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Year 4 Block E - Securing number facts, relationships and calculating Unit 2

Objectives Children's learning outcomes are emphasised	Assessment for learning
Represent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problem I can write down number sentences or drawings to help me solve a problem When I have solved a problem I re-read the question to make sure the answer makes sense	What could you write down or draw to help you to think about this problem? One length of the swimming pool is 25 metres. Jane swims 5 lengths of the pool. How far does Jane swim altogether? How can you check that your answer makes sense? Look at this problem. Jan is 9 years old. Her mother is 31 years old. How many years older is Jan's mother? Circle which of these you could use to work out the answer. 40 – 31 31 + 9 31 × 9 31 – 9 40 – 9
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 7 times-tables, even when they are not in the right order If you give me a multiplication fact I can give you one or two division facts to go with it	Count from zero in sevens. If someone has forgotten the 7 times-table, what tips would you give them to help work it out? How could you work out the 7 times-table from the 5 and 2 times-tables? How could you work it out from the 10 and 3 times-tables? How else could you work it out? You know that 2 + 5 = 7. How could you work out 8 × 7 from this addition fact? Are there any multiples of 7 that are also multiples of 8? Which multiples of 7 are the hardest to remember? What can you do to help you remember them?
Recognise the equivalence between decimal and fraction forms of one half, quarters, tenths and hundredths I can recognise decimals and fractions that are equivalent	Which of these is the same as 0.4? A four B four tenths C four hundredths D one fourth Tell me two fractions that are the same as 0.25. Are there any other possibilities? How many centimetres are the same as 0.75m? How many hundredths are the same as 0.75? How else could you write seventy-five hundredths? You have been using your calculator to find an answer. The answer on the display reads 8.25. What could this mean? Write down a number lying between 7 and 8. Write it as a fraction and then as a decimal.
Use diagrams to identify equivalent fractions (e.g. ⁶/₈ and ³/₄, or ⁷⁰/₁₀₀ and ⁷/₁₀); interpret mixed numbers and position them on a number line (e.g. 3 ¹/₂) I can find fractions that are equivalent to ¹/₄ I can order mixed numbers and put them on a number line	What fraction of these rabbits is grey? How do you know when a fraction is equivalent to ¹/₂? Tell me some fractions that are equivalent to ¹/₄. How do you know? Are there any others? What about ³/₄? Draw an arrow on the number line to show 1 ³/₄. Write the two missing numbers in this sequence. Tell me a fraction that is bigger than 3.
Find fractions of numbers, quantities or shapes (e.g. ¹/₅ of 30 plums, ³/₈ of a 6 by 4 rectangle) I can find one fifth of a number by dividing it by 5	What numbers/shapes are easy to find one third, one quarter, one fifth, one tenth of? Why? Tell me how to find one sixth of 42. Would you rather have ¹/₅ of 30 sweets or ³/₄ of 12 sweets? Why?
Identify pairs of fractions that total Using diagrams, I can find pairs of fractions that make one whole	Can you find a pair of fractions that make less than one whole?
Identify the main points of each speaker, compare their arguments and how they are presented I can listen carefully while someone else explains what they have done	Listen carefully while Sarah tells you about her method of finding two fractions with a total of 1. Now listen while Sam explains his method. Which explanation do you think was the best? Why?

Learning overview

Children continue to derive and recall multiplication facts and corresponding division facts. They begin to develop knowledge of multiples of 7. They count on and back in different steps, including counting in sevens, using this to help them respond to problems such as:

There are exactly 7 weeks until my birthday. How many days is that?

There are 56 days until my holiday. How many weeks do I have to wait?

They recognise that previously learned facts can help them to remember multiples, for example that a multiple of 7 is the sum of a multiple of 3 and a multiple of 4.

Children continue to apply their knowledge of place value to derive answers to calculations such as 70 × 5 and 2000 ÷ 4. They continue to solve problems, representing and then interpreting information. For example, they solve this problem:

Sean counts his books in fours. He has one left over. He then counts his books in fives. He has three left over. How many books has Sean?

They write a list of multiples of 4, adding 1 to each multiple. They write a list of multiples of 5, adding 3 to each multiple. They look for a number common to both lists then check that it works in the context of the question.

Children count in fractions along a number line from 0 to 1, for example, in tenths. When they reach 10 tenths they realise that this is equivalent to 1. They extend this by counting beyond 1 from 10 tenths to 20 tenths, realising that 20 tenths is equivalent to 2. They establish that fractions bigger than one whole can be written as mixed numbers, for example that 17 tenths can be written as 1 ⁷/₁₀. They draw diagrams to represent a mixed number such as 2 ¹/₄.

Children continue to establish pairs of numbers that total 1, recording these as, say, ³/₁₀ + ⁷/₁₀ = 1. They use fractions with a sum of 1 to solve problems. When faced with a problem such as: Max has £48. He spends ³/₄ of it. How much has he got left? they realise that he would have ¹/₄ left. They calculate ¹/₄ of 48 to answer the question. Using 8 cubes they make a model that is ³/₄ one colour and ¹/₄ another. Keeping the same fractions, they increase the number of cubes, investigating how many cubes they can and can't use. They discover and generalise that they can use multiples of 4.

Children continue to develop their understanding of equivalent fractions. Using a fraction wall, number lines or the 'Fractions' ITP, they work in pairs to start from a given fraction and identify other fractions that are equivalent to it.

Screen shot from ITP 'Fractions'

For example, they find different ways of expressing one half. They discuss what makes a fraction equivalent to ¹/₂ at first informally in pairs, then giving feedback to a larger group. They vary their talk depending on the audience, using more precise mathematical language when presenting to a larger group.

Children continue to develop the link between fractions and multiplication and division. They use this to find fractions of numbers and quantities. They know that to find ¹/₄ they divide by 2, to find ¹/₃ they divide by 3, and so on. This helps them find fractions of numbers; for example, when they find ¹/₃ of 30, they need to share 30 into 3 equal groups, or work out 30 ÷ 3 = 10. Having established that ¹/₃ of 30 is 10, they then realise that ²/₃ of 30 is 20. The concept is reinforced by shading squares on a 6 by 5 grid.

Children begin to link familiar decimals with corresponding fractions. They recognise the equivalence between the decimal and fraction forms of one half, one quarter and three quarters. They are shown how, on a 0 to 1 number line divided into tenths, the tenths can be marked as fractions (¹/₁₀, ²/₁₀, ³/₁₀, ...) or as decimals (0.1, 0.2, 0.3, ...). They then explore a 0 to 1 line marked in hundredths. They see that 1 tenth is the same as 10 hundredths, and that 43 hundredths is the same as 4 tenths and 3 hundredths. They relate this to 0.43 = 0.4 plus 0.03.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 923KB
Activity 51 - Lighthouse

Intervention programmes

Springboard units

None currently available

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)
Assumes that the commutative law holds for division	5 Y4 ×/÷ DfES 1154-2005 (PDF 85KB)

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