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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 addition and subtraction and their understanding of place value in decimals to derive sums and differences, doubles and halves of numbers with up to two decimal places. For example, given the calculation 7 - 48 = 24, they generate a range of linked calculations, such as:
Children explain how they work out answers to calculations such as 3.8 × 2, 0.28 + 0.46, 9.7 - 3.9, demonstrating their understanding of the place value in the numbers.
Children recall multiplication and linked division facts to 10 × 10. They find, for example, the seventh multiple of 8, or a number that is a factor of both 12 and 20. They use these facts to multiply and divide multiples of 10 and 100, for example calculating 70 × 80, 3500 ÷ 5 and 600 × 40. They explain how they worked out the answers. They generate families of related calculations such as: 8 × 3 = 24, 80 × 3 = 240, 800 × 3 = 2400 and 8 × 0.3 = 2.4. They use division facts to find factors of numbers, determining, for example, that 56 has a factor pair of 7 and 8, so 560 has a factor pair of 70 and 8 or 7 and 80. They solve problems such as:
Find as many pairs of numbers as you can with a product of 160.
Children use their knowledge of number properties to investigate general statements such as: The product of an odd number and an even number is always even. They test examples and use reasoning to explain why they think that the statement is true. They suggest similar general statements such as: The product of two odd numbers is odd and test them.
Assessment focus: Ma1, Communicating
As they investigate numbers and shapes, look for evidence of children organising their results in ways that help them to identify patterns or check for repeats. For example, when investigating the products of odd and even numbers, they might start with 2 and multiply by 3, then by 5, then by 7.
Children solve word problems. They identify the calculations that they need to do and the best way to do them: mentally, on paper or using a calculator. They estimate the answer by rounding the numbers involved. They solve problems such as:
A rectangular play area is covered in concrete slabs. There are 20 slabs along the length of the play area and 14 slabs along the width of the play area. How many slabs cover the play area?
Samira has a 1kg bag of flour. She uses 0.2kg to make biscuits and 0.35kg to bake a cake. How much flour is left in the bag?
How many jugs each holding 0.3 litres can be filled from a bottle containing 1.5 litres of juice?
Children make up 'number stories' to reflect statements such 300 ÷ 25 = 12 or 3.5 - 1.7 = 1.8.
Assessment focus: Ma2, Solving numerical problems
As children solve problems involving money and measures, look for their awareness and use of units in their calculations. For example, look for children recording amounts given in pence as a decimal fraction of a pound when they add money. Look for children who convert 1.5 kg to 1500 g, for example, to calculate the number of 30 g portions that can be served from a pack of 1.5 kg.
Children complete patterns with two lines of symmetry, using, for example, peg boards or a suitable computer program. They solve problems involving symmetry such as:
Place eight squares together (edge to edge) to make a shape with two lines of symmetry. How many different shapes can you make?
Children investigate the line symmetry of regular polygons, finding how many lines of symmetry there are in an equilateral triangle, square, regular pentagon, regular hexagon, and so on. They suggest a general statement based on their findings.
Children extend their knowledge of the properties of 3-D and 2-D shapes, including the tetrahedron and octahedron. They identify shapes that have pairs of parallel or perpendicular sides or edges. They learn about different types of triangles (equilateral, isosceles, scalene, right-angled). They draw or create right-angled and isosceles triangles, using pencil and paper, peg boards or ICT. They collaborate in groups to explore how many different shapes they can make from five squares touching edge to edge. They understand that if rotations and reflections of the shapes are not counted as different there are 12 shapes to be found. They investigate which of these shapes can be folded up to make an open cube.
Assessment focus: Ma3, Properties of shapes
As they sort shapes or reason about shapes they have created, look for evidence of children’s understanding of the properties of shapes. Look for children recognising reflection symmetry within shapes, for example identifying right angles and angles of 45° when they draw the diagonals in a square. Look for children who use criteria such as ‘exactly one pair of parallel lines’ to sort 2-D shapes, and recognise that each shape that satisfies the criterion is a trapezium. Look out for the range of mathematical language children use to describe shapes.
They might use terms such as ‘acute’ and ‘obtuse’ to describe angles, or ‘congruent’ to describe two shapes that are the same shape and size. Look for children refining their descriptions of triangles to include ‘right-angled’, ‘isosceles’, ‘equilateral’ and ‘scalene’. They might recognise that a triangle can be right-angled and scalene, or right-angled and isosceles, but not right-angled and equilateral.
| Objectives
Children's learning outcomes are emphasised |
Assessment for learning |
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Ella says: 'The sum of two even numbers is always a multiple of 4.' Is she correct? Give some examples to justify your answer. |
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Tanya has read the first 78 pages in a book that is 130 pages long. Which number sentence could Tanya use to find the number of pages she must read to finish the book?
A 130 + 78 =
Tilly's parcel cost 55p to post. She stuck on eight stamps. Each stamp was either 10p or 5p. How many of each stamp did Tilly stick on her parcel? Show how you worked out your answer. |
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Look at this number sentence: |
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How many multiplication and division facts can you make, using what you know about 48? How did you work out the division facts? Make up some division questions that have a remainder of 1. How did you do it? What tips would you give someone who had forgotten the 9 times-table to help them to work it out? |
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How could you check that your answer is correct? |
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How would you check if two lines are parallel? How would you check if two lines are perpendicular?
Join three dots to make a different isosceles triangle. |
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Use these tiles to make a symmetrical shape. Can you take one tile away and keep your shape symmetrical? Can you change one or more tiles so that your shape is no longer symmetrical?
Here is a shaded square on a grid. Shade in three more squares so that the design is symmetrical in both mirror lines.
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Explain to the class how you solved that problem. |
| Activities | PDF 1MB |
| Activity 55 - Money bags | |
| Activity 53 - Square it up | |
| Activity 54 - Joins | |
| Activity 56 - A perfect match | |
| Activity 57 - Presents | |
| Activity 58 - Spot the shapes 2 | |
| Activity 59 - Four by four | |
| Activity 61 - Make five numbers | |
| Activity 63 - Jack's book | |
| Activity 65 - Age old problems | |
| Activity 66 - Zids and Zods |
| Objectives for Springboard intervention unit | Springboard units |
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Identify doubles and also near doubles using doubles already known |
Springboard 5 Unit 1 (PDF 305KB) |
| Springboard 5 Unit 1 supplementary (PDF 77KB) | |
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Know by heart: all +/- facts for each number up to 20, all pairs of multiples of 100 with a total of 1000, all pairs of multiples of 5 with a total of 100, all pairs of numbers with a total of 100 |
Springboard 5 Unit 3 (PDF 305KB) |
| Springboard 5 Unit 3 supplementary (PDF 85KB) | |
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Know the three- and four-times tables |
Springboard 5 Unit 9 (PDF 269KB) |
| Springboard 5 Unit 9 supplementary (PDF 110KB) |
| Diagnostic focus | Resource |
| Has an insecure understanding of the number system resulting in addition and subtraction errors and difficulty estimating | 1 Y4  /-DfES 1128-2005 (PDF 101KB) |
| Has difficulty in partitioning | 2 Y4 /- DfES 1129-2005 (PDF 78KB) |
| Is not confident when recalling multiplication facts | 1 Y4 ×/÷ DfES 1150-2005 (PDF 104KB) |
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