand that given an angle and the opposite side in a right-angled triangle, it is possible to use tan to find the adjacent side and then Pythagoras to find the hypotenuse. However, it is more efficient to use the sine ratio.

Use the sine ratio to work out an unknown side of a right-angled triangle.

Use the sine ratio to work out an unknown side of a right-angled triangle.

Use the tangent or sine ratio to find lengths in shapes made up of right angled triangles.

10.5 The cosine ratio 2 Work out the cosine ratio of any angle. Work out the cosine ratio of any angle. Understand bearings and use trigonometry to solve bearing problems (distances ONLY; NOT angles).

Use the cosine ratio to work out an unknown side of a right-angled triangle.

Use the cosine ratio to work out an unknown side of a right-angled triangle.

10.6 Using trigonometry to find angles2

Use the trigonometric ratios to work out an unknown angle in a right-angled triangle.

Use the trigonometric ratios to work out an unknown angle in a right-angled triangle.

Identify right-angled triangles in cubes and cuboids.

Use trigonometry to find missing lengths and angles in cubes and cuboids


END OF TERM TEST 1END OF YEAR TEST 1

HALF TERM

YEAR 10 (F) Edexcel GCSE (9-1) Mathematics Foundation Student BookTERM UNIT / LESSON HOURS PRIOR KNOWLEDGE GCSE (9-1) SPEC

REFERENCESTEPSFROM …

STEPSTO …

OBJECTIVES

Key: Italic specification references are assumed prior knowledge and are covered in the prior knowledge check rather than the main teaching.AUTUMN 1 Number 11 N1 N2 N3 N4 N5 N6

N7 N13 N14 N152nd 7th

Identify the value of digits in a whole number or decimal.Round to the nearest integer, and to a given power.

Apply the four operations.Recall all multiplication facts to 10 × 10, and use them to derive quickly the corresponding division facts.

Know strategies for multiplying and dividing whole numbers by 2, 4, 5 and 10.Recognise odd and even numbers.Use brackets and the hierarchy of operations (not including powers).Understand and use positive and negative numbers.

Interpret scales on thermometers using °F and °C (positive and negative).

1.1 Calculations Order positive and negative integers and decimals. N3 N6 4th 4th Use priority of operations with positive and negative numbers.

Use the symbols =, <, > Simplify calculations by cancelling.Find a fraction of a number. Use inverse operations.Recall square numbers.Understand the commutative property of multiplication.

1.2 Decimal numbers Identify place value. N2 N13 N15 3rd 7th Round to a given number of decimal place.Convert between metric measures. Multiply and divide decimal numbers.

1.3 Place value Round to the nearest 100, 10 and whole number. N14 N15 2nd 6th Write decimal numbers of millions.

Multiply and divide by powers of 10. Round to a given number of significant figures.Estimate answers to calculations.Use one calculation to find the answer to another.

1.4 Factors and multiples Understand the meaning of the words prime, factor, multiple and product.

N4 N5 3rd 7th Recognise 2-digit prime numbers.

List the multiples of a given number. Find factors and multiples of numbers.Find common factors and common multiples of two numbers.Find the HCF and LCM of two numbers by listing.

1.5 Squares, cubes and roots Understand the meaning of the words prime, factor, multiple and product.

N3 N6 N7 4th 7th Find square roots and cube roots.

Round numbers to a specified degree of accuracy. Recognise powers of 2, 3, 4 and 5.

Understand surd notation on a calculator.1.6 Index notation Use simple powers of 10. N7 4th 7th Find square roots and cube roots.

Convert between metric units. Recognise powers of 2, 3, 4 and 5.Evaluate numeric expressions with powers. Understand surd notation on a calculator.

1.7 Prime factors List the factors of numbers; identify which factors are prime.

N4 7th 7th Write a number as the product of its prime factors.

Evaluate numeric expressions with powers. Use prime factor decomposition and Venn diagrams to find the HCF and LCM.

AUTUMN 2 Algebra 10 N1 N3 N4 A1 A2 A3 A4 A5 A6 A7 A21

3rd 7th

Use the four operations with positive and negative integers.Recall and use the hierarchy of operations.Evaluate numerical expressions involving powers and roots.Multiply and divide numbers with indices.Find the HCF of two numbers.Simplify simple algebraic expressions.

2.1 Algebraic expressions Simplify simple algebraic expressions. A1 A4 3rd 5th Use correct algebraic notation. Write and simplify expressions.

2.2 Simplifying expressions Multiply and divide simple terms. A1 A4 4th 7th Use the index laws.Calculate with positive and negative integers. Multiply and divide expressions.Use index notation.

2.3 Substitution Recognise equivalent expressions. A1 A2 A4 4th 7th Substitute numbers into expressions.Calculate with positive and negative integers.Apply the four operations.

2.4 Formulae Calculate with negative numbers and terms. A1 A2 A7 A21 5th 7th Recognise the difference between a formula and an expression.

Recall square numbers. Substitute numbers into a simple formula.Substitute into and evaluate expressions.Write simple expressions.

2.5 Expanding brackets Multiply negative and positive terms. A1 A4 4th 7th Expand brackets.Simplify algebraic expressions. Simplify expressions with brackets.Write simple formulae. Substitute numbers into expressions with brackets and powers.

2.6 Factorising Find HCFs of number pairs. N1 N4 A1 A3 A4 A6 6th 7th Recognise factors of algebraic terms.Multiply a single term over brackets. Factorise algebraic expressions.

Use the identity symbol ≡ and the not equals symbol ≠2.7 Using expressions and formulae Write simple expressions. A2 A5 A21 5th 7th Write expressions and simple formulae to solve problems.

Substitute into and evaluate expressions. Use maths and science formulae.AUTUMN 3 Graphs, tables and charts 12 G2 G14 G15 S2 S4 S5

S63rd 7th

Read scales on graphs and plot coordinates in the first quadrant.Draw circles.Measure and draw angles. Know that there are 360 degrees in a full turn and 180 degrees at a point on a straight line.Have experience of tally charts.Have used inequality notation. Use correct notation for time using 12 & 24-hour clocks.Find the midpoint of two numbers.

3.1 Frequency tables Addition of numbers. S2 4th 6th Designing tables and data collection sheets.Counting tally symbols and drawing tally charts. Reading data from tables.

Interpret a frequency table, including calculating the total population.

3.2 Two-way tables Convert between 12 and 24 hour clock times. G14 S2 S5 4th 6th Use data from tables.Calculate with time. Design and use two-way tables.Understand use of fractions.

3.3 Representing data Determine what features are missing from a graph. S2 3rd 6th Draw and interpret comparative and composite bar charts.

Interpret bar charts. Interpret and compare data shown in bar charts, line graphs and histograms.

3.4 Time series Write decimal numbers of millions. S2 4th 5th Plot and interpret time series graphs.

Plot a line graph. Use trends to predict what might happen in the future.

3.5 Stem and leaf diagrams Place numbers in order of size. S2 6th 6th Construct and interpret stem and leaf and back-to-back stem and leaf diagrams.

3.6 Pie charts Express a part of a circle as a fraction or percentage of the whole.

G2 G25 S2 S4 3rd 7th Draw and interpret pie charts.

Know the number of degrees in a circle. Draw a circle.Draw a given angle.

3.7 Scatter graphs Understand depreciation of value as things age, as well as an understanding of exceptions (e.g. classic cars)

S6 6th 7th Plot and interpret scatter graphs.

Plot coordinates in the first quadrant. Determine whether or not there is a relationship between sets of data.

3.8 Line of best fit Recall definitions of positive, negative and no correlation.

S6 6th 7th Draw a line of best fit on a scatter graph.

Read values from a graph. Use the line of best fit to predict values.AUTUMN 4 Fractions and percentages 12 N1 N2 N3 N4 N8 N10

N12 N15 R3 R9 S23rd 7th

Use the four operations of number.Find common factors. Have a basic understanding of fractions as being ‘parts of a whole’ and be able to write one value as a fraction of another.Define percentage as ‘number of parts per hundred’.

Know number complements to 10 and multiplication tables.Convert between common fractions, decimals and percentages.

4.1 Working with fractions Identify equivalence in fractions. N2 N4 N8 3rd 6th Compare fractions.Identify the denominator of a fraction. Add and subtract fractions.Identify the numerator of a fraction. Use fractions to solve problems.Find the LCM.Write fractions in their simplest form.

4.2 Operations with fractions Convert between units of length. N2 N8 N12 4th 7th Find a fraction of a quantity or measurement.Add and subtract fractions. Use fractions to solve problems.Convert between mixed numbers and improper fractions.

4.3 Multiplying fractions Find a fraction of a quantity. N2 N3 N4 N8 N12 4th 6th Multiply whole numbers, fractions and mixed numbers.Know that 1000 g = 1 kg. Simplify calculations by cancelling.Know the commutative rule a x b = b x a.Write 1 million pounds as a figure.

4.4 Dividing fractions Divide larger numbers by smaller numbers. N2 N3 N8 N12 5th 7th Divide a whole number by a fraction. Convert between mixed numbers and improper fractions.

Divide a fraction by a whole number or a fraction.

Multiply a whole number or a fraction by a fraction.

4.5 Fractions and decimals Identify the (place) value of a digit in a decimal number.

N2 N8 N10 N15 R3 S2 3rd 5th Convert fractions to decimals and vice versa.

Convert between common fractions and decimals. Use decimals to find quantities.

Write one value as a fraction of another. Write one number as a fraction of another.4.6 Fractions and percentages Write common fractions and decimals as

percentages.N2 N3 N8 N10 N12 S2 3rd 6th Convert percentages to fractions and vice versa.

