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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 continue to solve practical problems involving estimating and measuring. For example, they suggest how to estimate the weight of one grain of rice or the thickness of one sheet of paper. When finding the thickness of one sheet of paper, they measure the thickness of 100 sheets and then divide their answer mentally by 100.
They understand that the measurement found for the thickness of one sheet of paper is approximate. They communicate clearly how a problem was solved, explaining each step and commenting on the accuracy of their answer.
Assessment focus: Ma1, Problem solving
Look for evidence of children drawing on a range of mathematics to solve problems. As they consider how to estimate very small measurements, look for children drawing on their knowledge of place value. For example, children might recognise that dividing a number by 10, 100 or 1000 is easier to calculate than dividing by other numbers, and so understand the approach of first measuring the weight of 100 grains of rice or the thickness of 100 sheets of paper. Some children might be able to draw on their understanding of area and their calculation skills to estimate the weight of one sheet of paper, given the description from a packet of paper of ‘80 g per m2’.
Children use decimal notation in the context of measures and convert between units where necessary, for example, to solve word problems such as:
How many 250 ml cups of tea can you pour from a tea urn that holds 8.5 litres?
How many 30 cm square tiles would you need to buy to cover a rectangular floor which is 2.5 m wide by 3.5 m long?
There is 60 g of rice in one portion. How many portions are there in a 3 kg bag of rice?
A packet contains 1.5 kilograms of guinea pig food. Remi feeds her guinea pig 30 grams of food each day. How many days does the packet of food last?
Assessment focus: Ma2, Operations, relationships between them
Look for evidence of the range of relationships between operations that children use in their calculations, particularly when they use a calculator to work with larger numbers or decimal numbers. Look for children who understand that the missing number in 8.5 ÷ 
= 34 can be calculated by entering 8.5 ÷ 34 = into the calculator. Look for children who check the answer to a division calculation by entering the same calculation again, and those who check by using multiplication as the inverse operation.
Look for evidence of children who are aware of the order of operations, particularly when using a four-function calculator that is not scientific. For example, look for children calculating the cost of three books at £3.75 and five at £2.45 and recognising the order in which this should be entered into their calculator. They might use the memory, for example, storing the result of 3.75 × 3, entering 2.45 × 5 = and then using + MR (memory recall).
Children estimate angles, and use a protractor to measure and draw angles on their own and in shapes. They know the angles of a triangle add up to 180° and that the angles around a point add up to 360°, and they use this information to calculate missing angles.
Here is an isosceles triangle.
Calculate the value of angle x.
Do not use a protractor (angle measurer).
Children read and plot coordinates in order to draw, complete and locate shapes. For example, given half a shape and a line of symmetry, they complete the shape, or given three vertices of a rectangle, they establish the coordinates of the fourth vertex.
Assessment focus: Ma3, Properties of position and movement
Look for evidence of children using coordinates to describe the position of points on a grid. Look for children who use coordinates in the first quadrant and those who use them in other quadrants. Look for evidence of children reasoning about shapes and the position of vertices on the grid. For example, look for children who, given the coordinates of three vertices of a rectangle, work out the coordinates of the fourth vertex. Look for children who identify the fourth vertex when one edge of the rectangle is parallel to an axis. Look out for children who can identify the fourth vertex even when the rectangle is placed obliquely on the grid.
Children predict then check where the image of a shape will be after a reflection, rotation or translation. They use equipment (such as tracing paper) or ICT to rotate shapes through 90° and 180° about their centres or one of their vertices.
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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Mr Singh buys paving slabs to go around his pond. 
He buys 4 rectangular slabs and 4 square slabs. What is the total cost of the slabs he buys? |
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The answer is 10.6 kg. What was the question? |
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Cashew nuts cost 90p for 100 grams. |
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I want to divide a number by 8 but the '8' key on my calculator is broken. How could I do it? 
My question was about length. Complete this: |
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What would be the best approximation to work out 2 × (8.4 + 19.7)? Give your reasons. |
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A pupil measured the angles in a triangle. She said: 'The angles are 30°, 60° and 100°.' Could she be correct? Give reasons. 
Ring the measurement that is the approximate size of the angle. |
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A, B and C are three corners of a rectangle. What are the coordinates of the fourth corner? 
Plot (2, 3) and (5, 3). The line joining these coordinates is one side of a square. Find the coordinates of the two other vertices of the square. Find three possible answers. |
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Draw the reflection of this shape. 
The shape below is rotated 90° clockwise about point A. Draw the shape in its new position on the grid.  |
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What measurement is 10 times as big as 0.01 kg? How do you know that it is 10 times 0.01 kg? |
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Debate with the class the usefulness of various benchmarks for estimating measurements. For example, how useful is it to know that a door is roughly 2 metres tall? What other heights can be estimated, using this benchmark? |
| Activities | PDF 1MB |
| Activity 62 - Maze |
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Objectives for Springboard intervention unit |
Springboard unit |
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Calculate angles in a triangle and around a point |
Springboard 6 Unit 14 (PDF 379KB) |
| 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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