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In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils’ Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children’s learning, this accumulating evidence will help you to determine the level at which they are working.
To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum as well as through the application of skills across the curriculum.
In this unit the illustrated assessment focuses are:
Children count on and back from zero in steps of 2, 3, 4, 5, 6 and 10 to answer questions like: What is 6 multiplied by 8? and How many 4s make 36?
Children derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and are able to state corresponding division facts. They use these facts to answer questions like:
A box holds 6 eggs. How many eggs are in 7 boxes?
What number when divided by 6 gives an answer of 4?
Leila puts 4 seeds in each of her pots. She uses 6 pots and has 1 seed left over. How many seeds did she start with?
Assessment focus: Ma2, Mental methods
Look for evidence of the range of multiplication facts that children recall quickly as they solve problems and investigate. Look for children using the multiplication facts they know to derive division facts and for children who begin to use their knowledge of multiplication tables and place value to multiply and divide multiples of 10 by a single-digit number.
Children investigate patterns and relationships. For example, they add together the digits of any multiple of 3 and generalise to help them recognise two-and three-digit multiples of 3. Using the 'Number dials' ITP they recognise that they can use their knowledge of number facts and place value to derive new facts; for example, by knowing 8×4 = 32 they can derive the answers to 80×4 and 320÷4.
Assessment focus: Ma1, Problem solving
Look out for children who recognise patterns in results and use them to understand the problem more clearly, to check results and generate others. For example, as they use the ITP ‘Number dials’ to investigate repeating patterns in the units digits of multiples of different numbers, look for evidence of children noticing relationships between patterns. Look for children who, for example, with the support of probing questions, recognise that the pattern for the last digit in multiples of 6 is the reverse of the pattern for multiples of 4: 0, 6, 2, 8, 4, 0 and 0, 4, 8, 2, 6, 0. Look for evidence of children searching for other pairs for which the patterns are linked and beginning to reason about why this occurs.
Children solve problems using knowledge of multiplication facts. For example, they use their knowledge of multiples of 2, 3 and 5 to tackle this problem:
Little has size 2 boots, Middle has size 3 boots and Big has size 5 boots. They all start with the heels of their boots on the same line and walk heel to toe. When will all their heels be in line again?
They decide what form of recording they will use to represent the problem and then evaluate their ideas, showing empathy with others.
Children read, write and understand fraction notation. For example, they read and write 1/10 as one tenth. They recognise that unit fractions such as 1/4 or 1/5 represent one part of a whole. They extend this to recognise fractions that represent several parts of a whole, and represent these fractions on diagrams. Using visual representations, such as a fraction wall, children look at ways of making one whole. They recognise that one whole is equivalent to two halves, three thirds, four quarters, five fifths. Using this knowledge they begin to identify pairs of fractions that total 1, such as 1/3 
2/3, 1/4 3/4. They solve simple problems, such as: I have eaten 3/10 of my bar of chocolate. What fraction do I have left to eat?
Children begin to recognise the equivalence between some fractions. They fold a number line from 0 to 1 in half and half again and label the 1/4 divisions. They then fold it again and identify the eighths. From this they establish the equivalences between halves, quarters and eighths. Using a 0 to 1 line marked with 10 divisions, they mark on fifths and tenths and again establish equivalences such as 2/10 and 1/5. They also represent these equivalences by shading shapes that have been divided into equal parts.
Children find fractions of shapes. For example they shade 3/8 of an octagon, understanding that any 3 of the 8 triangles can be shaded.
Working practically using objects, they find 1/3 of 12 pencils or 1/8 of 16 cubes, then present this pictorially. They make links between fractions and division, realising that when they find 1/5 of an amount they are dividing it into 5 equal groups. They recognise that finding one half is equivalent to dividing by 2, so that 1/2 of 16 is equivalent to 16 ÷ 2. They understand that when one whole cake is divided equally into 4, each person gets one quarter, or 1 ÷ 4 = 1/4
Children explore the equivalence between tenths and hundredths, and link this to their work on place value. They cut a 10 by 10 square into ten strips to find tenths, and observe that 1 tenth is equivalent to 10 hundredths, or that 4 tenths and 3 hundredths is equivalent to 43 hundredths. They note that 43p, or £0.43, is 4 lots of 10p and 3 lots of 1p. They record in both fraction and decimal form:
Assessment focus: Ma2, Fractions and decimals
Look for evidence of children using fractions that are several equal parts of the whole and using fraction notation to record them. Look for examples of children drawing on their greater practical experience of representing fractions on diagrams to recognise a wider range of fractions that are equal to one half, for example, 5/10 and 50/100. Look out for children who also recognise other fractions that are equivalent, for example, some fractions that equal one-quarter. Notice if children make connections to decimals, in the context of pounds and pence, metres and centimetres or, for example, fractions of hundred-squares. Look for children who begin to recognise equivalence between fractions they use often and their decimal representations, for example, 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75 or 1/10 = 0.1
| Objectives Children's learning outcomes are emphasised | Assessment for learning |
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What could you write down or draw to help you to think about this problem? How can you check that your answer makes sense? Jan is 9 years old. Her mother is 31 years old. How many years older is Jan's mother? Which of these could you use to work out the answer? 40 - 31 31 + 9 31 × 9 31 - 9 40 - 9 |
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How does knowing your 3 times table help you to recall multiples of 6?
Leila puts 4 seeds in each of her pots. She uses 6 pots and has 1 seed left over. Nineteen marbles are shared among some children. Each child receives six marbles and there is one marble left over. How many children share the marbles? How does 6 × 4 = 24 help you to know the answer to 6 × 40? And the answer to 240 ÷ 6? |
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What fraction of these tiles is circled?
What fraction of the square is shaded?
Tell me some fractions that are equivalent to 1/2. How do you know? Are there any others? The pizza was sliced into six equal slices. I ate two of the slices. What fraction of the pizza did I eat? |
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Tell me two fractions that are the same as 0.5. Are there any other possibilities? How many pence are the same as £0.25? How many hundredths are the same as 0.25? How else could you write twenty-five hundredths? You have been using your calculator to find an answer. The answer on the display reads 8.5. What could this mean? Which of these fractions is the same as 0.5?
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Use this 3 by 4 rectangle to find two fractions that add up to 1. |
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How can you find 1/3 of 27? Is there more than one way to shade 2/3 of a 2 by 6 grid? Why? |
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Did anyone solve the problem in a different way? Which do you think was the best way to solve the problem? Why? If you were given another problem like this, would you use that method? Why or why not? |
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Activities |
PDF 923KB |
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Activity 49 - Footsteps in the snow |
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Objectives for Springboard intervention unit |
Springboard unit |
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Recognise unit fractions such as 1/2, 1/3, 1/4, 1/5, 1/10 and use them to find fractions of shapes and numbers |
Springboard 4 Unit 7 (PDF 234KB) |
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Choose and use appropriate operations (including multiplication and division) to solve word problems |
Springboard 4 Unit 6 (PDF 196KB) |
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Diagnostic focus |
Resource |
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Is not confident when recalling multiplication facts |
1 Y4 ×/÷ |
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Is muddled about the correspondence between multiplication and division facts |
2 Y4 ×/÷ |
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Assumes that the commutative law holds for division |
5 Y4 ×/÷ |
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