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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 following assessment focuses are illustrated:
Children count on and back in regular steps of 1, 2, 3, 4, 5, 6, 10 and 100 using their knowledge of addition and subtraction facts to help them to count accurately. They find the difference between consecutive numbers to establish the step size to complete sequences such as:
1, 7, 13, 19, 
, ; , 26, 22, , , 10, 6, 2
Children identify patterns and relationships and use these to support their count. They investigate general statements such as: When you count in fives, the units digits form a pattern. Where they work in groups on a task, they ensure that all members try out examples and discuss what they have found.
Children know by heart the 2, 5 and 10 multiplication facts and use them to solve questions like:
If I have three 5p coins, how much money do I have?
They recognise questions that involve division, such as:
If I have 30p in 10p coins, how many coins do I have?
They count on and back from zero in steps of 2, 3, 4, 5, 6 and 10 to answer questions like:
What is 4 multiplied by 6?
How many 3s make 21?
Children research the question: What digits can multiples of 2 end in? What about multiples of 3, multiples of 4? They investigate by joining the last digits of each multiple in order on a digit wheel. For example, the last digits of the multiples of 2 ( 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 ) form this pentagon:
Children record the outcomes of this enquiry by recording in a table the number, the last digits of its multiples and the shape that they form on the digit wheel. They use their results to answer questions such as:
Can 113 be a multiple of 5? How do you know?
Can a multiple of 4 ever end in a 7?
Assessment focus: Ma1, Reasoning
Look for children who find examples that match general statements, for example, those who record sequences of numbers to match general statements such as: ‘When you count from zero in tens, the unit digit is always zero,’ or: ‘When you count in fives from zero, the unit digit is always five or zero.’ Look for children who respond to ‘What if…?’ or ‘What if … not…?’ questions. For example, look for children who respond to a question such as: ‘What if we do not start the count from zero?’ by adapting the general statement to match the changed situation.
Children review multiplication as repeated addition and division as repeated subtraction by counting hops on a number line. For example, they find 6 fours by making 6 hops of 4.
Children divide a number of objects by using grouping . They understand that one way to find 30÷6 is to find how many sixes there are in 30 . Through practical experience, they understand that some division calculations have a remainder, for example 13 ÷ 4 = 3 R 1:
Children understand the relationship between multiplication and division . For example, they state two multiplication sentences and two division sentences that relate to a particular array, for example:
5 × 2 = 10, 2 × 5 = 10
10 ÷ 2 = 5, 10 ÷ 5 = 2
They use the image of an array to explain why, for example, 2 × 5 gives the same answer as 5 × 2. They also use the image to show how many fives make 10 and how many twos make 10.
Children derive quickly the doubles of all numbers 1 to 20 . They recognise that halving is the inverse of doubling. They understand that doubling is equivalent to multiplying by 2 and halving is equivalent to dividing by 2.
Assessment focus: Ma2, Operations and relationships between them
Look for children who recognise that multiplication can be done in any order and who use division as the inverse of multiplication. Notice children who generate related multiplication and division sentences, for example, using the numbers 3, 4 and 12. Look for children who understand the relationship between halving and doubling and recognise that halving is a way of ‘undoing’ doubling and vice versa.
Children begin to use practical and informal methods to solve simple TU × U calculations. For example, to find 12 × 5 they appreciate that 10 fives are 50 and add on another 2 fives to make 60.
Children fold shapes in half and, where possible, repeat this to find 1/2, 1/4 or 1/8 of a variety of shapes . By folding three identical rectangles into halves, quarters and eighths, they show and explain that 1/2 is equivalent to 2/4 and is also equivalent to 4/8. They understand that a whole is, for example, two halves, four quarters or eight eighths.
Children recognise other unit fractions of shapes, realising, for example, that 1/5 of this shape is shaded because 1 piece out of 5 equal pieces is shaded.
Assessment focus: Ma2, Fractions and decimals
Look out for children who can understand and use unit fractions to describe one region when shapes are divided into different numbers of equal regions. Look for children using fractions that are several parts of a whole. For example, look for children who count the number of equal parts and the number shaded to record the fraction of the whole shape that is shaded. Look for children who recognise fractions that are equivalent to one half.
Children find 1/2, 1/4 or 1/8 of collections of objects by sharing or repeated halving. They recognise and use the notation of 1/2,1/4 or 1/8, understanding that the numbers on the bottom of the fraction relate to sharing equally between 2, 4 or 8. They place 1/2 and 1/4 between 0 and 1 on a number line and half past, quarter past and quarter to on a 12-hour time line.
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
|---|---|
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What information will you find? How will you record it? |
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What are the missing numbers in this pattern? How did you find them? 83, 78, |
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What is the missing number in this pattern? |
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How many fives make the same number as three tens? |
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Paul buys 12 lollies that cost 5p each. Work out how much this will
cost altogether. How did you find the answer? Did you jot anything down? |
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Which is heavier: 1/2 of 18 kg or 1/4 of 32 kg? |
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You are going to solve this problem as a group. Start by agreeing what everyone in the group is going to do. How can you make sure that the discussion involves everyone and that everyone has a chance to express their point of view? |
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Activities |
PDF 923KB |
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Activity 29 - Spaceship |
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Objectives for Springboard intervention unit |
Springboard unit |
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Know by heart doubles of numbers to 10; doubles of multiples of ten up to 50 |
Springboard 3 Unit 4 sessions 1 and 2 (PDF 181KB) |
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Understand the operation of multiplication as describing an array |
Springboard 3 Unit 7 sessions 1 and 2 (PDF 191KB) |
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Diagnostic focus |
Resource |
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Confuses numbers when counting in twos; has difficulty understanding that a pair consists of two objects |
1 YR×/÷ |
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Makes unequal groups and is unable to compare groups |
3 YR×/÷ |
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Has difficulty with counting reliably in tens from a multiple of ten |
5 YR×/÷ |
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When halving, makes two unequal groups or splits a single object unequally |
6 YR×/÷ |
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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×/÷ |
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Does not link counting up in equal steps to the operation of multiplication; does not use the vocabulary associated with multiplication |
2 Y2×/÷ |
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Does not focus on 'rows of' or ' columns of', but only sees an array as a collection of ones |
3 Y2×/÷ |
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Has difficulty relating multiplying by two to known facts about doubles; records double 4 as 4 |
4a Y2×/÷ |
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Does not use knowledge of doubles to find half of a number |
5 Y2×/÷ |
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Does not understand that 'sets of' or 'groups of' need to be subtracted to solve the problem |
7 Y2×/÷ |
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Is not confident in 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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