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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 solve problems in different contexts. They identify and record the calculations needed, interpreting the solutions back in the original context and checking their accuracy. They use symbols where appropriate to explain their reasoning. For example, they work out how many different flights there would be connecting two, three and four airports if each airport is connected by return flights. They sketch a diagram to help to make sense of the problem. They tabulate information and look for patterns. They predict how many flights will be needed for five airports, then six, then ten, testing their predictions. They find a general rule and express it in words, then using symbols.
Assessment focus: Ma1, Problem solving
Look for evidence of children explaining problems in their own words to clarify what is involved, and representing problems using number sentences and diagrams. Look for children identifying each of the calculations that should be performed to solve a numerical problem. Look out for children who start with a simple case: for example, starting with two airports then three airports, when they investigate how many different flights would be needed to connect different numbers of airports. Look for evidence of children checking their results and ensuring that they make sense in the context of the original problem.
Children relate fractions to multiplication and division. They express 18 as 1 1/2 of 12, or 500 ml as 5/4 of 400 ml. They simplify fractions by cancelling common factors. They divide the numerator and the denominator of, say, 14/35 by 7 to simplify it to 2/5. They order fractions by converting them to fractions with a common denominator or by using a calculator to find the decimal equivalents. For example, they order 3/5, 2/3 and 7/15 by converting them to a common denominator. Alternatively, they use a calculator to change the fractions to decimals, rounding the decimals as necessary, and considering the position of the decimal numbers on the number line. Children use similar strategies to find a fraction that lies between two given fractions, such as between 2/3 and 4/5. They investigate problems such as: Which would you rather have: 7/9 or 4/5 of the prize money in the school raffle?
Children identify equivalent fractions, decimals and percentages. They recognise that 1/10 = 10% and 1/5 = 20%, so 3/4 = 60%. They shade given percentages of shapes by thinking of the percentage as a fraction. They work out, say, that 45 out of 60 is equivalent to 3/4 or 75%, so that 45 is 75% of 60. They find fractions and percentages of whole-number quantities.
Assessment focus: Ma2, Fractions, decimals, percentages, ratio and proportion
Look for evidence of children recognising equivalence between simple fractions, decimal numbers and percentages such as 1/10, 0.1 and 10%, and beginning to convert other fractions into tenths and hundredths in order to find equivalent decimal numbers and percentages.
Children use the vocabulary of ratio and proportion to describe the relationships between two quantities. They work out the required quantities for a recipe for seven people when given the quantities for two people. They study repeating bead patterns such as three red, two blue, three red, two blue, ... and work out how many blue beads are needed for 15 red beads. They solve problems such as:
Two letters have a total weight of 120 grams. One letter weighs twice as much as the other. Write the weight of the heavier letter.
The distance from A to B is three times as far as from B to C. The distance from A to C is 60 centimetres. Calculate the distance from A to B.
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?
There are 45 children at the gym club. There are two boys for every three girls. How many boys are at the gym club?
Assessment focus: Ma2, Solving numerical problems
Look for children who solve simple ratio problems. Look for children who solve them by scaling up or by using trial and improvement. For example, when solving the problem ‘Two letters have a total weight of 120 grams. One letter weighs twice as much as the other. What is the weight of the heavier letter?’, they might use 10 + 20 = 30, 20 + 40 = 60, 30 + 60 = 90 and 40 + 80 = 120. Look out for those children who begin to use multiplication to solve ratio problems. In this example, they might recognise that the weight of the heavier letter is 2/3 of the combined weight, and calculate 120 ÷ 3 × 2.
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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Compare your table or diagram with those of others around you. Discuss the different representations you have used. Which do you think is more effective? 30 children are going on a trip. It costs £5 including lunch. Some children take their own packed lunch. They pay only £3. The 30 children pay a total of £110. How many children take their own packed lunch? |
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Give me a sentence that explains the general rule. |
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Sam used a calculator to work out 15% of £40, and got the answer of £5.50. How would you have tackled this problem? What might Sam have done wrong? 50 000 people visited a theme park in one year. 15% of the people visited in April and 40% of the people visited in August. How many people visited the park in the rest of the year?Write in the missing digit:  92 ÷ 14 = 28 |
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What fraction of 6 is 3? What fraction of 6 is 6? |
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What is 1/3 of 9, 12, 15, ...? How did you work it out? |
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What is twenty out of forty as a percentage? Make up some more questions like this for me to answer. You must tell me whether I am right or wrong.  |
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A recipe for 3 people needs 75 g of butter. How much butter do you need for 2 people? 8 people? Peanuts cost 60p for 100 grams. |
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Suggest ways in which Peter could improve his method for finding 5% of a quantity. |
| Activities | PDF 1MB |
| Activity 69 - Coins on the table |
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Objectives for Springboard intervention unit |
Springboard unit |
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Express a quotient as a fraction or as a decimal when dividing a whole number by 2, 4, 5 or 10 |
Springboard 6 Unit 3 (PDF 1.4MB) |
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Express percentages as simple fractions and simple fractions as percentages |
Springboard 6 Unit 8 (PDF 1.4MB) |
| Diagnostic focus | Resource |
| Has difficulty interpreting a remainder as a fraction | 2 Y6 ×/÷ DfES 1160-2005 (PDF 109KB) |
| Interprets division as sharing but not grouping | 3 Y6 ×/÷ DfES 1161-2005 (PDF 94KB) |
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