Write one number as a percentage of another.4.7 Calculating percentages 1 Find percentages of quantities. N2 N8 N10 N12 R9 4th 6th Convert percentages to decimals and vice versa.

Convert a fraction to a decimal. Find a percentage of a quantity.Convert a percentage to a fraction. Use percentages to solve problems.

Calculate simple interest.4.8 Calculating percentages 2 Calculate with percentages. N2 N3 N12 R9 4th 6th Calculate percentage increases and decreases.

Convert a percentage to a decimal. Use percentages in real-life situations.Find a percentage of a quantity. Calculate VAT (value added tax).

AUTUMN 5 Equations, inequalities and sequences

12 N1 N3 A2 A3 A5 A7 A17 A21 A22 A23 A24 A25

3rd 7th

Use inequality signs between numbers. Use negative numbers with the four operations, recall and use the hierarchy of operations and understand inverse operations.Deal with decimals and negatives on a calculator.

Use index laws numerically.Draw a number line.Write the next terms in a sequence, and find the term to term rule.Use function machines.Multiply a term over brackets.Substitute into and evaluate an expression.

5.1 Solving equations 1 Understand the meaning of the term ‘inverse operation’.

N3 A7 A21 3rd 5th Understand and use inverse equations.

Find the output of a function machine when given the input.

Rearrange simple linear equations.

Solve simple linear equations.5.2 Solving equations 2 Use all four operations to solve simple, single one-

step equations.A17 A21 3rd 6th Solve two-step equations.

Work out the outputs of a function machine.Simplify expressions.

5.3 Solving equations with brackets Expand a single bracket, involving positive and negative numbers.

A17 A21 6th 7th Solve linear equations with brackets.

Solve two-step equations. Solve equations with unknowns on both sides.5.4 Introducing inequalities Identify numbers that satisfy an inequality. A22 4th 7th Use correct notation to show inclusive and exclusive inequalities.

Use the inequality signs between numbers. Solve simple linear inequalities.Write down whole numbers which satisfy an inequality.Represent inequalities on a number line.

5.5 More inequalities List integer values that satisfy an inequality. A22 5th 7th Solve two-sided inequalities.

5.6 More formulae Identify the inverse of all four operations. A2 A3 A5 A17 3rd 7th Substitute values into formulae and solve equations.Substitute into and evaluate expressions. Change the subject of a formula.

Know the difference between an expression, an equation, a formula and an identity.

5.7 Generating sequences Find the missing numbers in simple arithmetic sequences.

A23 A24 6th 7th Recognise and extend sequences.

Write down missing terms in sequences.Find the term-to-term rule.

5.8 Using the nth term of a sequence Substitute into a simple expression. A23 A24 A25 Use the nth term to generate terms of a sequence.

Solve simple equations. Find the nth term of an arithmetic sequence.END OF TERM 1 TESTSPRING 6 Angles 9 G1 G3 G4 G6 G7 G11 3rd 8th

Be able to use a ruler and protractor.

Have an understanding of angles as a measure of turning.Name angles and distinguish between acute, obtuse, reflex and right angles.Recognise reflection symmetry, be able to identify and draw lines of symmetry, and complete diagrams with given number of lines of symmetry.

Recognise rotation symmetry and be able to identify orders of rotational symmetry, and complete diagrams with given order of rotational symmetry.

Know the properties of special triangles and quadrilaterals.

6.1 Properties of shapes Identify lines of symmetry and rotational symmetry in 2D shapes.

G1 G3 G4 G7 G11 4th 5th Solve geometric problems using side and angle properties of quadrilaterals.

Draw angles. Identify congruent shapes.Know that the angles in a quadrilateral sum to 360°.

6.2 Angles in parallel lines Identify parallel and perpendicular lines. G1 G3 G4 5th 6th Understand and use the angle properties of parallel lines.Identify acute and obtuse angles. Find missing angles using corresponding and alternate angles.

6.3 Angles in triangles Identify different types of triangles. G1 G3 G6 3rd 6th Solve angle problems in triangles.Know that the angles in a triangle sum to 180°. Understand angle proofs about triangles.

6.4 Exterior and interior angles Recall the number of sides of different polygons. G1 G3 4th 7th Calculate the interior and exterior angles of regular polygons.

Know the properties of special triangles and quadrilaterals.

6.5 More exterior and interior angles Recall the number of interior angles in different polygons.

G1 G3 4th 8th Calculate the interior and exterior angles of polygons.

Identify exterior and interior angles. Explain why some polygons fit together and some others do not

6.6 Geometrical patterns Using angle facts to find missing angles. G1 G3 G4 6th 8th Solve angle problems using equations.Write an equation to solve a problem. Solve geometrical problems showing reasoning.

SPRING 7 Averages and range 9 S1 S2 S4 S5 2nd 7thCalculate the midpoint of two numbers. Draw the statistical diagrams in unit 3.Use inequality notation.Calculate the mode, median and the range.

7.1 Mean and range Understand that sharing equally involves dividing a total.

S2 S4 S5 3rd 6th Calculate the mean from a list and from a frequency table.

Identify the mode. Compare sets of data using the mean and range.7.2 Mode, median and range Identify the mode, median and range. S2 S4 4th 6th Find the mode, median and range from a stem and leaf diagram.

Identify an incorrect value. Identify outliers.Draw a stem and leaf diagram. Estimate the range from a grouped frequency table.Understand inequality notation.

7.3 Types of average Find the mode, median and mean. S2 S4 2nd 6th Recognise the advantages and disadvantages of each type of average.

Find the modal class.Find the median from a frequency table.

7.4 Estimating the mean Calculate the value halfway between pairs of numbers.

S2 S4 7th 7th Estimate the mean of grouped data.

Calculate the mean.Read data from a frequency table.

7.5 Sampling Understand the use of random numbers in a real-life situation.

S1 6th 6th Understand the need for sampling.

Understand how to avoid bias.SPRING 8 Perimeter, area and volume 1 10 N13 N14 R1 G12 G14

G16 G17 R14th 8th

Measure lines.Recall the names of 2D shapes.Identify and name common 3D solids: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

Use strategies for multiplying and dividing by powers of 10.Find areas by counting squares and volumes by counting cubes.Interpret scales on a range of measuring instruments.

Convert metric units to metric units.8.1 Rectangles, parallelograms and triangles

Understand the meaning of ‘perpendicular’. N14 G14 G16 G17 6th 6th Calculate the perimeter and area of rectangles, parallelograms and triangles.

Work out the perimeter and area of triangles and rectangles.

Estimate lengths, areas and costs.

Calculate a missing length, given the area.8.2 Trapezia and changing units Multiplying and dividing by powers of 10, converting

between millimetres, centimetres and metres.R1 G16 6th 6th Calculate the area and perimeter of trapezia.

Find the height of a trapezium given its area.Convert between area measures.

8.3 Area of compound shapes Know that 1 km = 1000 m R1 G16 G17 6th 6th Calculate the perimeter and area of shapes made from triangles and rectangles.

Multiply and divide by powers of 10. Calculate areas in hectares, and convert between ha and m2.Convert between metric measures of area.

8.4 Surface area of 3D solids Describe shapes using correct vocabulary, including face, edge and vertex.

G16 G17 6th 7th Calculate the surface area of a cuboid.

Sketch the net of a cuboid. Calculate the surface area of a prism.Work out the area of rectangles, triangles and trapezia.

8.5 Volume of prisms Identify cross sections of prisms. G16 G17 4th 7th Calculate the volume of a cuboid.Decide whether a 3D solid is a prism. Calculate the volume of a prism.

8.6 More volume and surface area Multiply and divide by large powers of 10. R1 G16 G17 6th 8th Solve problems involving surface area and volume.Know that 1 litre = 1000 ml. Convert between measures of volume.Work out the volume and surface area of a prism.

SPRING 9 Graphs 10 N13 A7 A8 A9 A10 A12 A14 A17 R11 R14 G14

2nd 8th

Plot coordinates and read scales Substitute into a formula.

9.1 Coordinates Halve a number. A8 4th 6th Find the midpoint of a line segment.Substitute into an equation, and solve for an unknown.

Recognise, name and plot straight-line graphs parallel to the axes.

9.2 Linear graphs Use a function machine. A7 A9 A17 4th 6th Generate and plot coordinates from a rule.Read scales Plot straight-line graphs from tables of values.

Draw graphs to represent relationships.9.3 Gradient Understand that parallel lines will never meet. A9 A10 2nd 7th Find the gradient of a line.

Identify which line is steepest. Identify and interpret the gradient from an equation.Understand that parallel lines have the same gradient.

9.4 y = mx + c Understand that in a linear equation, the coefficient of x is the gradient.

A9 A10 A12 7th 7th Understand what m and c represent in y = mx + c.

Understand that parallel lines have the same gradient.

Find the equations of straight-line graphs.

Draw a line with a given gradient. Sketch graphs given the values of m and c.9.5 Real-life graphs Interpret scales. A9 A10 R14 G14 3rd 7th Draw and interpret graphs from real data.

Draw a graph of an equation in the form y = mx + c.

9.6 Distance-time graphs Understand and use the relationship between distance, average speed and time.

N13 A10 A14 R11 G14 6th 8th Use distance–time graphs to solve problems.

Draw distance–time graphs.Interpret rate of change graphs.

9.7 More real-life graphs Interpret a distance–time graph. A10 A14 Draw and interpret a range of graphs.Recall the definitions of positive, negative and no correlation.

Understand when predictions are reliable.

