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Calculation Methods used in Mile Post 3 (Years 5 and 6)

Calculation Methods used in Mile Post 3 (Years 5 and 6)

Learning Why to explain the How

These methods are in line with the standard expectations of the National Curriculum Mathematics Framework of England and Wales for this age group. They are progressive and build on the methods learned in Mile Post 2. The aim of this progression is that students fully understand the concept of number, the properties of numbers and the relationships between numbers. An understanding of multiple calculation methods can assist children to independently choose suitable strategies to solve problems and apply in real life situations. The methods listed below are sequential and assist with mental arithmetic as well as written calculations. What are Levels?There is wide range of levels of mathematical understanding throughout Mile Post 3. Students will work sequentially through the National Curriculum Levels (or stages) at their own rate. The number of the levels do not relate to Year Groups number. Please see the Assessment section at the back of this booklet which explains the report grade system and how it relates to the Levels below. Please see your childs teacher if you would like more details about the level at which your child is working. Please also note that while your child is working at a particular level in Mathematics, their competency in different areas of the subject may vary. A solid foundation of Mathematics in the primary years will help your child understand more complex processes and problems in their secondary education.ADDITION

Year 5 and Year 6Examples

Level 2, Level 3, Level 4, Level 5 and Level 6

AdditionLevel 2Using empty number linesSteps in addition can be recorded on a number line. The steps often bridge through a multiple of10.

8+7=15

48+36=84

or:

Partitioning

Add the tens and then the ones to form partial sums and then add these partial sums.

Partitioning both numbers into tens and ones mirrors the column method where ones are placed under ones and tens under tens. This also links to mental methods.Record steps in addition using partitioning:

47+76=47+70+6=117+6=123

47+76=40+70+7+6=110+13=123

Jun Seo has 14 counters and Rui has 18 counters. How many counters do they have altogether?

65 people visit Linhs Art Gallery on Saturday and 58 people come on Sunday. What is the total number of visitors to Linhs shop during the weekend?

A box holds 120 pieces of fruit.

Will 37 mangoes and 84 dragon fruits fit into the box?

Explain your answer.

A strip of paper is 35 cm long. Another 86 cm is stuck on to it. How long is the strip of paper now?

ADDITION

Year 5 and Year 6Examples

Level 2, Level 3, Level 4, level 5 and Level 6

Addition

Level 3 Informal expanded column addition

Partitioned numbers are then written under one another:

4 6 8 = 400 + 60 + 8

+ 2 8 6 = 200 + 80 + 6

600 + 140 + 12 = 752

68 boys and 76 girls enter a competition. What is the total number of competitors?

365 people visited the Museum in the morning. 258 more visitors came in the afternoon, How many people visited the museum during the day?

Level 4 and Level 5Compact column additionIn this method, recording is reduced further. Carry digits are recorded below the line (or above the top digit), using the words carry ten or carry one hundred, not carry one.

Later, extend to adding three two-digit numbers, two three-digit numbers and numbers with different numbers of digits.

Column addition remains efficient when used with larger whole numbers and decimals. Once learned, the method is quick and reliable.

In a cricket match, Lan scores 76 runs in the morning and another 78 runs in the afternoon. What is his final score?

Level 5 and Level 6Compact column addition with decimals

1 9 . 5 6

+ 2 4 . 7 3

4 4 .2 9

1 1

Karl buys a CD costing $18.95 and a book priced $16.65. How much will both items cost?

Examples of Quick Mental Strategies Encouraged in Mile Post 3

34 + 19 = (34 + 20 ) 1 = 53

354 + 95 = (354 + 100) 5 = 449

76 + 13 + 45 = (70 + 10 + 40) + (6 + 3 + 5) = 120 + 14 = 134

Make mental arithmetic practicalPlease add up all the house points earned in your class this week.

We need to take this cake out of the oven in 35 minutes time. At what time should we remove the cake?

SUBTRACTION

Year 5 and Year 6Examples

Subtraction

Level 2, Level 3, Level 4, level 5 and Level 6

Level 2 Partitioning on a number line

The empty number line helps to record or explain the steps in mental subtraction. A calculation like 7427 can be recorded by counting back 27 from 74 to reach 47. The empty number line is also a useful way of modelling processes such as bridging through a multiple of ten.

The steps can also be recorded by counting up from the smaller to the larger number to find the difference, for example by counting up from 27 to 74 in steps totalling 47.

