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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 develop their problem-solving skills in the context of measurement, focusing on mass. They continue to solve real-life problems involving one or two steps and any of the four operations. They recognise that they may need to change the units of measurement to the same unit in problems such as:
A horse eats 560 g of feed from a 2 kg bag. How much of the feed is left?Children refine their written methods of calculation to make them efficient. They decide the best way to solve a problem and explain why they chose, say, a written method rather than a mental method. They use their knowledge of number facts, place value, inverse operations and rounding to make estimates and check calculations.
Children extend their knowledge of multiplication and division by 10, 100 and 1000 to include decimals. They use this knowledge to convert units of mass; for example, they convert grams to kilograms and vice versa. They work out mentally conversions such as:
How many grams are there in 3.6 kilograms?
How many kilograms is 4200 grams?
Assessment focus: Ma2, Numbers and the number system
Look out for children who use understanding of place value to explain the effect of multiplying a number by 10 or by 100. Look for children who understand the effect of dividing by 10 or by 100, including examples that give rise to decimal answers. Look for children who can multiply and divide by 1000 and who can apply this when converting between grams and kilograms, and between millilitres and litres.
Children use efficient written methods to add and subtract whole numbers (with up to five digits) and numbers with up to two decimal places. They refine their multiplication methods to multiply TU × U and HTU × U.
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They multiply, for example, 5.6 × 7 by relating this to 56 × 7 and dividing the answer by 10.
Children extend their knowledge of division to short division of HTU by U, by repeated subtraction of multiples of the divisor (taking away chunks), aiming to subtract as few chunks as necessary.
Children use these methods when they solve word problems involving mass to give meaning to their work, such as:
Two parcels together weigh 2.4 kg. One parcel weighs 1.68 kg. What is the mass of the other parcel?
Mary posts seven identical parcels. Each parcel weighs 3.2 kg. What is the total mass of the parcels?
When they measure weight, children use a range of weighing scales, kitchen scales, bathroom scales. They weigh to a suitable degree of accuracy, depending on the object, for example to the nearest 100 g or to the nearest 1 g. They read scales with some unnumbered divisions, for example kitchen scales with divisions of 10 g numbered every 100 g, or bathroom scales with divisions of 1 kg numbered every 10 kg. They estimate the masses of everyday objects, say how they made their estimates and then measure to see how accurate their estimates were. They investigate the cost of sending different parcels by first-class post, researching postage costs on the Post Office website.
Assessment focus: Ma1, Problem solving
Look for children selecting appropriate equipment and units to measure in a range of contexts. Look out for children estimating and then measuring with an appropriate degree of accuracy. When measuring the mass of a bag of apples, they might decide that measuring to the nearest 25 g is sufficiently accurate, whereas measuring to the nearest kilogram would be more appropriate for the mass of a child.
Children use their knowledge of measuring lengths to revise how to measure the sides of regular and irregular polygons and calculate the perimeter, either by totalling the sides or, for regular polygons, by multiplying the length of one side. They derive a formula for the area of a rectangle and calculate areas of rectangles and squares.
Assessment focus: Ma3, Measures
Look for evidence of children who can explain what the terms ‘area’ and ‘perimeter’ mean and who can use the associated notation, for example, cm and cm2, consistently and accurately. Look for children who find an area by counting squares and for those who can begin to express the formula for the area of a rectangle as ‘number of squares in a row times number of rows’.
Children know that angles are measured in degrees and learn to say whether an angle is acute, obtuse or a right angle. Given a set of cards with pictures of angles on, they sort them into sets or order them from smallest to largest. They make sensible estimates of the size of angles less than 180° and then measure them to within 5 degrees, using a protractor or angle measurer. They apply this knowledge to work with shapes drawn on a coordinate grid. For example, they plot the missing vertex of a square with sides not parallel or perpendicular to the axes and then check that each angle is 90°.