Find the equation of a line.SPRING 10 Transformations 10 R6 G1 G7 G24 4th 7th

Recall basic shapes.Be able to plot points in all four quadrants. Understand the concept of rotation.Reflect a shape in a mirror line.Translate a shape on a squared grid using instructions such as left/right and up/down. Draw and recognise lines parallel to axes and y = x, y = –x.Understand the terms 'clockwise' and 'anticlockwise'.

10.1 Translation Use the words left and right G7 G24 7th 7th Translate a shape on a coordinate grid.List the four types of transformations Use a column vector to describe a translation.Describe translations using left/right and up/down.

10.2 Reflection Define the word perpendicular G7 4th 7th Draw a reflection of a shape in a mirror line.Reflect a shape in a mirror line. Draw reflections on a coordinate grid.

Describe reflections on a coordinate grid.10.3 Rotation Know the number of degrees in fractions of a turn. G7 6th 7th Rotate a shape on a coordinate grid.

Use the words clockwise and anticlockwise. Describe a rotation.10.4 Enlargement Find scale factor from object to image and from

image to object.G7 5th 6th Enlarge a shape by a scale factor.

Enlarge a shape using a centre of enlargement.10.5 Describing enlargements Recognise the properties of enlargements. R6 G7 6th 6th Identify the scale factor of an enlargement.

Simplify fractions. Find the centre of enlargement.Describe an enlargement.

10.6 Combining transformations State key information for describing transformations. G7 G24 7th 7th Transform shapes using more than one transformation.

Identify the type of transformation used. Describe combined transformations of shapes on a grid.END OF TERM 2 TESTSUMMER 11 Ratio and proportion 10 N11 N13 R1 R4 R5 R6

R7 R8 R10 R11 R12 R14

4th 8th

Know the four operations of number.Have a basic understanding of fractions as being ‘parts of a whole’. Find the scale factor of an enlargement.Draw a line graph from a table of values.

11.1 Writing ratios Multiply and divide whole numbers. N11 R4 4th 5th Use ratio notation.Interpret bar charts. Write a ratio in its simplest form.

Solve problems using ratios.11.2 Using ratios 1 Know and use metric conversions. R5 4th 6th Solve simple problems using ratios.

Find the HCF of a pair of numbers.

11.3 Ratios and measures Convert units of weight, length, capacity and time. N13 R1 R5 R12 4th 7th Use ratios to convert between units.

Use index notation. Write and use ratios for shapes and their enlargements.Work out areas of recangles and volumes of cubes.

11.4 Using ratios 2 Write ratios using correct notation. R5 6th 8th Divide a quantity into 2 parts in a given ratio. Round to a specified degree of accuracy. Divide a quantity into 3 parts in a given ratio.Write a ratio in its simplest form. Solve word problems using ratios.

11.5 Comparing using ratios Interpret ratios. N11 R4 R5 R6 R7 R8 6th 7th Use ratios involving decimals.Write a ratio in its simplest form. Compare ratios.

Solve ratio and proportion problems.11.6 Using proportion Understand and use place value to order decimals. R5 R10 R11 6th 6th Use the unitary method to solve proportion problems.

Write a ratio in the form 1 : n. Solve proportion problems in words.Work out which product is better value for money.

11.7 Proportion and graphs Understand and use y = mx + c. R10 R14 6th 7th Recognise and use direct proportion on a graph.Use conversion graphs. Understand the link between the unit ratio and the gradient.Plot a line graph from a table of values.

11.8 Proportion problems Relate common sense to real life problems. R10 Recognise different types of proportion.Solve word problems involving direct and inverse proportion.

SUMMER 12 Right-angled triangles 10 N7 N15 R12 G6 G11 G20 G21

3rd 8th

Rearrange simple formulae and equations, as preparation for rearranging trigonometric formulae.

Recall basic angle facts.Understand when to leave an answer in surd form.

Plot coordinates in all four quadrants and draw axes.

Round to a specified degree of accuracy.12.1 Pythagoras' theorem 1 Calculate of simple squares and square roots. N7 N15 G6 G20 3rd 7th Understand Pythagoras’ theorem.

Substitute into and evaluate expressions. Calculate the length of the hypotenuse in a right-angled triangle.

Round answers to a specified degree of accuracy. Solve problems using Pythagoras’ theorem.

12.2 Pythagoras' theorem 2 Understand the meaning of ≠. N7 N15 G11 G20 7th 8th Calculate the length of a line segment AB.Interpret a surd expression shown on the calculator display.

Calculate the length of a shorter side in a right-angled triangle.

Identify the hypotenuse, and calculate its length.

12.3 Trigonometry: the sine ratio 1 Simplify fractions. R12 N15 G20 6th 8th Understand and recall the sine ratio in right-angled triangles.Convert fractions to decimals using a calculator. Use the sine ratio to calculate the length of a side in a right-angled

triangle.Use the sine ratio to solve problems.

12.4 Trigonometry: the sine ratio 2 Calculate the sine of an angle in a right-angled triangle.

N15 G20 6th 8th Use the sine ratio to calculate an angle in a right-angled triangle.

Use the sin key on a calculator. Use the sine ratio to solve problems.

12.5 Trigonometry: the cosine ratio Identify the hypotenuse and adjacent side in a right-angled triangle.

G20 6th 8th Understand and recall the cosine ratio in right-angled triangles.

Use the cosine ratio to calculate the length of a side in a right-angled triangle.Use the cosine ratio to calculate an angle in a right-angled triangle.

Use the cosine ratio to solve problems.

12.6 Trigonometry: the tangent ratio Identify the opposite and adjacent sides in right-angled triangles.

G20 6th 8th Understand and recall the tangent ratio in right-angled triangles.

Use the tangent ratio to calculate the length of a side in a right-anglesd triangleUse the tangent ratio to calculate an angle in a right-angled triangle.

Solve problems using an angle of elevation or depression.12.7 Finding lengths and angles using trigonometry

Identify the sine, cosine and tangent ratios. G20 G21 7th 8th Understand and recall trigonometric ratios in right-angled triangles.

Use trigonometric ratios to solve problems.Know the exact values of the sine, cosine and tangent of some angles.

SUMMER 13 Probability 9 N5 P1 P2 P3 P4 P5 P6 P7 P8

3rd 8th

Add and multiply fractions and decimals.Have experience of expressing one number as a fraction or percentage of another number.Convert between fractions, decimals and percentages.Understand the terms impossible, unlikely, even chance, likely, certain.Calculate theoretical probabilities for simple situations, e.g. spinner landing on a given colour.

13.1 Calculating probability Write probability as a fraction, a decimal and a percentage.

P1 P2 P3 P4 3rd 6th Calculate simple probabilities from equally likely events.

Add and subtract fractions. Understand mutually exclusive and exhaustive outcomes.13.2 Two events List outcomes. N5 P1 P2 P3 P4 P7 6th 6th Use two-way tables to record the outcomes from two events.

Simplify fractions. Work out probabilities from sample space diagrams.13.3 Experimental probability Convert fractions, decimals and percentages. P1 P2 P3 P4 P7 3rd 7th Find and interpret probabilities based on experimental data.

Compare fractions. Make predictions from experimental data.Understand theoretical probability (single event).

Use two-way tables.13.4 Venn diagrams Add and subtracting equivalent fractions. P1 P2 P3 P4 P5 4th 6th Use Venn diagrams to work out probabilities.

List primes and multiples. Understand the language of sets and Venn diagrams.Calculate probabilities.

13.5 Tree diagrams Calculate with fractions. P1 P2 P3 P4 P5 P6 P8 5th 8th Use frequency trees and tree diagrams.

List the possible outcomes for two events. Work out probabilities using tree diagrams.Work out the probability of something not happening.

Understand independent events.

Calculate probabilities.13.6 More tree diagrams Calculate with and simplify fractions. P1 P2 P3 P4 P5 P6 P8 6th 8th Understand when events are not independent.

Work out probabilities using tree diagrams. Solve probability problems involving events that are not independent.

SUMMER 14 Multiplicative reasoning 9 N13 R1 R7 R9 R10 R11 R13 R16 G14

5th 8th

Interpret scales on a range of measuring instruments.

Convert between metric measures.Understand ratio notation, and be able to write a ratio in its simplest form.Find a percentage of an amount and relate percentages to decimals.Rearrange equations and use these to solve problems. Know speed = distance/time, density = mass/volume.Find the equation of a line from a graph.Identify a graph showing direct proportion.

14.1 Percentages Convert percentages to decimals. R9 7th 7th Calculate a percentage profit or loss.Express one number as a percentage of another. Express a given number as a percentage of another in more complex

situations.Work out percentage increases and decreases. Find the original amount given the final amount after a percentage

increase or decrease14.2 Growth and decay Write powers of numbers in index form. R16 7th 7th Find an amount after repeated percentage change.

Relate percentages to decimals. Solve growth and decay problems.14.3 Compound measures Understand ‘rate’ as a mathematical concept. N13 R1 R11 G14 5th 7th Solve problems involving compound measures.

Substitute into and solve equations.Rearrange equations.Convert between metric units of volume.Calculate the area of a trapezium.Calculate the volume of a prism.

14.4 Distance, speed and time Find speed in km/h, given distance travelled in minutes.

N13 R1 R11 G14 5th 7th Convert between metric speed measures.

Convert between metric units of length. Calculate average speed, distance and time.Use formulae to calculate speed and acceleration.

14.5 Direct and inverse proportion Identify graphs showing direct proportion. R7 R10 R13 6th 8th Use ratio and proportion in measures and conversions.Write a ratio as a unit ratio. Use inverse proportions.

