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In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils’ Progress 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 use decimal notation for tenths, hundredths and thousandths. They partition numbers with up to three decimal places. They state the value of the digit 4 in the number 13.648 and recognise that you add 2 tenths to the number 5.235 to make 5.435. They replace the digit 6 with a 0 by subtracting 0.6 from 13.648 on a calculator.
Children count in steps of 0.1, 0.01 and 0.001, for example 2.4, 2.41. 2.42, 2.43, ..., 2.49, 2.5. They order numbers with up to three decimal places and position them on a number line. For example, they locate 0.111 on this line.
Children round decimal numbers to the nearest whole number and to the nearest tenth; for example, they round a set of given lengths to the nearest centimetre or millimetre. They use rounding to estimate the answer to calculations such as 17.15 – 8.9, by using the approximation 17 – 9 = 8. They calculate mentally problems such as:
A length of ribbon is 2.4 m long. I need to cut it into three equal pieces. What is the length of each piece?
The dimensions of my garden are 6.7 m by 6 m. What is its area?
Assessment focus: Ma2, Numbers and the number system
Look for evidence of children using their knowledge of place value and measuring units to interpret a number such as 2.5 in the context of a range of measures: pounds and pence, centimetres and millimetres or metres and centimetres, litres and millilitres, kilograms and grams.
Children find the unknown number in an equation such as 0.215 + 
= 0.275, using their knowledge of place value and using an inverse operation to check. They explain their reasoning: 'I compared the two numbers and realised that the difference between them was 6 hundredths, so I added 0.06 to 0.215 to check.'
Before they use a written method to add and subtract decimal numbers, children estimate the answer. For example, they calculate 13.86 + 9.481 or 0.236 – 0.154, and use rounding to check that their answer is approximately 23 or 0.08 respectively.
or 
Children discuss the efficiency of their written methods. They consider different calculations and choose the appropriate method: an efficient written method, a mental method (with jottings if necessary), or a calculator. They use their calculators to solve 'missing-number' problems, using their knowledge of inverse operations:
4.2 =
500 ÷
What number multiplied by itself gives 400?
Assessment focus: Ma2, Operations, relationships between them
Look for the operations and relationships that children use when, for example, they investigate situations such as: ‘The answer is 24.8. What could the calculation be?’ Look for evidence of children using inverse operations, rather than trial and improvement, to find missing numbers in calculations. For example, look for the calculator operations children use to find missing numbers in different positions in a number sentence such as: 224 = × 8; 224 = 28 × ; ÷ 28 = 8; or 224 ÷ = 8. Look for children’s understanding of operations and relationships and their understanding of notation when they solve equations such as 3 × 4 = 4 + or 2x + 8 = 16.
Children solve multi-step problems, including some with negative numbers or decimal numbers, explaining and evaluating their choices, and approximating first:
By midday the temperature rose to 8°C. By midnight it dropped to -4 °C. What was the temperature difference between midday and midnight? The temperature regained half of its drop (from midday to midnight) by 6:00 am the following morning. What was the temperature at 6:00 am?
Two adults and two children go to a cinema. Adult tickets cost £5.85 and children's tickets cost £2.85. How much change will they get from a £20 note?
Children record stages of solving the problems, explaining clearly the calculations that they have done. They compare and evaluate different methods, discussing the appropriateness and efficiency of their chosen method.
Assessment focus: Ma1, Communicating
Look for evidence of children organising results, for example as they use a trial and improvement method to solve: ‘A number multiplied by itself gives the result 33. What is the number?’ Look for evidence of children recording in a systematic way that helps them to keep track of their approach, of the calculations they have tried, and of whether these were overestimates or underestimates, so that further trials bring them closer to a solution.
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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I am thinking of a number. If you add 3 to my number and then multiply the result by 5, the answer is 35. What is my number? Show me how you worked it out. |
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How do you know whether you need to add, subtract, multiply or divide? What clues do you look for? |
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The distance to the park is 5 km when rounded to the nearest kilometre. What is the greatest/least distance it could be? How would you give somebody instructions to round distances to the nearest kilometre? |
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You know that 42 ÷ 6 = 7. What other division and multiplication facts can you derive from this? |
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The answer is 18.6. What is the question? |
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Look at these long-multiplication calculations. They have mistakes in them. Tell me what is wrong with each calculation. How should it be corrected? |
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My calculator shows: 
My question was about money. Complete this: |
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What would be the best approximation to work out 4.4 × 18.6? Give your reasons. |
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Debate with the class the advantages and disadvantages of different methods of multiplying 23 by 16. |
| Activities | PDF 1MB |
| Activity 83 - Albert Square |
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Objectives for Springboard intervention unit |
Springboard unit |
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Identify and use appropriate operations (including combinations of operations) to solve word problems |
Springboard 6 Unit 5 (PDF 1.4MB) |
| Diagnostic focus | Resource |
| Misuses half understood rules about multiplication and division by powers of ten | 1 Y6 ×/÷ DfES 1134-2005 (PDF 90KB) |
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