| Objectives Children's learning outcomes are emphasised | Assessment for learning |
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The answer is 15.4 kg. What was the question? A spoonful is 5 ml. How many spoonfuls can you get from a bottle that holds one quarter of a litre?Did you have to change any of the information to help you solve the problem, e.g. convert units of measurement? Did you need to use the calculator to solve the problem? What key sequence did you use? |
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Roughly, what will the answer to this calculation be? How did you arrive at that estimate? Do you expect your answer to be greater or less than your estimate? Why? |
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Tell me a quick way of multiplying a number by 10. By 100. |
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What tips would you give to someone to help with column addition of decimals? What about subtraction? Three parcels weigh 785 g, 55 g and 0.25 kg. How much do they weigh altogether? |
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How would you solve these problems? I have 9 parcels each weighing 346g. How much do they weigh altogether? |
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What key presses would you make on a calculator to work out 14.6 × 4 × 13.8? I use 1375 g of sugar to make 5 cakes. How much sugar do I need for 1 cake? For 3 cakes?How will you check your answers to the problems? |
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Give an example of parallel lines in everyday life. How can you recognise them? What about perpendicular lines? |
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Look at these angles.
Estimate the size of each of the angles. Now use your protractor to measure the angles to the nearest 5 degrees. |
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How do I write 6 kilograms 400 grams as a decimal? What about 9 kilograms 50 grams? weighing a tomato?Circle one amount each time to make these sentences correct. The distance from London to Manchester is about: |
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What is the total mass of the apples on the scales?
A piece of cheese has a mass of 350 grams. Mark an arrow on the scale to show the reading for 350 g.
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Measure accurately the longest side of this shape. Give your answer in millimetres.
What tips would you give someone who wanted to measure a line in millimetres? What is the area of a rectangle measuring 34 cm by 29 cm? Explain how you worked out your answers. |
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Why did you decide to use a mental/written/calculator method for this calculation? Why did you decide to change all the units to metres rather than centimetres? Why did you decide to use the scales rather than the balance? |
| Activities | PDF 1MB |
| Activity 67 - Franco's fast food | |
| Activity 70 - A bit fishy |
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Objectives for Springboard intervention unit |
Springboard unit |
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Multiply and divide whole numbers by 10 and 100 and understand the effect |
Springboard 5 Unit 6 (PDF 305KB) |
| Springboard 5 Unit 6 supplementary (PDF 57KB) | |
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Develop and refine written methods for subtraction, building on mental methods. |
Springboard 5 Unit 8 (PDF 245KB) |
| Springboard 5 Unit 8a Part 1 supplementary (PDF 77KB) | |
| Springboard 5 Unit 8a Part 2 supplementary (PDF 75KB) | |
| Know the three- and four-times tables Begin to know the six-times tables |
Springboard 5 Unit 9 (PDF 269KB) |
| Springboard 5 Unit 9 supplementary (PDF 110KB) |
| Diagnostic focus | Resource |
| Describes the operation of multiplying by 10 as adding a nought/zero | 3 Y4 ×/÷ DfES 1152-2005 (PDF 68KB) |
| Has an insecure understanding of the number system resulting in addition and subtraction errors and difficulty estimating | 1 Y4  /-DfES 1128-2005 (PDF 101KB) |
| Does not make sensible decisions about when to use calculations laid out in columns | 3 Y4 /- DfES 1130-2005 (PDF 101KB) |
| Has difficulty with adding three numbers in a column | 4 Y4 /- DfES 1131-2005 (PDF 95KB) |
| Does not apply partitioning and recombining when multiplying and confuses the value of two digit numbers | 4 Y4 ×/÷ DfES 1153-2005 (PDF 104KB) |
| Assumes the commutative law holds for division also | 5 Y4 ×/÷ DfES 1154-2005 (PDF 85KB) |
| Writes a remainder that is larger than the divisor | 6a Y4 ×/÷ DfES 1155-2005 (PDF 76KB) |
| Discards the remainder; does not understand its significance | 6b Y4 ×/÷ DfES 1156-2005 (PDF 93KB) |
| Does not recognise when the remainder is significant when rounding up or down | 6c Y4 ×/÷ DfES 1157-2005 (PDF 65KB) |
| Continues to subtract 2s without using knowledge of times tables | 7 Y4 ×/÷ DfES 1158-2005 (PDF 89KB) |
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