SUMMER 15 Constructions, loci and bearings 10 R2 R6 G1 G2 G4 G5 G6 G7 G12 G13 G15

1st 7th

Measure and draw lines.Write a ratio in the form 1 : m and in its simplest form.Know the 8 points of the compass.Draw a net of a 3D shape.Know clockwise, anticlockwise.Identify congruent shapes.

15.1 3D solids Recall names of common 2D shapes. G1 G4 G12 1st 4th Recognise 3D shapes and their properties.Describe 3D shapes using the correct mathematical words.Understand the 2D shapes that make up 3D objects.

15.2 Plans and elevations Identify names of 2D shapes from faces of 3D solids. G12 G13 6th 6th Identify and sketch planes of symmetry of 3D shapes.

Recall names of common 3D shapes. Understand and draw plans and elevations of 3D shapes.Know the properties of special triangles and quadrilaterals.

Sketch 3D shapes based on their plans and elevations.

15.3 Accurate drawings 1 Understand of the meaning of ‘congruence’. G5 G6 G7 5th 6th Make accurate drawings of triangles using a ruler, protractor and compasses.

Draw lines, angles and circles accurately Identify SSS, ASA, SAS and RHS triangles as unique from a given description.Identify congruent triangles

15.4 Scale drawings and maps Work out scale factor of an enlargement. R2 R6 G15 4th 6th Draw diagrams to scale.Write a ratio in the form 1 : m, and write equivalent ratios.

Correctly interpret scales in real-life contexts.

Convert between metric measurements of length. Use scales on maps and diagrams to work out lengths and distances.

Know when to use exact measurements and estimations on scale drawings and maps.Draw lengths and distances correctly on given scale drawings.

15.5 Accurate drawings 2 Knowledge of scale factors of enlargement. G1 G2 G12 6th 6th Accurately draw angles and 2D shapes using a ruler, protractor and compasses.

Identify a solid from its net. Construct a polygon inside a circle.Recognise nets and make accurate drawings of nets of common 3D objects.

15.6 Constructions Identify parallel and perpendicular lines. G2 7th 7th Draw accurately using rulers and compasses.Draw lines accurately. Bisect angles and lines using rulers and compasses.

15.7 Loci and regions Convert distances from map scale to real life distance and vice versa.

G2 7th 7th Draw loci for the path of points that follow a given rule.

Construct the perpendicular bisector. Identify regions bounded by loci to solve practical problems.15.8 Bearings Working out the complement to 180 or 360 (addition

and subtraction).G2 G15 4th 7th Find and use three-figure bearings.

Recall the properties of angles at a point, angles on a straight line, alternate and corrsponding angles.

Use angles at parallel lines to work out bearings.

Solve problems involving bearings and scale diagrams.END OF TERM 3 TESTEND OF YEAR TEST

Year 11 (F) Foundation Student BookTERM UNIT / LESSON HOURS PRIOR KNOWLEDGE GCSE (9-1) SPEC


STEPSTO …

OBJECTIVES

Key: Italic specification references are assumed prior knowledge and are covered in the prior knowledge check rather than the main teaching.AUTUMN 16 Quadratic equations and graphs 11 N4 A1 A3 A4 A6 A8

A11 A12 A14 A186th 8th

Square negative numbers.Substitute into formulae.Plot points on a coordinate grid.Expand single brackets and collect ‘like’ terms.

16.1 Expanding double brackets Be able to work out area of a shape using algebraic terms.

A1 A4 6th 7th Multiply double brackets.

# Simplify algebraic expressions. Recognise quadratic expressions.Multiply a single term over brackets. Square single brackets.

16.2 Plotting quadratic graphs Be able to square terms. A8 A11 A12 7th 7th Plot graphs of quadratic functions.Identify the equation of the mirror line. Recognise a quadratic function.Copy and complete a table of values and plot a straight line graph.

Use quadratic graphs to solve problems.

16.3 Using quadratic graphs Define the origin and x-axis on a graph. A8 A11 A12 A14 7th 8th Solve quadratic equations ax2 + bx + c = 0 using a graph.Copy and complete a table of values and plot a quadratic graph.

Solve quadratic equations ax2 + bx + c = k

Using a graph.16.4 Factorising quadratic expressions Work out factor pairs of negative numbers N4 A1 A3 A4 7th 8th

Multiply double brackets.

16.5 Solving quadratic equations algebraically

Know that taking the square root of a number will result in both a positive and a negative answer.

A1 A3 A4 A6 A8 7th 7th

Factorise quadratic expressions.

AUTUMN 17 Perimeter, area and volume 2 12 N8 N14 N15 N16 G9 G14 G16 G17 G18

4th 8th

Know the formula for calculating the area of a rectangle. Know how to use the four operations on a calculator.

Name common 3D shapes.Define centre, radius and diameter for a circle.Substitute into formulae and solve for the unknown.

Work out the volume of cuboids and prisms.17.1 Circumference of a circle 1 Round accurately to a given number of significant

figures or decimal place.G9 G17 5th 6th Calculate the circumference of a circle.

Rearrange equations. Solve problems involving the circumference of a circle.17.2 Circumference of a circle 2 Round to nearest metre. N8 N15 N16 G9 G17 4th 6th Calculate the circumference and radius of a circle.

Solve equations. Work out percentage error intervals.Understand inequality notation.Rearrange equations.

17.3 Area of a circle Evaluate squares and square roots. N8 N15 N16 G9 G17 6th 7th Work out the area of a circle.Substitute into formulae and solve for the unknown. Work out the radius or diameter of a circle.

Solve problems involving the area of a circle.Give answers in terms of π.

17.4 Semicircles and sectors Know number of degrees in a full turn, half turn or quarter turn.

N15 G9 G17 G18 6th 8th Understand and use maths language for circles and perimeters.

Simplify fractions. Work out areas of semicircles and quarter circle and perimeters.

Find the area and circumference of a circle. Solve problems involving sectors of circles.17.5 Composite 2D shapes and cylinders Know and use the formula for the volume of a prism. N15 G9 G14 G16 G17

G187th 8th Solve problems involving areas and perimeters of 2D shapes.

Sketch the net of a cylinder. Work out the volume and surface area of cylinders.Work out the area and perimeter of rectangles, semicircles and quarter circles.Give answers in terms of π.

17.6 Pyramids and cones Understand and use maths language for 3-D shapes. N14 G17 7th 8th Work out the volume of a pyramid.

Work out the area of 2D shapes. Work out the surface area of a pyramid.Give answers in terms of π. Work out the volume of a cone.

Work out the surface area of a cone.17.7 Spheres and composite solids Know volume and surface area formulae. G17 8th 8th Work out the volume of a sphere.

Work out the length of the hypotenuse using Pythagoras' theorem.

Work out the surface area of a sphere.

Work out the volume and surface area of composite solids.AUTUMN 18 Fractions, indices and standard

form10 N2 N3 N6 N7 N8 N9 6th 8th

Know how to do the four operations with fractions.

Convert between improper fractions and mixed numbers.Write powers of 10 in index form and recognise and recall powers of 10, i.e. 10² = 100.Recall the index laws for multiplying and dividing positive integer powers.

18.1 Multiplying and dividing fractions Convert between fractions, mixed numbers and improper fractions.

N2 N3 N8 6th 8th Multiply and divide mixed numbers and fractions.

Work out reciprocals of whole numbers, fractions, and decimals.Four operations with fractions.

18.2 The laws of indices Evaluate simple powers. N3 N6 N7 7th 8th To know and use the laws of indices.Recall the index laws for multiplying and dividing positive integer powers.

18.3 Writing large numbers in standard form

Evaluate powers of 10. N9 8th 8th Write large numbers in standard form.

Write 1 million and 1 billion in figures. Convert large numbers from standard form into ordinary numbers.

18.4 Writing small numbers in standard form

Divide integers and decimals by powers of ten. N9 8th 8th Write small numbers in standard form.

Convert numbers from standard form with negative powers of ordinary numbers

18.5 Calculating with standard form Use correct priority of operations. N9 8th 8th To multiply and divide numbers in standard form.

Write numbers in standard form. To add and subtract numbers in standard form.AUTUMN 19 Congruence, similarity and vectors 12 R6 R12 G3 G5 G6 G7

G17 G19 G24 G256th 8th

Begin to use column vectors when dealing with translations.Recall and apply Pythagoras’ Theorem on a coordinate grid.Recognise and enlarge shapes and calculate scale factors.Know how to calculate area and volume in various metric measures.Measure lines and angles and using compasses, ruler and protractor, and construct standard constructions.

Know the properties of alternate, corresponding and vertically opposite angles.Identify congruent and similar shapes.

19.1 Similarity and enlargement Understand the scale factor of an enlargement. R12 G6 G7 6th 8th Understand similarity.Equivalent fractions. Use similarity to solve angle problems.

19.2 More similarity Calculating fractions of whole numbers. R6 G6 G7 G19 6th 8th Find the scale factor of an enlargement.Using similarity of triangles to identify equal angles and lengths of corresponding sides.

Use similarity to solve problems.

Identify similar shapes.19.3 Using similarity Understand squares and cubes of whole numbers and

decimals.G6 G7 G17 G19 6th 8th Understand the similarity of regular polygons.

Use similarity to find unknown lengths. Calculate perimeters of similar shapes.19.4 Congruence 1 Know that the sum of the angles in a triangle must be

180°.G5 G6 G7 G19 5th 7th Recognise congruent shapes.

Identify congrent shapes. Use congruence to work out unknown angles.19.5 Congruence 2 Recognise corresponding and alternate angles. G3 G6 G7 G19 6th 7th Use congruence to work out unknown sides.