Steps in subtraction can be recorded on a number line. The steps often bridge through a multiple of 10. 157=8

7427=47 worked by counting back:

The steps may be recorded in a different order:

or combined:

What is 8 less than 26?

Hanoi gains 35 house points this week. Last week Hanoi achieved 67 house points. How many more house points did Hanoi score last week?

There are 64 biscuits in the box. 19 of them are broken. How many are unbroken?

Decrease 72 by 48.

Level 3 Counting on using a number line and vertical columns

The method can be used with decimals where no more than three columns are required. However, it becomes less efficient when more than three columns are needed. Eg. 22.4 17.8 =

or:

You have 22.3 metres of string. Your friend cuts of 18.6 metres, how much will you have left?

In Ho Chi Minh the temperature is 33.5 C. In London the temperature is 22.8 C. What is the difference in temperature between these two cities?

A pencil is 12.3 cm long. A month later it length is 5.9 cm. How much pencil have I used?

SUBTRACTION

Year 5 and Year 6Examples

Level 2, Level 3, Level 4, level 5 and Level 6

SubtractionLevel 4 and Level 5Expanded column method leading to decomposition

Example: 563 241, no adjustment or decomposition needed

Expanded methodleading to

Start by subtracting the ones, then the tens, then the hundreds. Refer to subtracting the tens, for example, by saying sixty take away forty, not six take away four.Peter has 648 stamps. He gives 354 to his brother. How many stamps will Peter have left?

Level 5 and Level 6Expanded column method leading to decompositionExample: 563 278, adjustment from the hundreds to the tens and the tens to the ones

Here both the tens and the ones digits to be subtracted are bigger than both the tens and the ones digits from which you are subtracting.

Vertical subtraction Vertical Subtraction with decimals

3 11 14 7 11Example : 4 2 4 8 . 1 5

- 2 5 5 - 5 . 4 1 1 6 9 2 . 7 4

259km

A B C

The total journey from A to C is 863 km.

How far is it from B to C?

Examples of Quick Mental Strategies encouraged in Mile Post 3

63 19 = (63 20) + 1 = 44360 90 - (360 100) + 10 = 270

574 290 = (574 300) + 10 = 284When subtracting time, take away time in chunks.10 minutes + 3 hours + 15 minutes

2.50pm 3.00pm 5/00pm 5.15pm = 3 hours 25 minutes

There are 106 students in the year group. 19 students are absent, how many are present?What change will I receive from 100,000 VND when I spend 35,000 VND?The time is now 2.50 pm.? Our flight departs at 5.15pm. How much time do we have before we take off?

MULTIPLICATION

Year 5 and Year 6Examples

Level 2, Level 3, Level 4, level 5 and Level 6

Level 3Use practical, visual, arrays7 x 3 = ( 5 x 3) + (2 x 3)

Partitioning

Partition the numbers into multiplication tables with which the child is familiar

6 x 7 = (3 x 7) + (3 x 7) = 21 + 21 = 42

9 x 3 = (4 x 3) + (5 x 3) = 12 + 15 = 276 children have 5 books each. How many do they have altogether?

How many legs on 8 spiders?

Which is greater, 7 groups of 5 or 9 groups of4? Explain your answer.

Multiplication

Level 3 and Level 4Expanded short multiplication

Compact short multiplication

There are 26 CDs on each shelf. How many CDs are there on 8 full shelves?

There are 15 volleyball teams enter a competition. There are 6 players in each team and a reserve player. How many people are in the competition including the reserve players?

Level 4 and Level 5The grid method

This is based on the distributive law and links directly to the mental method. It is an alternative way of recording the same steps.

It is better to place the number with the most digits in the left-hand column of the grid so that it is easier to add the partial products. Children who are left handed may find it easier to add the figures vertically.

Children need to be competent at multiplying by multiples of 10, 100, 1000.

Practice at this skill is very valuable.Each bus carries 46 passengers. How many people can travel on 21 buses?

A hotel in Hong Kong has 32 floors. There are 29 rooms on each floor. How many rooms are there in the hotel?

A bus travels 262 km each week. How far will it travel in a year?

MULTIPLICATION

Year 5 and Year 6Examples

MultiplicationLevel 2, Level 3, Level 4, level 5 and Level 6

Level 5 and Level 6Compact short multiplication

Expanded long multiplication

Compact long multiplication

What is the product of 7 and 38?

The entrance fee to Disney World is $38.00 per person.

