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Year 4 Block B - Securing number facts, understanding shape

Objectives Children's learning outcomes are emphasised	Assessment for learning
Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples I can see number patterns in the answers to the 3 times-table and can explain how the pattern works I can spot a rule about the number of lines of symmetry that regular polygons have	What are the two missing numbers in this sequence? Look at these coins. Which of these amounts can you make using only two coins each time? 61p 52p 20p £1.05 80p
Use knowledge of rounding, number operations and inverses to estimate and check calculations If I add two numbers I can use subtraction to check whether my answer is correct If I divide one number by another I can use multiplication to check whether my answer is correct	I rounded a number to the nearest 10. The answer is 320. What number could I have started with? The local newspaper says that 1200 people watched a local football match. This was given to the nearest 100. What is the smallest number that could have attended? What is the largest number? If the answer to a subtraction is 59 and I subtracted 45, what number did I start with? How do you know?
Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols I can write an explanation of how I solved a problem. I can include number sentences using the +, -, × or ÷ signs where I need to	A shop has these special offers. Joe wants to buy six pencils. Which is the cheaper offer: half price, or 3 packets for the price of 2? Explain how you know.
Identify the doubles of two-digit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halves Because I know that double 7 is 14, I know that double 70 is 140 I can work out doubles of numbers with two digits	I'm thinking of a number. I halve it and get the answer 55. What number was I thinking of? How do you know? Double 13 is 26. What other number facts can you work out from this? Tell me about the connection between halving and doubling. Start with 86 to explain the connection. Ben told me that if you double 16 you get 32. He says that this means that double 160 is 320. Is Ben right? How do you know?
Derive and recall multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple I can tell you answers to the 8 times-table, even when the questions are not in order	How can doubling help you work out multiples of 8? Which are the multiples of 8 in this list of numbers? 18 32 56 68 72
Draw polygons and classify them by identifying their properties, including their line symmetry I can use what I know about triangles to group them into equilateral triangles, isosceles triangles and other triangles I can pick out triangles that have a right angle from other triangles I can recognise symmetrical polygons, including those with more than one line of symmetry	What is the difference between a regular and an irregular polygon? [Use a set of regular and irregular polygons, and criteria written on cards, such as 'is a regular polygon', 'is an irregular polygon', 'has no lines of symmetry', 'has at least one line of symmetry', 'has no right angles', 'has one right angle', etc. Select a card, e.g. 'is an irregular polygon'.] Show me a polygon in this group? How do you know it is in the group? What do you look for? [Select two cards, such as 'is a regular polygon' and 'has at least one line of symmetry'.] Show me a polygon that fits both of these criteria. What do you look for?
Visualise 3-D objects from 2-D drawings; make nets of common solids If I see a drawing of a cube I can imagine the solid shape I can make different nets for cubes and fold them to check they are correct	Name three different 3-D shapes that can have at least one square face. Here is a cereal packet. Describe what you think its net might look like. Anna makes a cube using straws. First she joins four straws to make a square. Then she joins more straws to make a cube. Altogether, how many straws has she used?
Investigate how talk varies with age, familiarity, gender and purpose I can compare the way my teacher describes a shape with the way that my friend describes the same shape	There is a 3-D shape inside this drawstring bag. Feel it and then describe the shape to me. Now I will feel it and describe it to you. What were the main differences between the way that I described the shape and the way that you described the shape?

Learning overview

Children count forwards and backwards in steps of different sizes and rehearse knowledge of multiplication and division facts for the 2, 3, 4, 5, 6 and 10 times-tables. They know that multiplication and division are inverse operations and they use this to derive the associated division facts for any given multiplication fact. They apply their knowledge of multiplication and division facts to solve equations, such as square ÷ 6 = 9, and word problems such as:

There are 8 biscuits in a pack. I want 48 biscuits for a party. How many packs do I need to buy?
I bought 72 biscuits for another party. How many packs of biscuits did I buy?

Children show their understanding by creating similar multiplication and division problems for others to solve.

Children begin to learn the 8 times-table. They know that multiplication can be done in any order and they relate previously learnt multiplication facts to the new facts that they are learning. They investigate how doubling, doubling and doubling again is equivalent to multiplying by 8. Through listing multiples of 2, 4 and 8 they recognise that multiples of 4 are double multiples of 2 and multiples of 8 are double multiples of 4. They respond to questions such as: Can you tell me five numbers that are both multiples of 4 and multiples of 8? They recognise that knowing 4 × 8 = 32 helps them to work out 32 ÷ 8, 8 × 8, 40 × 8, 320 ÷ 8, etc. They identify patterns in multiplication facts. For example, they look at the last digit of multiples of 4 and discover that multiples of 4 end in 0, 2, 4, 6 or 8. They use a calculator to test larger numbers and discover that although a multiple of 4 can end in 8, it does not necessarily mean that all numbers that end in 8 are multiples of 4.

Children relate doubling to both addition and multiplication. They realise that 7 + 7 is equivalent to 7 × 2. They know the doubles of one-digit numbers and learn how to double two-digit numbers, first multiples of 10, then numbers 11 to 20, and then numbers beyond 20. They discuss mental strategies such as 'double the tens, double the ones, and add them together'. Using their knowledge of inverses, they relate halving to dividing by 2. They first halve multiples of 10, then numbers in the twenties, forties, sixties and eighties, and then the remaining two-digit numbers. They record their mental strategies in jottings, as in:

Addition sums showing partitioning and halving: 84 is shown as 80 plus 4 along the top with 40 plus 2 underneath with arrows connecting the halving and the total 42 recorded to the side

Children extend their knowledge of properties of 2-D shapes. They name equilateral, isosceles and right-angled triangles, and identify whether a polygon is concave or convex. They recognise symmetrical polygons, both regular and irregular, and cases where a polygon has no lines of symmetry, or one, two or more lines of symmetry; for example, they try to draw a hexagon with no lines of symmetry, one line of symmetry, two lines of symmetry, etc.

Children apply their understanding of properties of 2-D shapes to solve problems. For example, they investigate a statement such as: 'The number of lines of symmetry in a regular polygon is equal to the number of sides of the polygon' by finding examples that match it.

Children continue to develop the skill of visualising 3-D objects from 2-D drawings. They look at a picture of a model made from interlocking cubes and predict the least number of cubes needed to build it. They then build the shape to check whether they are correct.

Two 3D shapes that could be made from cubes

Children describe 2-D and 3-D shapes using mathematical vocabulary. In pairs they sit back to back and pretend to have a telephone conversation during which they describe a shape to each other. They note how talk varies with purpose and how precise their language needs to be when they cannot use drawings to convey meaning. They use their knowledge of the faces of 3-D shapes to begin to construct their own net of a cuboid. They respond to questions such as: What 3-D shape has a face that is an equilateral triangle? They construct the net of an open cube using a set-square and ruler to draw the five squares. They then construct the net of an open cuboid.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 923KB
Activity 47 - Straw Squares

Intervention programmes

Objectives for Springboard intervention unit	Springboard unit
Understand and use £.p notation Find totals and work out which coins to use Give change	Springboard 4 Unit 10 (PDF 231KB)

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

Diagnostic focus	Resource
Is not confident when recalling multiplication facts	1 Y4 ×/÷ DfES 1150-2005 (PDF 104KB)
Is muddled about the correspondence between multiplication and division facts	2 Y4 ×/÷ DfES 1151-2005 (PDF 93KB)

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