Find angles using corresponding and alternate angles.

Draw triangles accurately.19.6 Vectors 1 Add and subtract with negative numbers. G25 7th 8th Add and subtract vectors.

Use column vectors. Find the resultant of two vectors.19.7 Vectors 2 Calculate with negative numbers. G25 7th 8th Subtract vectors.

Find the resultant of two vectors. Find multiples of a vector.AUTUMN 20 More algebra 12 A2 A3 A5 A6 A12 A14

A17 A19 A21 R10 R13 R14 R16

4th 8th

Draw linear graphs.Plot coordinates and sketch simple functions with a table of values.Substitute into and solve equations. Have experience of using formulae.Recall and use the priority of operations and use of inequality symbols.

20.1 Graphs of cubic and reciprocal functions

Recognise the shape of linear and quadratic graphs. A12 8th 8th Draw and interpret graphs of cubic functions.

Find reciprocals of fractions and integers. Draw and interpret graphs of y = 1/x.20.2 Non-linear graphs Recognise statements and equations describing direct

and indirect proportion.A14 R10 R13 R14 R16 8th 8th Draw and interpret non-linear graphs to solve problems.

Recognise the graphs of y = x and y = 1/x.20.3 Solving simultaneous equations graphically

Write algebraic expressions. A19 A21 8th 8th Solve simultaneous equations by drawing a graph.

Write and solve simultaneous equations.20.4 Solving simultaneous equations algebraically

Add and subtract positive and negative terms, substitute integer and decimal values into a simple expression.

A19 A21 8th 8th Solve simultaneous equations algebraically.

20.5 Rearranging formulae Identify inverse operations for algebraic terms. A2 A5 A17 4th 8th Change the subject of a formula.Identify parallel lines from the equations of the lines.

20.6 Proof Identify expressions, formulae and equations from a list.

A6 7th 8th Identify expressions, equations, formulae and identities.

Prove results using algebra.END OF TERM 4 TEST

YEAR 10 Higher) Edexcel GCSE (9-1) Mathematics Higher Student BookTERM UNIT / LESSON HOURS PRIOR KNOWLEDGE GCSE (9-1) SPEC


STEPSTO …

OBJECTIVES

Key: Italic specification references are assumed prior knowledge and are covered in the prior knowledge check rather than the main teaching.AUTUMN 1 Number 11 N2 N3 N4 N5 N6 N7

N8 N9 N14 N156th 12th

Have a firm grasp of place value and be able to order integers and decimals and use the four operations.

Know integer complements to 10 and to 100, multiplication facts to 10 × 10, strategies for multiplying and dividing by 10, 100 and 1000.Have encountered squares, square roots, cubes and cube roots and have knowledge of classifying integers.

1.1 Number problems and reasoning Multiply numbers in a similar format to questions later in the section.

N3 N5 6th 9th Work out the total number of ways of performing a series of tasks.

List possible outcomes from two events.1.2 Place value and estimating Estimate the value of a square root. N3 N6 N14 N15 6th 7th Estimate an answer.

Round numbers to a specified degree of accuracy. Use place value to answer questions.

Apply the four operations.1.3 HCF and LCM Multiply prime factors together. N3 N4 7th 8th Write a number of the product of its prime factors.

List the factors of a number. Find the HCF and LCM of two numbers.1.4 Calculating with powers (indices) Work out simple powers. N3 N6 N7 6th 8th Use powers and roots in calculations.

Apply the four operations. Multiply and divide using index laws.Work out a power raised to a power.

1.5 Zero, negative and fractional indices

Convert between fractions and decimals. N3 N6 N7 8th 12th Use negative indices.

Use the laws of indices for positive indices. Use fractional indices.1.6 Powers of 10 and standard form Multiply by powers of 10 when the number is

written as an ordinary number and not an index.N3 N6 N9 7th 9th Write a number in standard form.

Review different ways to divide by 10. Calculate with numbers in standard form.Use negative indices.

1.7 Surds Review the meaning of the dot in the recurring notation.

N3 N8 10th 11th Understand the difference between rational and irrational numbers.

Identify the missing multiple which practices the skills of searching for a perfect square factor.

Simplify a surd.

Rationalise a denominator.AUTUMN 2 Algebra 12 N1 N3 N8 N9 A1 A2

A3 A4 A5 A6 A7 A17 A21 A22 A23 A24 A25

6th 10th

Use negative numbers with the four operations and recall and use hierarchy of operations and understand inverse operations.Use a calculator for decimals and negative numbers.

Use index laws numerically.Use and interpret algebraic notation.Set up and solve simple equations.Recall the definitions of geometric and arithmetic sequences.

2.1 Algebraic indices Recognise that squaring and taking the square roots, and cubing and taking the cube root, are inverse operations.

A4 7th 10th Use the rules of indices to simplify algebraic expressions.

Calculate with powers.2.2 Expanding and factorising Simplify algebraic terms, including using index

notation.N1 A3 A4 A6 6th 10th Expand brackets.

Multiply a single term over a bracket. Factorise algebraic expressions.Find highest common factors.

2.3 Equations Solve a simple equation expressed in words. N8 A4 A17 A21 6th 9th Solve equations involving brackets and numerical fractions.Solve simple algrebraic equations Use equations to solve problems.Find lowest common multiples.

2.4 Formulae Substitute values into a one-step formula. N9 A2 A3 A5 A6 6th 9th Substitute numbers into formulae.Write numbers in standard form. Rearrange formulae.

Distinguish between expressions, equations, formulae and identities.

2.5 Linear sequences Find the next term of a given arithmetic sequence. A7 A22 A23 A25 6th 8th Find a general formula for the nth term of an arithmetic sequence.

Substitute values in a simple linear expression. Determine whether a particular number is a term of a given arithmetic sequence.

Write terms in a sequence given the nth term.Use a function machine to find outputs.

2.6 Non-linear sequences Find the next term of given sequences. A6 A23 A24 A25 6th 9th Solve problems using geometric sequences.Identify arithmetic and geometric sequences. Work out terms in Fibonnaci-like sequences.Find the term-to-term rule for a sequence. Find the nth term of a quadratic sequence.

2.7 More expanding and factorising Recalling a square root. A4 7th 10th Expand the product of two brackets.Finding the factor pairs of small integers. Use the difference of two squares.

Factorise quadratics of the form x2 + bx + c.AUTUMN 3 Interpreting and representing data 11 G14 S1 S2 S3 S4 S5 S6 4th 8th

Read scales on graphs, draw circles, measure angles and plot coordinates in the first quadrant.

Have experience of tally charts.Use inequality notation.Find midpoint of two numbers.Find the range, mean, median and mode of a data set.

3.1 Statistical diagrams 1 Work out mode, median and range from a list of numbers.

S1 S2 S3 4th 7th Construct and use back-to-back stem and leaf diagrams.

Construct and use frequency polygons and pie charts.3.2 Time series Identify trends by noticing whether sequences of

numbers increase, decrease or oscillate.S2 6th 6th Plot and interpret time series graphs.

Use trends to predict what might happen in the future.3.3 Scatter graphs Recognise when a line has a positive, negative or

zero gradient.S6 6th 7th Plot and interpret scatter graphs.

Plot points on a coordinate grid, and identify points that do not lie on a straight line.

Determine whether or not there is a linear relationship between two variables.

3.4 Line of best fit Understand and be able to define the meaning of correlation.

S6 6th 7th Draw a line of best fit on a scatter graph.

Read values from graphs. Use the line of best fit to predict values.3.5 Averages and range Find the range of a list of numbers. S4 S5 5th 8th Decide which average is best for a set of data.

Find the midpoint of two numbers. Estimate the mean and range from a grouped frequency table.Find the modal class and the group containing the median.

3.6 Statistical diagrams 2 Use subtraction to find missing values. S2 5th 6th Construct and use two-way tables.Draw a bar chart. Choose appropriate diagrams to display data.Draw a pie chart. Recognise misleading graphs.

AUTUMN 4 Fractions, ratio and percentages 10 N2 N3 N8 N10 N11 N12 N13 R3 R4 R5 R6 R7 R8 R9 R10

6th 10th

Know the four operations of number.Find common factors. Have a basic understanding of fractions as being ‘parts of a whole’. Define percentage as ‘number of parts per hundred’.

Be aware that percentages are used in everyday life.

Use ratio notation, and to write a ratio in its simplest form.

4.1 Fractions Identify unit fractions, improper fractions and mixed numbers.

N2 N3 6th 8th Add, subtract, multiply and divide fractions and mixed numbers.

Multiply a whole number by a fraction. Find the reciprocal of an integer, decimal or fraction.Know the priority of operations.

4.2 Ratios Multiply a fraction by its reciprocal for a product of 1.

N11 N13 R4 R5 6th 7th Write ratios in the form 1 : n or n : 1.

Simplify ratios. Compare ratios.Write ratios in the form n : 1. Find quantities using ratios.

Solve problems involving ratios.4.3 Ratio and proportion Write one number as a proportion of the total. N13 R4 R5 R6 R7 R8

R106th 8th Convert between currencies and measures.

Identify equivalent ratios. Recognise and use direct proportion.Solve problems involving ratios and proportion.

4.4 Percentages Find a percentage of a given amount. N12 N13 R9 6th 9th Work out percentage increases and decreases.Work out percentage multipliers. Solve real-life problems involving percentages.

4.5 Fractions, decimals and percentages

Convert between fractions, decimals and percentages.

N2 N8 N10 R3 R6 R9 6th 10th Work out percentage increases and decreases.