What is the total cost for a group of 27 people?

What is the area of this rectangle?

47 m

134 m

Examples of Mental StrategiesExamples of Quick Mental Strategies Encouraged in Mile Post 3

When multiplying by 10 o 100 or 1000, students are taught to move the digits up the required number of decimal place value columns. Please do not encourage children to add zeros or to move the decimal point. The place values remain constant and the digits move.

34 x 10 = 340 Th H T U

3 4

3 4 0

Use Partitioning

62 x 40 = (62 x 4) x 10 = 248 x 10 = 2480

4.5 x 10 = 45

3.7 x 30 = (3 x 30) + (0.7 x 30)

= 90 + 21

= 111

or:

3.7 x 30 = (3.7 x 3 x 10) = 11.1 x 10 = 11124 x 50 = (24 x 100) 2 = 2400 2 = 1200

32 x 25 = (32 x 100) 4 = 3200 4 = 800

14 x 19 = (14 x 20) 14 = (14 x 2 x 10) 14 = 280 14 = 266

Halving and Doubling

18 x 27 = (9 x 27) x 2 = 243 x 2 = 486

28 x 5 = (14 x 5) x 2 = 70 x 2 = 140How many centimetres in 14 metres?

Write 36 kg in grams.

Which is further 6.5km or 700 metres?

It is my 10th birthday today. How many days have I lived?Entrance tickets to a Water Park cost $6.75 each? What is the total cost for 10 people?

What is the cost for 20 people?Change 9.8 metres into centimetres.

I have twenty six $20 dollar bills. How much money do I have?

DIVISION

Year 5 and Year 6Examples

Level 2, Level 3, Level 4, level 5 and Level 6

Practical, visual

Make links between division and multiplication (times tables). Children will develop their understanding of division and use jottings to support calculations. Give division problems in context. Ensure children are exposed to both ideas of division as grouping as well as sharing

Sharing equally

6 sweets shared between 2 people, how many do they each get?

Grouping or repeated subtraction

There are 6 sweets, how many people can have 2 sweets each?

Repeated subtraction using a numbered line or bead bar

There are 12 sweets, how many people can have 3 sweets each? - 3 - 3 - 3 - 3

4 3 2 1Begin to introduce simple remainders. If I have 13 sweets and I share them between 2 of my friends will I have any left over for myself?

There are 5 pencils in each box. How many boxes are needed for 30 pencils?

$32 is shared evenly between 4 people. How much will each person receive?

Which is greater 28 7 or

30 6? Explain your answer.

Level 3Division as repeated subtraction on a number line

Ensure that the emphasis in Y3 is on grouping rather than sharing. Children will continue to use:

Repeated subtraction using a number line

There are 24 sweets, how many people can have 4 sweets each?

24 4 = 6 -4 - 4 - 4 - 4 - 4 -4

6 5 4 3 2 1 0 4 8 12 16 20 24

There are 13 sweets, how many people can have 4 sweets each?

13 4 = 3 r 1 - 4 - 4 - 4

3 2 1

0 1 5 9 13 Remainder can be written as 3 r 1 or 3 rem, 1 or 3 1 It should not be written 3.1 or 3..1Each pencil pot holds 4 pencils.

How many pots will you need to hold 53 pencils?Zack makes 52 cakes. Each baking tray holds 6 cakes. How many baking trays will be full? How many cakes will go in the incomplete baking tray?

DIVISION

Year 5 and Year 6Examples

Level 2, Level 3, Level 4, level 5 and Level 6

Level 4Division by chunking vertically

Start the division by first subtracting 180, leaving 16, and then subtracting the largest possible multiple of 6, which is 12, leaving 4.

The quotient 32 (with a remainder of 4) lies between 30 and 40, as predicted.I have 197 sweets. I share them between 9 friends each.

How many will each friend receive?

How many sweets left over?

What shall I do with the remaining sweets?

Level 5Any remainders can be shown as fractions, i.e. if the children were dividing 34 by 8, the answer should be shown as 4 2/8, = 4

This method will be extended to decimals with up to two decimal places. Children should know that decimal points line up under each other and the digits represent the place value they are in.

In 39 556 the 9 represents nine thousand.87.5 7

12.5

7 ) 87.5

- 70.0 10x

17.5

- 14.0 2x

3.5

- 3.5 0.5x

0

Answer : 12.5

There are 8 runners in a relay team. They each run the same distance. The total race is 280 km. What distance will each runner complete?

