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Year 3 Block B - Securing number facts, understanding shape Unit 2

Objectives Children's learning outcomes are emphasised	Assessment for learning
Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations I can explain how I solve problems	Look at this problem. I buy two comics that cost 30p each. How much change will I get from £1? Wayne starts to solve the problem by working out 30 × 2 = 60. What does this answer tell us? What does he need to do next? Eggs are bought in boxes of six. How many boxes do I need to buy if I want 18 eggs? How would you work out this problem? What are the answers to 8 × 4, 8 ÷ 4? Make up a problem to match each calculation.
Represent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and present it in context, where appropriate using £.p notation or units of measure I can draw pictures and make notes to help me solve a problem	Tell me how you solved this problem. Did you make any notes or drawings to help you? Can you describe them to me? Work out 47 + 29. Show me how you worked it out on a number line. How many wheels are there on seven cars? What did you write down/draw to help you work this out? Think of a problem that this picture could represent.
Identify patterns and relationships involving numbers or shapes, and use these to solve problems I can describe and continue patterns	What fact can help you to work out 60 + 61? 14 + 3 = 17, 14 + 13 = 27, 14 + = 37 . What is the missing number? How do you know? Mark multiplies 7 by 4 to get 28. What operation will now turn 28 into 7? Shade more squares so that this rectangle has one line of symmetry.
Read and write proper fractions (e.g.³/₇,⁹/₁₀), 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 I can find ¹/₂ and ¹/₄ of different shapes	Complete the shading on this diagram so that one half of the shape is shaded. Take 20 cubes. Make a shape which is ¹/₂ red and ¹/₄ blue. What fraction of the shape is not red or blue? Is this shape divided into quarters? Explain how you know.
Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100 I know and use addition and subtraction facts for all numbers to 20 I can add and subtract multiples of 10 in my head	What is 3 + 7? Give me two other pairs that total 10. What is 30 + 70? Give me other pairs that total 100. What is 40 + 50? What is 70 – 40? Here are four multiples of 10: 50, 80, 30, 60. Pick one, now add this one, now subtract this one. What must I add to the answer to make 100? What would I subtract to make 30?
Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000 I know the 2, 3, 4, 5, 6 and 10 times-tables and use them for division facts I recognise multiples of 2, 5 and 10	Count in threes from zero, and back again. Draw jumps of 3 on a number line. How would you use this to find 8 × 3, 18 ÷ 3? What multiplication fact can you use to work out 30 ÷ 6? What is 4 × 3? What is 8 × 3? What is the relationship between these? Use the digits 4, 0 and 5 to make a number that is a multiple of 2. Now make a multiple of 5. Now make a multiple of 10.
Relate 2-D shapes and 3-D solids to drawings of them; describe, visualise, classify, draw and make the shapes I can name and describe shapes I can sort shapes into sets, saying what is the same about each of the shapes I can recognise whether a 2-D shape is symmetrical or not and describe how I know	Which of these drawings shows a sphere? A pyramid? A cube? How did you recognise these shapes? To draw a picture of a cube, would you use straight or curved lines? What about a cylinder? Select from this set a shape that has: no right angles; all sides equal; five vertices. One of the shapes does not belong in this set. Find the odd one out. Explain how you found it.
Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side I can draw a symmetrical shape I can reflect a shape when the mirror line is one of its sides	Which of the shapes on this page are symmetrical? How could you check? Reflect this semicircle in the mirror line. What shape does this make?
Sustain conversation, explaining or giving reasons for their views or choices I can discuss how I solved a problem with other children and explain why I chose my method	Did everyone on this table use the same method? Which method would you choose now if you had to do a similar problem? Ask Mark to explain how he solved this problem. What did you do differently?

Learning overview

Children choose and use the appropriate operations to solve problems and puzzles involving all four operations. They use their knowledge of number facts and place value to add and subtract a pair of numbers mentally or using pencil-and-paper jottings. They solve problems such as:

Three monkeys ate a total of 25 nuts. Each of them ate a different odd number of nuts. How many nuts did each of the monkeys eat? Find as many different ways to do it as you can.

Children discuss how they found their solutions, explaining their choice of method.