Solve simple equations. Solve real-life problems involving percentages.AUTUMN 5 Angles and trigonometry 12 N7 N8 N15 G1 G3 G4

G6 G20 G216th 9th

Rearrange simple formulae and equations, as preparation for rearranging trig formulae. Recall basic angle facts.Understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents.Recall the properties of special types of triangles and quadrilaterals.

5.1 Angle properties of triangles and quadrilaterals

Recognise special types of triangle and quadrilateral. G1 G3 G4 G6 6th 6th Derive and use the sum of angles in a triangle and in a quadrilateral.

Recall basic angle facts. Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

5.2 Interior angles of a polygon Name polygons and understand the meaning of ‘regular polygon’.

G3 6th 7th Calculate the sum of the interior angles of a polygon.

Substitute numbers into an expression. Use the interior angles of polygons to solve problems. Find missing angles in triangles, quadrilaterals and at a point.

5.3 Exterior angles of a polygon Find missing angles on a straight line. G3 6th 8th Know the sum of the exterior angles of a polygon.Calculate the sum of interior angles of a polygon. Use the angles of polygons to solve problems.

5.4 Pythagoras’ theorem 1 Recall square numbers and square roots. N15 G20 7th 7th Calculate the length of the hypotenuse in a right-angled triangle.

Find the area of a square. Solve problems using Pythagoras’ theorem.5.4 Pythagoras’ theorem 1 Find square roots. N7 N8 G20 8th 8th Calculate the length of a shorter side in a right-angled triangle.

Recognise perfect squares. Solve problems using Pythagoras’ theorem.Use Pythagoras' theorem to find the length of the hypotenuse.

5.6 Trigonometry 1 Convert fractions to decimals. G20 6th 9th Use trigonometric ratios to find lengths in a right-angled triangle.

Identify the hypotenuse. Use trigonometric ratios to solve problems.Use the angle sum of a triangle to work out missing angles.

5.7 Trigonometry 2 Identify the opposite and adjacent sides of a given angle in right-angled triangles.

G20 G21 6th 9th Use trigonometric ratios to calculate an angle in a right-angled triangle.

Use the trigonometric ratios to find lengths in right-angled triangles.

Find angles of elevation and angles of depression.

Use trigonometric ratios to solve problems.Know the exact values of the sine, cosine and tangent of some angles.

END OF TERM 1 TESTSPRING 6 Graphs 11 N13 A8 A9 A10 A11

A12 A14 A15 A16 A17 G11 R8 R10 R11

6th 10th

Identify coordinates of given points in the first quadrant or all four quadrants.Write the equation for a straight line graph. Use and draw conversion graphs. Use function machines and inverse operations.Use compound units, such a speed.

6.1 Linear graphs Identify positive and negative gradients and intercepts from graphs.

A8 A9 A10 6th 8th Find the gradient and y-intercept from a linear equation.

Rearrange equations. Rearrange an equation into the form y = mx + c.Compare two graphs from their equations.Plot graphs with equations ax + by = c.

6.2 More linear graphs Identify lines with the same gradient or y-intercept from their equations.

A8 A9 A10 A17 7th 8th Sketch graphs using the gradient and intercepts.

Write the equation of a line from a graph. Find the equation of a line, given its gradient and one point on the line.Find the gradient of a line through two points.

6.3 Graphing rates of change Find speed from given distance and time. A14 A15 R10 R11 6th 10th Draw and interpret distance–time graphs.Find the area of triangles and rectangles. Calculate average speed from a distance–time graph.

Understand velocity–time graphs.Find acceleration and distance from velocity–time graphs.

6.4 Real-life graphs Write the equation of a line from a sketch graph. A9 A14 A15 R8 R10 6th 8th Draw and interpret real-life linear graphs.

Plot a graph using values given in a table. Recognise direct proportion.Draw and use a line of best fit.

6.5 Line segments Identify parallel and perpendicular lines A9 A10 G11 6th 10th Find the coordinates of the midpoint of a line segment.Know properties of gradients of parallel lines. Find the gradient and length of a line segment.Identify the gradient and intercept from an equation in the form y = mx + c.

Find the equations of lines parallel or perpendicular to a given line.

6.6 Quadratic graphs Identify quadratic expressions. A8 A11 A12 7th 10th Draw quadratic graphs.Write the equation of a line from a graph. Solve quadratic equations using graphs.

Identify the line of symmetry of a quadratic graph.Interpret quadratic graphs relating to real-life situations.

6.7 Cubic and reciprocal graphs Know the shape of linear and quadratic graphs. A8 A12 8th 10th Draw graphs of cubic functions.Solve cubic equations using graphs.Draw graphs of reciprocal functions.Recognise a graph from its shape.

6.8 More graphs Match the shape of a container to the graph of depth of water against time.

A12 A14 A16 7th 9th Interpret linear and non-linear real-life graphs.

Read values from graphs. Draw the graph of a circle.SPRING 7 Area and volume 10 N8 N13 N14 N15 N16

R1 G1 G9 G12 G14 G16 G17 G18

6th 12th

Know the names and properties of 3D shapes.Know the concept of perimeter and area by measuring lengths of sides. Substitute numbers into an equation and give answers to an appropriate degree of accuracy.Know the various metric units. Identify planes of symmetry of 3D solids.Sketch a net of a 3D shape.Work out the volume of a 3D solid made of cuboids.

Recall Pythagoras' theorem.7.1 Perimeter and area Recognising units of length (perimeter) and area. G16 G17 6th 6th Find the perimeter and area of compound shapes.

Work out the area and perimeter of rectangles, triangles and parallelograms.

Recall and use the formula for the area of a trapezium.

7.2 Units and accuracy Recall the formulae for the area of quadrilaterals and triangles. Identify the possible integer values of x from an inequality.

N13 N14 N15 N16 R1 G14 G16

6th 10th Convert between metric units of area.

Round numbers to a specified degree of accuracy. Calculate the maximum and minimum possible values of a measurement.

Work out percentages of quantities. 7.3 Prisms Calculate the volume and surface area of a cuboid. N13 N14 N15 R1 G16 7th 9th Convert between metric units of volume.

Calculate the volume of a shape made from cuboids. Calculate volumes and surface areas of prisms.

7.4 Circles Understand ‘radius’ and ‘diameter’. N8 G9 G17 6th 8th Calculate the area and circumference of a circle.Solve and rearrange simple equations. Calculate area and circumference in terms of π.

7.5 Sectors of circles Work out fractions of a circle given the angle of a sector.

N8 N16 G9 G17 G18 8th 12th Calculate the perimeter and area of semicircles and quarter circles.

Simplify equations. Calculate arc lengths, angles and areas of sectors of circles.

7.6 Cylinders and spheres Find the area and circumference of a circle in terms of π.

N16 G16 G17 7th 11th Calculate volume and surface area of a cylinder and a sphere.

Sketch a net of a cylinder. Solve problems involving volumes and surface areas.Solve simple equations.

7.7 Pyramids and cones Find the volume of a cube. G17 6th 12th Calculate volume and surface area of pyramids and cones.Find the side length of a cube given its volume. Solve problems involving pyramids and cones.Calculate the area of a triangle.Use Pythagoras' theorem to work out the length of the hypotenuse.

SPRING 8 Transformations and constructions 10 R2 R6 G1 G2 G7 G8 G12 G13 G15 G24 G25

6th 10th

Recognise 2D shapes. Plot coordinates in four quadrants and linear equations parallel to the coordinate axes.Convert metric measures.Recognise congruent and similar shapes.Transform shapes using translation, reflection, rotation and enlargement.

8.1 3D solids Draw 3D shapes on an isometric grid. G12 G13 6th 7th Draw plans and elevations of 3D solids.Recognise dimensions of a cuboid.

8.2 Reflection and rotation Draw simple straight lines on a coordinate grid. G8 6th 7th Refl ect a 2D shape in a mirror line.Know whether the image is congruent to the original following a reflection or a rotation.

Rotate a 2D shape about a centre of rotation.

Describe refl ections and rotations.8.3 Enlargement Enlarge shapes on a coordinate grid in one quadrant. R2 R6 6th 10th Enlarge shapes by fractional and negative scale factors about a

centre of enlargement.8.4 Transformations and combinations of transformations

Describe translations. G7 G24 G25 7th 8th Translate a shape using a vector.

Carry out and describe combinations of transformations.8.5 Bearings and scale drawings Convert metric measures and apply to scales. R2 G1 G15 6th 7th Draw and use scales on maps and scale drawings.

Accurate drawing of right-angled triangle. Solve problems involving bearings.

8.6 Constructions 1 Accurate drawings of triangles given SSS and ASA. G1 G2 6th 7th Construct triangles using a ruler and compasses.

Know the meaning of the terms perpendicular, bisect, arc.

Construct the perpendicular bisector of a line.

Construct the shortest distance from a point to a line using a ruler and compasses.

8.7 Constructions 2 Draw angles with a protractor. R2 G1 G2 7th 8th Bisect an angle using a ruler and compasses.Construct triangles and deduce infomration from them.

Construct angles using a ruler and compasses.

Construct shapes made from triangles using a ruler and compasses.

8.8 Loci R2 G1 G2 7th 10th Draw a locus.Use loci to solve problems.

SPRING 9 Equations and inequalities 9 N1 N8 A3 A4 A5 A9 A11 A18 A19 A21 A22

6th 12th

Understand the ≥ and ≤ symbols.Substitute into, solve and rearrange linear equations.Factorise simple quadratic expressions.Recognise the equation of a circle.