Each box holds 8 books. How many boxes will we need to box up 384 books?

What is the length of one side of a regular octagon if its perimeter is 158 cm?

Level 5 and 6For 2913, because 390=270 and 3100=300, we use 270 and split the dividend of 291 into 270+21. Each part is then divided by 3.

The short division method is recorded like this:

This is then shortened to:

The carry digit 2 represents the 2 tens remaining that have been exchanged for 20 ones. This remainder is added to the next digit.Find two consecutive numbers whose product is equal to 552.

456 = 8

n

A minibus holds 9 people. A coach can seat 40 people. 210 need to be taken to the theatre. What transport would you arrange?

DivisionLevel 5 and 6Division at Level 5 and 6 continues

Children should know the different expressions for division

56 7 or 756 or 56 7

Children should be able to give remainders as a decimal, as a fraction and as a remaining number. They should be able to work out from the question which is the most appropriate form to give the remainder.

Division by a two digit numberMethod 1: 4 8 6 2 323 4 8 6

- 2 3 0 - 1 0 groups 2 5 6 - 2 3 0 - 10 groups

2 6 - 2 3 - 1 group

3Answer: 21 groups and 3 left over

The number is treated as a whole and groups of 10 or 100 etc are subtracted and recorded on the right hand side. This method can be speeded up when the child recognises multiples of 10, 100 etc. Can be subtracted.Method 2Example ...... 7 4 6 3 4 = 1 4 . 53 4 4 9 3 . 0 - 3 4 1 5 3

- 1 3 6 1 7 0 - 1 7 0 Answer = 1 4 . 5 0 0 0 Children should be reminded to keep the digits in the correct place value columns. Good estimation skills are necessary for this method.

This method may be easier to use when dealing with decimals. Is 432 divisible by 8?

There are five 2 litre bottles of orange juice at the party, There are 19 people present. How much orange juice is each entitled to if it is distributed evenly?

Special offer!

12 books for $246.00

One book normally costs $22.00

If you buy 12 books, how much do you save with the special offer?KnowledgeChildren should know the quick divisibility tests for 10, 5, 9, 6 and 3,

Example of Mental Division

We have 5 litres of lemonade.

Each glass holds 250 ml. How many glasses can we fill?

There are 106 students in the Year 5. Can we form groups of 3 students with no one left out?m x 5 = 9 0

What is the value of m?

How many $20 notes make up $500?

Vocabulary Associated with the Four Calculations+

addition

plus

in addition to

total

sum of

increase by

more than

greater thangain

larger thansubtract

take away

minus

decrease by

less than

fewer than

reducewhat is missing

a loss ofsmaller than

x

multiply bytimes greater than

product of

groups ofmultiple of

lots of double (x2) triple (x3)

quadruple (x4)divide

share betweentimes smaller than

quotient factor of

mid-point of . ( 2)

divisible bysplit evenly

Ways to help your child with Calculation Methods

What is Numeracy?Organisation of Mathematics LearningMathematics Lesson Time

5 x one hour lessons per weekWeekly homework will be set.Lesson Content

Our Mathematics Curriculum content is based on the English National Curriculum Primary Framework. Students will re-visit topics in Mathematics two or three times during the year. Each time prior knowledge and skills will be revisited, and then understanding and application ability will be extended.

Each term lessons will cover the following strands of Mathematics:

Number

Shape and space

Measure

Pattern of number and the relationship numbers have with each other

Handling data

During each unit students will participate in activities aimed to develop:-

mental arithmetic strategies to help promote speed, agility and understanding

understanding and use of new concepts

reinforcement of previous ideas

understanding and use of mathematical vocabulary

knowledge and application of mathematical facts

problem solving activities

apply Mathematics to real-life practical tasks.

During Mathematics lessons children will learn to work independently, in pairs, in small groups and as part of the whole class. Participating fully in group tasks through exploring and developing ideas is an important part of learning as is gaining the confidence to make mathematical decisions independently.Children will use their Mathematics skills with in other subject areas such as IPC, Science, Music and PE.

HomeworkThe aim of Mathematics homework is to reinforce, consolidate and apply concepts learnt in class. Homework tasks may consist of problem solving tasks, practical activities, reinforcement questions, mental agility exercises. Students will sometimes complete these tasks on-line on websites such as My Maths, sometimes home learning will be of a practical nature and sometimes guidance will be given on a worksheet. Homework may also be posted on Studywiz. Children are expected to record their homework tasks in their Homework Diary. Children can be helped at home by providing a quiet comfortable place to work and adequate time allowed for homework to be completed. Mile Post 3 students will need a ruler, a basic calculator, a protractor and access to a computer at home.

