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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 on 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 in whole-number, fraction and decimal steps. They count forwards in jumps of 19 from 7 and backwards in 7s starting at 19 and continuing below zero. They count in thirds from 0 using mixed numbers and in steps of 0.3 from 0, and backwards in 100s from 21 and 213. They are able to identify the rule for a given sequence. For example, for the sequence of numbers 1, 3, 7, 15, 31, ..., they are able to predict the next number by saying that you double the number and add 1 to get the next number in the sequence. Alternatively, they spot that the differences between one term and the next form the sequence 2, 4, 8, 16, ... They can say whether a particular number will or won't occur in a sequence and explain their reasoning.
Children use a number line to order a set of positive and negative numbers. They find the difference between pairs of negative numbers, or one positive and one negative number, in context. They say that a rise from –3 
C to +1 C shows that the temperature has risen by 4 degrees. They read a table showing temperatures in five different cities on the same day and put the temperatures in order from coldest to warmest. They find the new temperature in each city when the temperature rises by 2 degrees or drops by 5 degrees.
Children estimate the position of numbers on a number line. They suggest which number lies about two fifths of the way along a line from 0 to 1000 line, or a line from 0 to 1. They justify their decisions. They round large numbers to the nearest multiple of 10, 100 or 1000, and decimals to the nearest whole number or to one decimal place. They decide whether it would be appropriate to round the number of children in a school, marbles in a jar, grains of sand in a bucket or hairs on a dog to the nearest 10, 100, 1000 or 10 000. They partition and order decimals with up to three places.
Assessment focus: Ma2, Fractions, decimals, percentages and ratio
Look for evidence of children understanding the relative sizes of decimals. Look out for children rounding decimals to one or two decimal places. Look for children who can place in order a set of decimal numbers with a mixture of one, two and three decimal places, and position them on a number line from 0 to 1, for example.
Children use mental strategies to calculate in their heads, using jottings and/or diagrams where appropriate. For example, to calculate 24 × 15, they multiply 24 × 10 and then halve this to get 24 × 5, adding these two results together. They record their method as (24 × 10) + (24 × 5). Alternatively, they work out 24 × 5 = 120 (half of 24 × 10), then multiply 120 by 3 to get 360. To solve 5.6 - 
= 1.9, they use their ability to add or subtract any pair of two-digit numbers and their knowledge of inverse operations to work out 56 - 19. This tells them that the unknown number is 3.7. They can also show the calculation on a number line. They start at 5.6, jump back 3.6 to 2.0, and then 0.1 to 1.9, adding these two jumps to find the solution (3.7). They compare these different methods and discuss which
they prefer. They recognise that mental calculations need to be reasonably quick and, of course, accurate, and that jottings can range from jotting down an interim result to drawing an informal diagram.
Children consolidate the use of efficient written methods for multiplication and division of decimal numbers by one-digit whole numbers, such as 23.8 × 8 and 87.6 ÷ 6, building on and refining the methods for multiplication and division developed in Year 5. They find an approximation for each calculation first and use this to check that the answer is sensible.
Assessment focus: Ma2, Operations and relationships between them
Look for children who can explain how they know that a multiplication is correct. For example, look out for children who partition a two- or three-digit number in order to multiply it by a single-digit number, and can explain how they know they have multiplied each part of the larger number and how they can check each calculation. Look for children who explain how they would solve a multiplication such as 23 × 8 and who begin to make connections to the grid method, rectangular arrays or finding areas of rectangles.
Look for evidence of the range of multiplication facts that children recall and use when they divide. Look for children using multiplication facts up to 10 × 10, and place value, as they aim to complete a division in as few steps as possible.
Children use a calculator to explore the effect of brackets in calculations. They compare (17 + 3) × 15 and 17 + (3 × 15) and explain why the answers are different. They place brackets to make a calculation correct; for example, they write 250 - 45 ÷ 3 = 235 as 250 - (45 ÷ 3) = 235.
Children solve problems such as: A number multiplied by itself gives 2809. Find the number. They decide for themselves whether to use a calculator.
Assessment focus: Ma1, Problem solving
Look for evidence of children developing their own strategies and making links to previous work. Look out for children who begin to check their work in order to spot and correct calculation errors and to review their approach. They might, for example, compare their approaches with those of others in the group and begin to consider how efficient each approach is. For example, when using a trial and improvement method to find the square root of a number, they might recognise that a column for a comment on each trial would be useful to help them improve their next trial.
| What number multiplied by itself equal 4489? | ||
| Trial | Result | Comment |
| 63 | 3969 | Ends in 9 but too small |
| 73 | 5329 | Too large, try half-way |
| 68 | 4624 |
Closer but still too big. 7 in units would give a number ending with 9. 7 × 7 = 49 |
| 67 | 4489 | Right! |
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
|---|---|
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Here is a repeating pattern of shapes. Each shape is numbered. 
The pattern continues in the same way. What will the 35th shape be? Explain how you can tell. |
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Tell me two temperatures that lie between 0 |
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What do you look for first when you order a set of numbers? Which part of each number do you look at to help you? |
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Start from a two-digit number with at least six factors, e.g. 56. How many different multiplication and division facts can you make using what you know about 56? What facts involving decimals can you derive? |
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The answer is 12.6. What was the question? |
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What key presses would you make on a calculator to work out |
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Roughly, what will the answer to this calculation be? |
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John says that every multiple of 4 ends in 2, 4, 6 or 8. Persuade me that John is wrong. |
| Activities | PDF 1MB |
| Activity 64 - Flash Harry |
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Objectives for Springboard intervention unit |
Springboard unit |
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Order a set of decimal numbers and identify the most significant digit when sorting numbers |
Springboard 6 Unit 1 (PDF 1.4MB) |
| Diagnostic focus | Resource |
| Has difficulty partitioning numbers with zero place holders and/or numbers less than one | 3 Y6 +/- DfES 1134-2005 (PDF 90KB) |
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10 to derive related multiplication and division facts involving decimals (e.g. 0.8 
6)
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