Children recall number facts quickly and apply them accurately in a range of situations. They recognise and generate patterns of similar calculations, such as 14 + 3 = 17, 14 + 13 = 27, 14 + 23 = 37 and articulate what is the same and what is different about such related calculations. They use the patterns in such sequences to add and subtract one- and two-digit numbers; for example, they use the fact that 9 – 7 = 2 to work out that 19 – 7 = 12 or 89 – 7 = 82.

Children use number facts and place value to add or subtract a multiple of 10 to or from a two-digit number. They extend this to add or subtract a near-multiple of 10 . For example, they calculate 47 + 29 by calculating 47 + 30 then subtracting 1 from the answer. They may do the calculation entirely mentally, make notes of the steps taken or record them on a number line. Children use their recall of doubles to calculate near-doubles such as 60 + 61, asking: What do I know that will help me to work out 60 + 61?

Children know by heart the 2, 5 and 10 times-table facts and learn the 3, 4 and 6 times-tables . They understand that multiplication can be done in any order. Children appreciate that multiplication and division are inverse operations and use this to derive quickly the associated division facts for any given multiplication fact, and vice versa. They apply their knowledge of multiplication and division to solve missing-number problems, such as square ÷ 3 = 6, and word problems such as:

Eggs are bought in boxes of six. How many boxes do I need to buy if I want 18 eggs?
How many wheels are there on seven cars?

They show their understanding by creating multiplication and division problems of their own.

Children find halves and quarters of shapes by folding. They appreciate that finding ¹/₂ of a shape involves dividing it into two equal pieces and finding ¹/₄ of a shape involves dividing it into four equal pieces. Through practical experience, they appreciate that ²/₄ is equivalent to ¹/₂. They investigate which shapes can easily be divided into halves or quarters and which cannot. They find alternative ways of dividing squares and rectangles in half and into quarters.

Children develop their understanding of line symmetry . They identify examples in the environment of shapes with and without symmetry, describing similarities and differences between them. They identify lines of symmetry of assorted shapes and pictures and check them using a mirror or by folding. They complete partly drawn shapes and patterns to make them symmetrical about a given line. They recognise when shapes have no line of symmetry and create their own shapes with no line of symmetry.

Children apply their understanding of symmetry. They investigate the symmetry of common 2-D shapes such as squares, rectangles, semicircles and triangles. They solve puzzles involving symmetry, such as:
Combine these three shapes to make a shape with at least one line of symmetry. Describe the shape you have made. How many different shapes can you make?

A 4 square L shape, 2 square rectangle and 1 square

Children make models, patterns and shapes with increasing accuracy. They describe the features of shapes and patterns with increasing precision, using vocabulary such as "right-angled", "vertices"and "prism". They are able to build an unseen shape described to them by an adult or child. They match familiar 3-D shapes to pictures of them and build 3-D shapes from pictures, describing the key features that help them to do this.

Resource links to existing published material

Mathematical challenges for able pupils in Key Stages 1 and 2

Activities	PDF 923KB
Activity 32 - Card tricks
Activity 33 - Neighbours

Intervention programmes

Objectives for Springboard intervention unit	Springboard unit
Know by heart all addition and subtraction facts for 10 and 20 Understand that subtraction is the inverse of addition Know that addition can be done in any order Know all pairs of multiples of 10 with a total of 100	Springboard 3 Unit 2 lessons 1 and 2 (PDF 163KB)

Supporting children with gaps in their mathematical understanding (Wave 3)

Diagnostic focus	Resource
Has difficulty in remembering number pairs totalling between ten and twenty, resulting in calculation errors	2 Y2/- DfES 1123-2005 (PDF 75KB)
Is insecure in making links between addition and subtraction and/or recognising inverses	5 Y2/- DfES 1126-2005 (PDF 71KB)
Still counts in ones to find how many there are in a collection of equal groups; does not understand vocabulary, for example, 'groups of', ',multiplied by'	1 Y2×/÷ DfES 1143-2005 (PDF 73KB)
Does not link counting up in equal steps to the operation of multiplication; does not use the vocabulary associated with multiplication	2 Y2×/÷ DfES 1144-2005 (PDF 71KB)

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