Mathematics Sets

Year 5 and 6 students work in Mathematics Sets. The sets are known as Core Group, Extension Group and Support Group. These groups may be differentiated further depending upon need. In some Year Groups there may be five Mathematics Sets all working at different levels.Students are placed in sets which the teachers consider will best suit every childs learning needs to maximise progress. These decisions are based on the teachers assessment of class work contributions; formal assessment tests and the students ability to independently apply their knowledge in problem solving situations. In addition, the speed at which a child grasps new concepts, the amount of reinforcement needed to retain their understanding, their confidence in using knowledge and their preferred learning style is also considered when placing children in Mathematics sets.Maths Sets are always flexible and are reviewed regularly. Students will move groups at any point during the year when it is considered that the learning needs of a child will be best served in another Set. In this instance the situation will be discussed with the student and parents will be informed of the childs new Maths teacher. The aim is to give each child a solid foundation on which future learning can be understood.Some Mathematical Vocabulary learnt during Mile Post 3

NumberAlgebra and PatternShape and SpaceMeasureData handlingUsing and Applying

Estimate

Approximate

CalculateOperation

Consecutive

Ascending

Descending

Decimal place

Decimal fraction

Vulgar fractionDenominator

Numerator

Improper fraction

Mixed number

Digit

Integer

Positive

Negative

Square number

Square root

Cubic number

Prime number

Partition

Chunking

Place value

Factor

Multiple

Ratio

Proportion

Formula

equation

Pattern

Sequence

Relationship

RuleGeneralisation

Greater than

Less thanSymbol

Inverse

Brackets

Origin

Function

3 dimensionsFaces

Vertex/Vertices

Edges

Volume

Nets

Polygon

2 dimensionsRegular/Irregular

Width / Breadth

Length

Height

Perimeter

Area

Surface Area

Translate

Rotate

Reflect

Line of symmetry

Coordinates

Axis/axes

Mid-point

Intersection

Circumference

Diameter

Radius

Parallel Perpendicular

Opposite

Adjacent

CongruentMetric measurements

Imperial measurements

Degrees Celsius

Degrees

Acute angle

Obtuse angle

Reflex angle

Protractor

Speed

Accelerate

Decelerate

Scale

Analog clock

Digital clock

Weight

Mass

Column

Row

Vertical

Horizontal

Key

Constant

Trend

Bar chart

Line graph

Pie chart

Pictogram

Compound graph

Conversion graph

Frequency graph

Axis

Axes

Represent

interval

Probability

Likely

Conversion

Mode

Median

Mean average

Range

Minimum

Maximum

Carroll diagram

Venn diagram

ReasonHypothesisPredictCompare

Classify

Generalize

Criteria

Solution

Survey

Questionnaire

Analyse

Interpret

Strategy

Process

A more extensive Year Group vocabulary list is available on Studywiz. A good on-line Maths dictionary is at: http://www.amathsdictionaryforkids.com/Mile Post 3 Areas of Study in MathematicsBelow is a list of the general areas of Mathematics that will be explored by the end of the Mile Post. These topics may not be learnt in the order listed and each area of study will be re-visited during the year. These objectives are in line with the English National Curriculum Mathematics Framework for the Core Group in each Year Group. Work is differentiated between in classes to accommodate different current abilities. Number

Place Value Round, approximating and estimating

Decimal place value Equivalent Fractions

Improper fractions and mixed numbers Convert fractions, decimals and percentages

Order fractions, decimals and percentages by size Fractional parts of a quantity

Percentages Proportion and Ratio

Mental and written addition and subtraction methods

Mental and written multiplication and division methods Addition and subtraction decimal fractions

Multiplication and division of whole numbers by decimal fractions Two and three stage word problems

Use calculators to help solve word problems

Negative numbers

Properties of numbers (factors, multiples, square numbers, square roots, triangular number, prime numbers, even, odd, digital roots)Number Pattern and Algebra

Recognising patterns and sequences Using sequences to find unknowns

Solving simple equations Verbal explanation of equation or number sequence.

Use generalisations to explain a rule

Measures

Length

Weight Capacity

Money

Temperature

Use suitable equipment to measure length, weight, capacity and temperature.