9.1 Solving quadratic equations 1 Know that a square has two possible roots A3 A4 A11 A18 7th 9th Find the roots of quadratic functions.Find the factors of a given number. Rearrange and solve simple quadratic equations.Factorise expressions.Solve simple equations containing a squared term.

9.2 Solving quadratic equations 2 Understand the term quadratic N8 A3 A4 A18 8th 10th Solve more complex quadratic equations.Find positive and negative square roots. Use the quadratic formula to solve a quadratic equation.Solve quadratic equations by factorising. Expand two pairs of brackets.Simplify surds.

9.3 Completing the square Expand and simplify a square bracket. A3 A4 A5 A18 7th 12th Complete the square for a quadratic expression.Simplify surds. Solve quadratic equations by completing the square.Solve simple equations, giving the answer in surd form.

9.4 Solving simple simultaneous equations

Substitute into simple algebraic expressions. A3 A4 A5 A19 A21 8th 10th Solve simple simultaneous equations.

Rearrange equations. Solve simultaneous equations for real-life situations.9.5 More simultaneous equations Recall the equation of a straight line. A3 A4 A5 A9 A19 A21 9th 9th Use simultaneous equations to find the equation of a straight line.

Solve simple simultaneous equations. Solve linear simultaneous equations where both equations are multiplied.Interpret real-life situations involving two unknowns and solve them.

9.6 Solving linear and quadratic simultaneous equations

Identify different types of equations. A3 A4 A5 A19 A21 10th 12th Solve simultaneous equations with one quadratic equation.

Solve quadraric equations. Use real-life situations to construct quadratic and linear equations and solve them.

9.7 Solving linear inequalities Understand inequality signs A3 A4 A5 A22 6th 9th Solve inequalities and show the solution on a number line and using set notation.

Construct correct inequalities from given information

SPRING 10 Probability 9 N1 P1 P2 P3 P4 P5 P6 P7 P8 P9

5th 12th

Understand that a probability is a number between 0 and 1, and distinguish between events which are impossible, unlikely, even chance, likely, and certain to occur Mark events and/or probabilities on a probability scale of 0 to 1. Know how to add and multiply fractions and decimals.Express one number as a fraction of another.List all outcomes for a single event systematically.

Make predictions from experimental data.Complete a two-way table.

10.1 Combined events List all outcomes for a single event systematically. N5 P7 P8 5th 8th Use the product rule for finding the number of outcomes for two or more events.

List all outcomes for two events systemaically. List all the possible outcomes of two events in a sample space diagram.

10.2 Mutually exclusive events Add decimals. Subtract decimals and fractions from 1.

P4 P8 6th 7th Identify mutually exclusive outcomes and events.

Understand the relationship between ratios and fractions.

Find the probabilities of mutually exclusive outcomes and events.

Find the probability of an event not happening.

10.3 Experimental probability Simplify fractions. P1 P2 P3 P5 6th 8th Work out the expected results for experimental and theoretical probabilities.

Multilply whole numbers by decimals. Compare real results with theoretical expected values to see if a game is fair.

10.4 Independent events and tree diagrams

Add and multiply fractions and decimals. P1 P4 P8 P9 7th 10th Draw and use frequency trees.

Calculate probabilities of repeated events.Draw and use probability tree diagrams.

10.5 Conditional probability Know that the probability of something not happening is 1 minus the probability of the event happening.

P4 P8 P9 8th 12th Decide if two events are independent.

Draw and use probability tree diagrams. Draw and use tree diagrams to calculate conditional probability.

Draw and use tree diagrams without replacement.Use two-way tables to calculate conditional probability.

10.6 Venn diagrams and set notation Interpret inequalities. P4 P6 P8 P9 6th 10th Use Venn diagrams to calculate conditional probability.

Use Venn diagrams. Use set notation.END OF TERM 2 TESTSUMMER 11 Multiplicative reasoning 8 N12 N13 A2 A9 R1 R6

R9 R10 R11 R13 R14 R16

6th 9th

Find a percentage of an amount and relate percentages to decimals.Rearrange equations and use these to solve problems. Know speed = distance/time, density = mass/volume.Convert between metric units.Solve simple direct and indirect proportion problems, including currency conversion.

11.1 Growth and decay Understand the use of indices. N12 R9 R16 8th 9th Find an amount after repeated percentage changes.

Work out the decimal multiplier for a percentage increase/decrease.

Solve growth and decay problems.

11.2 Compound measures Calculate simple rates. A2 R1 R11 6th 7th Calculate rates.

Substitute numbers into equations, and solve for the unknown.

Convert between metric speed measures.

Use speed = distance/time to solve problems. Use a formula to calculate speed and acceleration.11.3 More compound measures Convert between metric units. N13 R1 R11 6th 8th Solve problems involving compound measures.

Recall the formulae for the area of a circle and volume of a prism.

11.4 Ratio and proportion Rearrange formulae. A9 R6 R10 R13 R14 6th 9th Use relationships involving ratio.

Recognise graphs of y = x and y = 1/x. Use direct and indirect proportion.Find the gradient of a line given its equation.Decide whether quantities are in direct proportion.

SUMMER 12 Similarity and congruence 8 R6 R12 G5 G6 G7 G17 G19

6th 12th

Recognise and enlarge shapes and calculate scale factors.Know how to calculate area and volume in various metric measures.Measure lines and angles, and use compasses, ruler and protractor to construct standard constructions.

Recognise congruent shapes.Know basic angle facts.

12.1 Congruence Know the angle sum of interior angles of a triangle. G5 G6 6th 10th Show that two triangles are congruent.

Recognise congruent shapes. Know the conditions of congruence.Recall basic angle facts.Find missing lengths using Pythagoras' theorem.

12.2 Geometric proof and congruence Know the conditions of congruence and use correct mathematical notation for equal angles and sides.

G5 G6 12th 12th Prove shapes are congruent.

Recall the properties of special triangles and quadrilaterals.

Solve problems involving congruence.

12.3 Similarity Use geometric properties to find similarities and differences between given polygons.

R6 R12 G6 G7 5th 9th Use the ratio of corresponding sides to work out scale factors.

Calculate scale factors. Find missing lengths on similar shapes.12.4 More similarity Find area scale factor, given length scale factor. G6 G7 G19 9th 11th Use similar triangles to work out lengths in real life.

Use the link between linear scale factor and area scale factor to solve problems.

12.5 Similarity in 3D solids Work out the volume and surface area of a cube. G6 G17 G19 9th 12th Use the link between scale factors for length, area and volume to solve problems.

Convert between metric units.Work out cubes and cube roots.

SUMMER 13 More trigonometry 13 N16 A8 A12 A13 G20 G22 G23

9th 12th

Use axes and coordinates to specify points in all four quadrants.Recall and apply Pythagoras’ Theorem and trigonometric ratios.Substitute into formulae.

13.1 Accuracy Find upper and lower bounds of a given measurement.

N16 10th 11th Understand and use upper and lower bounds in calculations involving trigonometry.

13.2 Graph of the sine function Know the exact values of sin θ for θ = 30°, 45° , 60° and 90°

A8 A12 G21 10th 12th Understand how to find the sine of any angle.

Use Pythagoras' theorem. Know the graph of the sine function and use it to solve equations.

Find angles using the sin function.13.3 Graph of the cosine function Know the exact values of cos θ for θ = 30°, 45° , 60°

and 90°A8 A12 G21 10th 12th Understand how to find the cosine of any angle.

Use Pythagoras' theorem. Know the graph of the cosine function and use it to solve equations.

Find angles using the cos function.13.4 The tangent function Know the exact values of tan θ for θ = 30°, 45° , 60° A8 A12 G21 10th 12th Understand how to fi nd the tangent of any angle.

Use Pythagoras' theorem. Know the graph of the tangent function and use it to solve equations.

Find angles using the tan function.13.5 Calculating areas and the sine rule Calculate the area of a triangle using (1/2)b × h G22 G23 9th 12th Find the area of a triangle and a segment of a circle.

Know the formula for calculating the area of a circle. Use the sine rule to solve 2D problems.

Use trigonometry13.6 The cosine rule and 2D trigonometric problems

Use bearings G22 G23 10th 12th Use the cosine rule to solve 2D problems.

Calculate the area of a triangle. Solve bearings problems using trigonometry. Solve calculations.

13.7 Solving problems in 3D Use the sine and cosine rule. G20 12th 12th Use Pythagoras’ theorem in 3D.Use trigonometry in 3D.

13.8 Transforming trigonometric graphs 1

Reflect and rotate a coordiante point. A8 A13 12th 12th Recognise how changes in a function affect trigonometric graphs.

Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45° , 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°Sketch y = sinx, y = cosx and y= tanx for x from 0° to 360°

13.9 Transforming trigonometric graphs 2

Translate coordinate points by column vectors. A8 A13 12th 12th Recognise how changes in a function affect trigonometric graphs.

Understand negative translations. SUMMER 14 Further statistics 10 S1 S3 S4 6th 12th

Understand the different types of data: discrete/continuous.Have experience of inequality notation.Multiply a fraction by a number.Understand the data handling cycle.

14.1 Sampling Use fractions and percentages to work out data from a table.

S1 6th 10th Understand how to take a simple random sample.

Understand how to take a stratifi ed sample.14.2 Cumulative frequency Find the median of a data set. S3 9th 9th Draw and interpret cumulative frequency tables and diagrams.

Work out the median, quartiles and interquartile range from a cumulative frequency diagram.

14.3 Box plots Find the median and range from a stem-and-leaf diagram.

S4 9th 9th Find the quartiles and the interquartile range from stem-and-leaf diagrams.Draw and interpret box plots.

