Year 3Number Conceptsand Guided WritingApril 2008

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Objectives

• To build subject knowledge• To help understand progression

within and beyond Year 3• To broaden the repertoire of teaching

approaches• To develop understanding of the

interrelationship between the elements in the cycle of reviewing, planning, teaching and assessing.

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Outline of the day

09:00 Refreshments on arrival09:15 Number Concepts10:30 Refreshments10:45 Number Concepts continued12:30 Lunch13:15 Guided Writing14:30 Refreshments15:15 School based activities15:45 Close

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Number Concepts Outline

• Session 1 - Establishing end-of-year expectations

• Session 2 - Review and progression

• Session 3 - Broadening the teaching and learning

experience

• Session 4 - School-based activity

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School-based activity

• Plan and teach Block E summer term and Block A autumn term. Include elements covered in this CPD.

• Prepare a short presentation for day 2 to feedback on your planning process, teaching and learning. How did the blocks differ?

• Feedback to HT and Maths Subject Leader key points of the CPD.

Year 3Number Concepts

Session 1Establishing end-of-year expectations

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‘Numeracy is a proficiency which involves confidence and competence with numbers and measures. It requires an understanding of the number system, a repertoire of computational skills and an inclination to solve problems in a variety of contexts.’Framework for teaching mathematics, 1999

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Planning cycle

Review (AfL)Prior learning to establish pitch of the work and any children who may need additional support or challenge

Plan

What and how to teach the children the mathematics so they build on their prior learning

Teach / ApplyUse fit-for-purpose approach which gives children time to think, practise, apply their learning

Assess & reviewAssess progress with focus on particular children, engage children in review of learning and next steps

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Number concepts within other strands

• Knowing and using number facts – they use doubles that they know to find other doubles or near doubles

• Calculating – children develop strategies for dealing with special cases e.g. finding 57 – 30, how numbers remain constant, using a number line to indicate steps, work out approximations by rounding numbers

• Measuring – children read scales and measure to the nearest division, they know the relationship between units, they read time to the nearest 5 minutes

• Understanding shape – children draw an angle and estimate its size in relation to a right angle e.g. about 1/3 of a right angle

• Handling data – they organise data using frequency tables, they understand how to interpret

• their tables and charts

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Year 3 Counting and understanding number

• Read, write and order whole numbers to at least 1000 and position them on a number line; count on from and back to zero in single-digit steps or multiples of 10

• Partition three-digit numbers into multiples of 100, 10 and 1 in different ways

• Round two-digit or three-digit numbers to the nearest 10 or 100 and give estimates for their sums and differences

• Read and write proper fractions interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents

Block ACounting,

partitioning and calculating

Block BSecuring number

Facts, understandingshape

Block CHandling

data and measures

Block DCalculating, measuring

and understanding shape

Block ESecuring number facts, calculationand relationships

Using and applying mathematics

Counting and understanding number

Calculating

Using and applying mathematics

Knowing and using number facts

Understanding shape

Using and applying mathematics

Measuring

Handling data

Using and applying mathematics

Using and applying mathematics

Calculating

Measuring

Counting and understanding number

Knowing and using number facts

Calculating

Understanding shape

Block CUnit 3

Block DUnit 3

Block EUnit 3

Block AUnit 3

Block AUnit 2

Block AUnit 1

Block ACounting,

partitioning and

calculating

Block BUnit 3

Block CUnit 2

Block BUnit 2

Block BUnit 1

Block BSecuring numberFacts,

understandingshape

Block EUnit 2

Block EUnit 1

Block ESecuring numberFacts,

calculationAnd

relationships

Block DUnit 2

Block DUnit 1

Block DCalculating,

Measuring andUnderstanding

shape

Block CUnit 1

Block CHandling data and measures

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Draw an empty number line and mark the numbers 456, 465 and 546 on it.

Explain to someone how you did it.

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Discussion

• How did you approach and carry out the task?

• What decisions did you have to make when drawing and labelling the number line?

• Did the number line you drew start at zero? Did it need to?

• What knowledge, skills and understanding did you need?