Read scales

Draw, measure and calculate angles

Read time on digital and analogue clocks and understand timetables Awareness of imperial measurements

Use scales on maps

Speed

Shape and Space Area of composite rectangles and triangles

Perimeter of shapes

Volume of cuboids and cubes Use co-ordinates in 4 quadrants to give location Reflection of shapes Rotation of shapes Translation of shapes Names and properties of 2 dimensional shapes

Names and properties of 3 dimensional shapes

Recognize and design nets of 3 dimensional shapes

Use a compass to draw a circle and name the parts. (radius, circumference, arc, diameter, segment)Data Handling

Draw and interpret bar charts, line graphs, pie charts, compound graphs, frequency charts and conversion graphs

Identify trends in graphs and suggest reasons for inflation/deflation Find the average (mode, median, mean) and range of sets of data

Interpret timetables

Probability Design a survey or questionnaire to find required information

Using and Applying Breakdown complex problems into stages.

Solve two and three stage written problems with and without a calculator. Choose suitable strategies to solve problems Knowledge and ability to use of mathematical vocabulary in explanations. Use mathematical skills in real life practical situations.

Analyse statistical information

Use technology to generate graphs and charts Formulate questions that will promote a mathematical investigation Develop lines of inquiry when conducting an investigation.

Justify reasoning

Suggest and test hypothesis

Work backwards through a problem Use estimation to check solutions Recognise connections, patterns and generate generalisations Explain relevance of solutions

AssessmentAssessment data is used to decide on the next steps for learning, set targets and monitor progress.

Student progress is continually assessed and is based on: - Contributions to small group and class discussions

Contributions to practical work

Written class work

Homework assignments

End of Unit written assessments

Problem solving exercises

Investigations

Standardised Assessment Tests (SATs) and Goal On-line (completed on the computer)

Student achievement is recorded as National Curriculum Level or on the childs report as an A, B or C grade.Report Grades and Teacher Assessment Level CorrelationThis chart shows the expected National Curriculum Levels in Mathematics at the end of each year group and the corresponding the British International Schools Report Grades.English

National curriculum levelsYear 1Year 2Year 3Year 4Year 5Year 6Year 7

6

5aA

5bB

5cAB

4aBB

4bABC

4cABBC

3aBBCC

3bABBD

3cABBCD

2aBBCD

2bABBE

2cBBCE

1aBCE

1bB

1cC

Some practical ways to help your child at homeGames can help children develop their mathematical skills and logical thinking.For example:

Snakes and Ladders involve counting, addition and subtraction. Card games that require quick mental agility. Chess or Checkers to promote spatial awareness and logical thinking.

Yahtzee

Sukuko

Practical Experiences: Counting in 2s, 3s, 4s, 5s, 6s, 10s and 100s Start at a number other than one.

How far can you reach in I minute? Number bonds to 50 (e.g. 18 + ? = 50) Doubles and halves of numbers to 100 (eg Double 27. Half of 84)

Addition and subtraction facts to 50 (Also in worded questions such as: There were 19 sweets, I ate 15 how many are there left?) Children to working at Level 2 and 3 should practice number bonds to equal 20(eg 13 + ? = 20) and find doubles and halves of number to 20

(half of 18, double 16) Recall of multiplication to 10 x 10 as associated division facts.

Match pairs of equivalent number/fraction/decimal cards. Throw 3 dice and add up numbers as quickly as possible. Talk about fractions when cutting up pizzas or a cake. Involve children in shopping - estimating bills, calculating change. Involve children in measuring at home. Eg length for new curtains. Will this chair fit in that space? Involve your child in measuring when cooking or changing recipe quantities. Ask questions such as: What time will it be in . ? How long is it until .

Can children tell the time? Link to TV programmes and programming the video/DVD. Estimating a length of time? Using time zones - What time is it in New York? Ask your child how they worked out a problem to help them explain clearly and systematically. Play shape bingo. At home or on a journey, how many circles, squares, etc. can they spot? Give them different point values. When cooking encourage to children estimate different measures? What does 10 grams/10 ml/1 kilogram looks/feels like? Involve your child in converting currencies when on holiday. Look at the speedometer when travelling in a car

Involve your child in map reading when travelling.

Ensure your child knows the mathematical vocabulary learnt and used in school in their mother tongue. This is particularly important if your child is likely to continue their education in their home country/language in the future.Other ways to help with homework exercises Encourage your child to use a number line to help understand and complete calculations.