14.4 Drawing histograms Division calculations S3 10th 11th Understand frequency density.Draw a frequency diagram. Draw histograms.Write the modal classEstimate the mean mass.

14.5 Interpreting histograms Write the modal class S3 11th 12th Interpret histograms.Estimate the mean mass.

14.6 Comparing and describing populations

Work out the mean, median and mode of data sets. S4 9th 10th Compare two sets of data.

Work out the mean and range from a table.SUMMER 15 Equations and graphs 9 N8 A4 A11 A12 A18

A19 A20 A21 A226th 12th

Solve quadratics and linear equations. Solve simultaneous equations algebraically.

15.1 Solving simultaneous equations graphically

Know and draw graphs of circles. A19 A21 9th 10th Solve simultaneous equations graphically.

15.2 Representing inequalities graphically

Know which integers satisfy an inequality A22 6th 12th Represent inequalities on graphs.

Solve inequalitites with one variable and show solution using set notation.

Interpret graphs of inequalities.

15.3 Graphs of quadratic functions Solve quadratic equations by factorising. N8 A11 A12 8th 12th Recognise and draw quadratic functions.Sketch simple quadratic graphsFind coordinates of maximum point.

15.4 Solving quadratic equations graphically

Understand manimum and minimum points. N8 A18 A20 9th 12th Find approximate solutions to quadratic equations graphically.

Find roots of an equation by completing the square and using the quadratic formula.

Solve quadratic equations using an iterative process.

15.5 Graphs of cubic functions Know where a graph will cross the x-axis A4 A12 A20 10th 12th Find the roots of cubic equations.Expand and simplify double brackets Sketch graphs of cubic functions.Find roots of a quadratic equation by completing the square

Solve cubic equations using an iterative process.

END OF TERM 3 TESTEND OF YEAR TEST

YEAR 11 Higher Edexcel GCSE (9-1) Mathematics Higher Student BookTERM UNIT / LESSON HOURS PRIOR KNOWLEDGE GCSE (9-1) SPEC


STEPSTO …

OBJECTIVES

Key: Italic specification references are assumed prior knowledge and are covered in the prior knowledge check rather than the main teaching.AUTUMN 16 Circle theorems 10 A16 G9 G10 7th 11th

Have practical experience of drawing circles with compasses.Recall the words, centre, radius, diameter, circumference, arc, sector and segmentRecall the relationship of the gradient between two perpendicular lines.Find the equation of the straight line, given a gradient and a coordinate.

16.1 Radii and chords Recall the properties of an isosceles triangle and the language of a circle.

G9 G10 7th 12th Solve problems involving angles, triangles and circles.

Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS).

Understand and use facts about chords and their distance from the centre of a circle.Solve problems involving chords and radii.

16.2 Tangents Recall that the line drawn from the centre of a circle to the midpoint of a chord is at right angles to the chord.

G9 G10 9th 12th Understand and use facts about tangents at a point and from a point.

Know that the sum of the angles in a triangle must be 180°

Give reasons for angle and length calculations involving tangents.

Recall the correct maths language for parts of a circle

16.3 Angles in circles 1 Recall simple maths facts. G10 9th 10th Understand, prove and use facts about angles subtended at the centre and the circumference of circles.

Recall the correct maths language for parts of a circle. Understand, prove and use facts about the angle in a semicircle being a right angle.Find missing angles using these theorems and give reasons for answers.

16.4 Angles in circles 2 Recall sum of angles of a triangle and a quadrilateral. G10 9th 10th Understand, prove and use facts about angles subtended at the circumference of a circle.

Recall correct maths language for parts of a circle. Understand, prove and use facts about cyclic quadrilaterals.

Prove the alternate segment theorem.16.5 Applying circle theorems Understand that x² + y² = r² is the equation of a circle

with centre at the origin. A16 G10 9th 11th Solve angle problems using circle theorems.

Find the gradient of a line from its equation and know the gradient of a line perpendicular to it.

Give reasons for angle sizes using mathematical language.

Find the equation of the straight line, given a gradient and a coordinate.

Find the equation of the tangent to a circle at a given point.

Recall circle theoremsAUTUMN 17 More algebra 13 N8 A4 A5 A6 A7 A18 8th 12th

Simplify surds. Use negative numbers with all four operations.Add and multiply numeric fractions.Recall and use the hierarchy of operations.Manipulate algebraic expressions. Recall and use the quadratic formula.

17.1 Rearranging formulae Substitute into linear equations. A5 9th 11th Change the subject of a formula where the power of the subject appears.

Change the subject of a formula. Change the subject of a formula where the subject appears twice.

Factorise linear expressions.17.2 Algebraic fractions Simplify numeric fractions and fractions containing

simple algebraic terms.A4 A5 8th 10th Add and subtract algebraic fractions.

Add and multiply numeric fractions. Multiply and divide algebraic fractions.Change the subject of a formula involving fractions where all the variables are in the denominators.

17.3 Simplifying algebraic fractions Factorise expressions by identifying the common factor between two terms.

A4 9th 12th Simplify algebraic fractions.

Simplify fractions containing simple algebraic terms.

Factorise quadratic expressions of the form x2 + bx + c

17.4 More algebraic fractions Simplify algebraic fractions by cancelling common factors.

A4 9th 12th Add and subtract more complex algebraic fractions.

Add, subtract, divide and multiply fractions containing simple algebraic terms.

Multiply and divide more complex algebraic fractions.

17.5 Surds Decide whether each number is rational or irrational. N8 A4 10th 12th Simplify expressions involving surds.

Expand expressions involving surds.Rationalise the denominator of a fraction.

17.6 Solving algebraic fraction equations

Find the lowest common multiple of two algebraic fractions.

A18 10th 12th Solve equations that involve algebraic fractions.

Solve quadratic equations by factorising.Manipulate expressions containing simple algebraic fractions.

17.7 Functions Calculate the output from a function machine for three different inputs.

A7 8th 12th Use function notation.

Solve simple equations Find composite functions.Write expressions using function machines Find inverse functions.

17.8 Proof Identify an odd number and an even number written algebraically.

A6 8th 12th Prove a result using algebra.

Recall the definitions of equations and identities.

AUTUMN 18 Vectors and geometric proof 10 G25 9th 12th

Use vectors to describe translations. Recall and use Pythagoras’ Theorem.Recall the properties of triangles and quadrilaterals.

Express the relationship between two quantities as a ratio.Simplify surds.

18.1 Vectors and vector notation Use vectors to describe translations. G25 9th 10th Understand and use vector notation. Recall and use Pythagoras' Theorem. Work out the magnitude of a vector. Simplify surds.

18.2 Vector arithmetic Understand the components of a vector and use vectors to describe translations.

G25 10th 10th Calculate using vectors and represent the solutions graphically.

Recall properties of triangles and quadrilaterals. Calculate the resultant of two vectors.

18.3 More vector arithmetic Use properties of a parallelogram to identify equal and parallel lines.

G25 10th 11th Solve problems using vectors.

Add two column vectors. Use the resultant of two vectors to solve vector problems.18.4 Parallel vectors and collinear points

Identify parallel column vectors. G25 10th 12th Express points as position vectors.

Add and subtract column vectors. Prove lines are parallel.Prove points are collinear.

18.5 Solving geometric problems Understand the relationship between ratio and fractional parts

G25 12th 12th Solve geometric problems in two dimensions using vector methods.

Identify parallel vectors Apply vector methods for simple geometric proofs.AUTUMN 19 Proportion and graphs 13 A7 A12 A13 A14 A15

R7 R10 R13 R14 R15 R16

7th 12th

Draw linear and quadratic graphs.Recognise linear and quadratic graphs.

Calculate the gradient of a linear function between two points.Recall transformations of trigonometric functions.

Write statements of direct proportion and forming an equation to find values.Recognise a graph showing direct proportion.Recall and use the formula speed = distance ÷ time.

19.1 Direct proportion Recognise direct proportion R7 R10 R13 R14 9th 10th Write and use equations to solve problems involving direct proportion.

Write equations for quantities in direct proportion.

19.2 More direct proportion Use direct proportion. R13 10th 10th Write and use equations to solve problems involving direct proportion.

Find the constant of proportionality. Solve problems involving square and cubic proportionality.19.3 Inverse proportion Using inverse proportion to solve simple problems. A12 A14 R10 R13 10th 11th Write and use equations to solve problems involving inverse

proportion.Write equations for quantities in direct proportion. Use and recognise graphs showing inverse proportion.

19.4 Exponential functions Evaluate indices A12 A14 R16 7th 11th Recognise graphs of exponential functions.Sketch graphs of exponential functions.

19.5 Non-linear graphs Work out the area of a trapezium A15 R14 R15 9th 12th Calculate the gradient of a tangent at a point. Recall and use the formula speed = distance ÷ time. Estimate the area under a non-linear graph.

Find the gradient of a line between two given points.

19.6 Translating graphs of functions Translating coordinates A7 A13 11th 12th Understand the relationship between translating a graph and the change in its function notation.

Function notation19.7 Reflecting and stretching graphs of functions

Transformation of functions A13 10th 12th Understand the effect stretching a curve parallel to one of the axes has on its function form.Understand the effect reflecting a curve in one of the axes has on its function form.

END OF TERM 4 TEST

Date post:	24-Apr-2020
Category:	Documents
Upload:	others
View:	12 times
Download:	0 times

REFERENCE STATEMENT FROM EDEXCEL ......REFERENCE STATEMENT FROM EDEXCEL SPECIFICATION FOR GCSE (9-1)...

Documents