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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 extend their knowledge of number facts and properties of numbers and shapes . They use this knowledge to solve mathematical problems.
Children strengthen their recall of number facts, recalling facts quickly and applying them accurately. They develop strategies to enable them to derive quickly all addition and subtraction facts for each number to 20 and sums and differences of multiples of 10. Children understand the relationship between addition and subtraction. They state the addition fact corresponding to any subtraction fact and vice versa. They use their understanding of this inverse relationship to check subtraction calculations.
Children count from zero in steps of 2, 3, 4, 5, 6 and 10 and use the sequences generated to establish multiplication and division facts . They recite these times-tables, begin to locate a fact from the relevant table and start to recognise multiples of 3, 4 and 6. They identify numbers to 1000 that are multiples of 2, 5 or 10. They sort a set of numbers using criteria such as: 'These numbers are multiples of 5', or: 'These numbers are in the 6 times-table''
Assessment focus: Ma2, Numbers and the number system
Look for evidence of the range of number properties children choose to use, for example, when they sort numbers for a partner to work out their ‘rules’ or criteria. Look for children choosing criteria such as multiples of 10, even or greater than 20, and applying them consistently and accurately.
Children use their knowledge of number pairs for 10 and 20 to add and subtract efficiently. For example, to calculate 48 7 they add 2 to bridge through 50 then add the remaining 5.
They use knowledge that addition can be done in any order to calculate efficiently. For example, they put the larger number first to work out 4 + 37, or identify pairs of numbers that total 10 to work out 3 + 4 + 5 + 6 + 7.
Children use their increasing understanding of place value to derive new facts from known facts. For example, they use the fact 7 – 2 = 5 to establish that 70 – 20 = 50 and 700 – 200 = 500. They calculate all pairs of multiples of 100 with a total of 1000 (e.g. 300 + 700), and doubles of multiples of 10 (e.g. 80 + 80). They explain their calculation strategies.
Children choose appropriate operations to solve one- and two-step problems involving number, money and measures, such as:
Jake wants to buy a comic that costs £1. He saves 25p one week and 40p the next. How much more money does he need to buy the comic?
A piece of tape is 100 cm long. I cut off seven pieces, each 5 cm long. How much tape is left?
Assessment focus: Ma2, Solving numerical problems
Look for evidence of children responding to a range of language used to describe numerical problems involving money or measures. Look for children identifying the information that is relevant and the steps to complete to solve problems. Look for children using addition, repeated addition or multiplication, subtraction, repeated subtraction or sharing/division appropriately in problems that involve one or two calculations.
Children follow and contribute to class discussions about possible methods for solving particular problems. They respond to suggestions and statements by others and suggest alternatives. They use their increasing understanding of the four operations to create their own word problems. They use patterns, properties and relationships between numbers to solve puzzles , such as:
Place the numbers 1 to 9 in a 3 by 3 grid so that the total of each row is 15.
I am a two-digit number. My digits total 12 and have a difference of 4. Who am I?
Assessment focus: Ma1, Problem solving
Look out for children beginning to ask questions and using class discussion to clarify a problem or investigation. Look for children adopting a suggested approach and those children who begin to suggest materials and ways to get started themselves.
Children use patterns, properties and relationships between shapes to solve problems . They recognise 3-D shapes and make collections, for example, of shapes that are prisms. They know that a prism has the same cross-section along its length, and that its two end-faces are identical. They name and describe solids, using the correct language: 'A triangular prism has two identical triangular faces at opposite ends and the other three faces are rectangles'; 'A hemisphere is a sphere cut in half. It has one flat face and a curved surface.' They sort 3-D shapes using criteria such as the number of vertices, edges or faces . They find the number of edges of assorted prisms to investigate the general statement : The number of edges of a prism is always a multiple of 3.
Assessment focus: Ma3, Properties of shapes
Look for evidence of children identifying and using the properties of 2-D and 3-D shapes to solve problems, for example, children using the properties of a given 2-D shape to select appropriate geo-strips to create a similar shape. Look out for children using the properties of a 3-D shape to choose which of several collections of 2-D shapes could be its faces.
Children extend their knowledge of 2-D shapes . They know that a quadrilateral is any flat shape with four straight sides. They choose a shape to match properties described by others; for example, they find a shape that is 'half a circle', or 'is not a right-angled triangle' or 'has four right angles and opposite sides equal'. Children create 2-D shapes using a variety of equipment. For example, they fold and cut paper to make squares, octagons and stars; they use geostrips; they put two identical shapes together then describe the new shape; they use a computer program to generate, identify and compare new shapes. They describe the properties of the shapes that they have generated.
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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Tell me how you solved this problem. Did you make any notes or drawings to help you? Describe them to me. |
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Sort the numbers 1 to 20 into two groups: 'multiples of 5' and 'not
multiples of 5'. What do you notice? Tell me a number bigger than 100
that would go in each group. |
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Tell me two numbers that sum to 17. And another pair? What would you add to 7 to make a total of 16? Give me three pairs of numbers that total 19. Now tell me some of the subtraction facts that use these numbers. What two numbers could I subtract to make 13? What is 15 – 2? What is 15 – 4? What is 15 – 6? Can you do a similar thing but start from 17 – 2? |
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What is 7 × 4? Did you know or did you work thorough one of the times table? Which table did you use? Start at 1 × 4 and work through the 4 times table with me to 10 × 4. Can you tell me the two multiplication facts either side of 7 × 4? Now tell me the answer to 5 × 4 and the two facts either side of it. |
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What is 50 + 30? If we know that 50 + 30 = 80, how can this help us to estimate 53 + 27? Give me an estimate for 83 – 28, 81 – 52. |
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Here are some drawings of 3-D solids. Which drawings show cylinders?
Name any other solids you can see in the drawings. Can you see any
prisms and pyramids? |
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This group said that to add 3 + 4 + 5 + 6 + 7 they would add the largest
numbers first. Is this the method you would choose? Why or why not? |
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Activities |
PDF 923KB |
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Activity 32 - Card tricks |
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Activity 33 - Neighbours |
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Objectives for Springboard intervention unit |
Springboard unit |
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Know by heart all addition and subtraction facts for 10 and 20 |
Springboard 3 Unit 2 sessions 1 and 2 (PDF 163KB) |
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Diagnostic focus |
Resource |
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Has difficulty in remembering number pairs totalling between ten and twenty, resulting in calculation errors |
2 Y2+/- |
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Is insecure in making links between addition and subtraction and/or recognising inverses |
5 Y2+/- |
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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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= 9. How would you find the missing number?
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