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500

456 465 546

Year 3Number Concepts

Session 2Review and progression

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Progression from Year 2 to Year 3

• Use the tracking poster to compare the objectives under the Counting and Understanding number strand in Year 2 and Year 3.

• What are the main differences?

What knowledge, skills and understanding would we expect children to have at the start of Year 3?

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Counting and understanding number strand

Year 2 – Year 3:• Partitioning - two-digit numbers in Year 2 and three-

digit in Year 3;• Ordering - order two digit numbers in Year 2 and

numbers up to 1000 in Year 3;• Rounding - round two-digit numbers to the nearest 10

in Year 2 and 2/3 digit numbers to nearest 10/100 in Year 3;

• Fractions - Year 2 has a focus on one half, one quarter and three quarters. This is extended in Year 3 to include a greater understanding of the denominator and numerator and by a focus on comparing fractions and establishes equivalents;

• Inequality – use of the greater than and less than signs is part of a Year 2 objective. It will therefore be important that understanding of these signs continues to develop into Year 3.

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0-9 digit cards

• Make five odd numbers using each card once - 1 three-digit number- 3 two-digit numbers- 1 one-digit number

• One person from each pair needs to explain how to put the numbers in order from smallest to largest. These instructions should be followed exactly.

• As a pair now work together to refine the original instructions ensuring the language used is a precise as possible.

• Finally join another pair and take it in turns to try out your instructions on each other.

.

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Discussion

• How did it help to talk informally in pairs first?• How did your original instructions need

refining? • Did your use of language change as you refined

your instructions?• If you didn’t have access to mathematical

language how would creating the instructions have been harder?

• Would the task have been harder if you couldn’t see each other e.g. if you were giving instructions over the phone?

• How would you need to refine your instructions if you were asked to order even numbers?

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Equality, inequality and equivalence

• Use language such as ‘more’ or ‘less’ to compare two numbers (Foundation Stage)

• Compare and order numbers, using the related vocabulary; use the equals (=) sign (Year 1)

• Order two-digit numbers and position them on a number line; use the greater than (>) and less than (<) signs (Year 2)

• Use diagrams to compare fractions and establish equivalents. (Year 3)

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Key experiences for children

• A clear understanding of the concepts of equality and inequality

• The ability to read and write proper fractions

• Recognising and representing fractions of a variety of shapes

• Knowing how to use diagrams to compare fractions and appreciate their relative size

• Gaining appreciation that fractions can be numbers that label a position on a number line

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Equality

• What is equality?• What is equality in mathematics?• When might children encounter the

mathematical concept of equality in everyday life?

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Fractions of shapes

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Comparing fractions

• Convince me that 1/2 is smaller than 3/5 but larger than 3/10.

• Record two ways of convincing me that 1/2 is smaller than 3/5 but larger than 3/10

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Fractions and number lines

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Year 6

• Karen makes a fraction using two number cards. She says, 'My fraction is equivalent to ½. One of the number cards is 6'What could Karen's fraction be? Give both possible answers.

• What do the fractions 6/9 ,14/21 and 18/27 have in common?

Year 3Number Concepts

Session 3Broadening the teaching and learning experience

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Good mathematics teaching

• Carefully planned blend of approaches• Children are challenged to think• They like to be challenged and enjoy the

opportunities to practice and apply their learning

• They are happy to share their ideas and to explain their reasoning and methods

• Broad repertoire of teaching and organisational approaches

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Good mathematics teaching

‘The teaching sequence incorporates practical, visual and ICT resources that children can use to test and confirm their learning. Children have access to these resources and understand how to use them. There are models and images demonstrated and displayed to support methods, promote thinking and develop strategies and these are used to build links between areas of mathematics.’

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Models and images

• Place value cards• Place value ITP • Partly numbered lines • Bundles of straws • Money• Beadsticks ITP

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ICT models and images

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Teaching approaches

‘Children use partitioning to add or subtract mentally one- and two-digit numbers. For example, they calculate 37+26 by using 37+20+6 and 37-26 by working out 37-20-6, recording the steps on a number line.’