Use beads, counters or beans to represent numbers. eg sharing out beans when dividing.

Use a multiplication square for multiplication and division facts.

Struggling with a written problem?

Ask your child to draw their interpretation of the problem or use real objects so they are able to see the situation visually.

Help your child to break the problem down into steps.

Replace the numbers with simpler alternatives to help your child gain confidence and understand the process, then try again with the given numbers.

Encourage estimation.

Use multiplication squares and calculators to help with the arithmetic calculations so that your child has a clearer understanding of the processes involved in the problem. Work on the calculations separately.

Useful websites to help develop mathematical skills and understanding

20.05.11

SK + - x + - x + - x + - x

+ - x + - + - x + - x

+ - + - x + - x

+ - x

Games to speed up agility of mental arithmetic operations

How many multiplication tables can you say in one minute?

Use flash cards of multiplication table questions, 6 x 3, 7 x 4 etc. How many can you answer in a minute?

Match up pairs of cards with equivalent answers eg 3 x 6 and 2 x 9 will be a pair.

Bingo using numbers that are the answers to multiplication tables questions.

Websites eg Tutpup Mental Arithmetic games against other children around the world. HYPERLINK "http://www.tutpup.com/" http://www.tutpup.com/

Practise multiplying and dividing numbers by 10, 100, 1000.

Practise multiplying and dividing by multiples of 10, 100, 1000.

Using practical everyday situations speed up agility of mental arithmetic operations

What will the bill come to?

How much change should we receive?

How many minutes until lunch time?

Share these sweets out equally between all the whole family.

We are travelling at 60 km per hour. How far are we likely to go in the next 15 minutes? How long will it take us to go 200 km?

Planning a party or a meal? Involve your child in working out quantities of food required.

Involve children in cooking, weighing ingredients, measuring, using scale and direction when reading maps.

A = above expected level of achievement

B = at expected level of achievement

C = below expected level of achievement

(The exact expected level at the end of each year group is indicated by shaded area or a thick black line.)

The blue section represents 24 students. Estimate the number represented by the yellow portion of this pie graph.

Reference

More detailed information regarding the curriculum content and vocabulary for each level can be found on Studywiz.

Full details of information relating to the National Curriculum of England

Primary Mathematics Framework for planning the teaching and learning of Mathematics can be found at:

HYPERLINK "http://nationalstrategies.standards.dcsf.gov.uk/primary/primaryframework/mathematics" http://nationalstrategies.standards.dcsf.gov.uk/primary/primaryframework/mathematics

Maths dictionary:

HYPERLINK "http://www.amathsdictionaryforkids.com/" http://www.amathsdictionaryforkids.com/

Practising skills:

HYPERLINK "http://www.bbc.co.uk/schools/ks2bitesize/maths/" http://www.bbc.co.uk/schools/ks2bitesize/maths/

HYPERLINK "http://www.woodlands-junior.kent.sch.uk/maths/" http://www.woodlands-junior.kent.sch.uk/maths/

HYPERLINK "http://www.mathplayground.com/games.html" http://www.mathplayground.com/games.html

HYPERLINK "http://www.ixl.com/" http://www.ixl.com/

(click on 4th Grade for Year 5 work and 5th Grade for Year 6 work.

For more advanced concepts try some 6th Grade exercises.)

HYPERLINK "http://www.tutpup.com/" http://www.tutpup.com/

(Play mental arithmetic games against students around the world. This website is free but you will need to join. Ask your teacher for your class code. They will set one up for you. You will need to enter the class code when you join.)

My.Maths use the Library to choose your own exercises or games at your own level. (Ask you teacher for advice about which level you should select.)

Investigations and Problem Solving Activities:

HYPERLINK "http://www.ngfl-cymru.org.uk/vtc-home/vtc-ks2-home/vtc-ks2-maths%282%29/vtc-ks2-maths-investigations.htm" http://www.ngfl-cymru.org.uk/vtc-home/vtc-ks2-home/vtc-ks2-maths%282%29/vtc-ks2-maths-investigations.htm

HYPERLINK "http://www.theproblemsite.com/math_games.asp" http://www.theproblemsite.com/math_games.asp

0 1 2 3 4 5 6 7 8 9 10 11 12

Estimate and try out solutions

3 4 x

4

1 3 6

1

1 1

Answer = 32 rem. 4

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yellow

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