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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 secure understanding of the value of each digit in decimal numbers with up to two places. For example, they use coins (£1, 10p and 1p) or base-10 apparatus (with a 'flat' representing one whole) to model the number 2.45, recognising that this number is made up of 2 wholes, 4 tenths and 5 hundredths. They understand the relationship between hundredths, tenths and wholes and use this to answer questions such as:
Which of these decimals is equal to 19/100? 1.9 10.19 0.19 19.1
How many hundredths are the same as three tenths?
Assessment focus: Ma1, Communicating
Look for evidence of children representing numbers in different ways to support their thinking, and for those who refer to the diagram or the apparatus that they have used to help them explain their thinking. Look for children who can represent whole numbers and decimal numbers with up to two decimal places using £1, 10 pence and penny coins, or base-10 materials, and who can use this ability to demonstrate how they know that 2.25 is less than 2.5, for example. Look for those children who use different representations of a number, such as place-value cards and base-10 materials, to represent 17.5, and who can explain how each digit is represented in each model.
Children use images such as bead strings or number lines to help them count in tenths and hundredths from various start numbers. They position decimals on number lines, explaining for example that 2.85 lies halfway between 2.8 and 2.9. They suggest numbers that lie between, say, 13.5 and 13.6. Children create and continue sequences of decimals, for example counting up from zero in steps of 0.2 or backwards from 3 in steps of 0.3. They identify the rule for a given sequence and use this to find the next or missing terms, e.g. finding the missing numbers in the sequence: 1.4, 
, 1.8, 2, 2.2, . They use counting to answer questions such as 0.2 × 6 or 1.8 ÷ 0.3, explaining how they worked out the answer.
Assessment focus: Ma2, Numbers and the number system
Look for children who recognise number patterns and for children who can create, describe and continue sequences of decimal numbers. Look for evidence of children who can predict whether a larger number will or will not be in a given sequence. For example, look for children who can say whether 5.2 would be in this sequence of numbers, 0.4, 0.8, 1.2, 1.6, 2.0, and who can give the reason behind their answer.
Children partition decimals using both decimal and fraction notation, for example, recording 6.38 as 6 + 3/10 + 8/100 and as 6 + 0.3 + 0.08. They write a decimal given its parts: e.g. they record the number that is made from 4 wholes, 2 tenths and 7 hundredths as 4.27. They apply their understanding in activities such as:
Children extend their understanding of multiplying and dividing by 10, 100 or 1000 to decimals. They use digit cards and a place value grid to practise multiplying and dividing numbers by 10, 100 and 1000, e.g. moving each digit two columns to the right to work out that 132 ÷ 100 = 1.32. They recognise that as each digit moves one column to the right, its value becomes 10 times smaller (and the reverse for multiplication). They apply this understanding in a range of activities such as:Find the missing number in 17.82 -
= 17.22.
Play 'Zap the digit': In pairs, choose a decimal number to enter into a calculator, for example 47.25.
Take turns to 'zap' (remove) a particular digit using subtraction. For example, to 'zap' the 2 in 47.25, subtract 0.2 to leave 47.05.
Find the missing number in 0.42 ×
Play 'Stepping stones': Work out what operation to enter into a calculator to turn the number in one stepping stone into the number in the next stepping stone.
Children extend written methods for addition to include numbers with one and two decimal places. They use their understanding that 10 tenths make one whole and 10 hundredths make one tenth to explain each stage of their calculation, for example, to add 72.8km and 54.6km.
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8 tenths add 6 tenths makes 14 tenths, or 1 whole and 4 tenths. The 1 whole is 'carried' into the units column and the 4 tenths is written in the tenths column. |
With subtraction of three-digit numbers and decimals, some children may be ready to use more compact methods. The number of steps in the vertical recording of the 'counting up' method is reduced.
For 326 – 178, they extend their understanding of 'difference' by counting up from 178 to 326, initially using an empty number line and then moving on to vertical recording.
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The examples below work towards the decomposition method.
Example: 563 – 248, adjustment from the tens to the ones, or 'borrowing ten'
Discuss how 60 + 3 can be partitioned into 50 + 13. The subtraction of the ones becomes 'thirteen minus eight', a known fact.
Example: 563 – 271, adjustment from the hundreds to the tens, or 'borrowing one hundred'
Discuss how 500 + 60 can be partitioned into 400 + 160. The subtraction of the tens becomes '160 minus 70', an application of subtraction of multiples of ten.
Children continue to rehearse their recall of multiplication and division facts and use these facts and their knowledge of place value to multiply and divide multiples of 10 and 100. They use jottings to record, support or explain mental multiplication and division of TU by U, forging links to the written methods that they are developing and refining.
Example: 38 × 7
38 × 7 = (30 × 7) + (8 × 7) = 210 + 56 = 266
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| The number with the most digits is placed in the left-hand column of the grid so that it is easier to add the partial products. | The next step is to move the number being multiplied (38) to an extra row at the top of the grid. Presenting the grid like this helps children to set out and add the partial products 210 and 56. |
The next step is to represent the method of recording to a column format, but showing the working. Point out the links with the grid method. | Children should describe what they do by referring to the actual values of the digits in the columns (e.g. the first step in 38 × 7 is 'thirty multiplied by seven', not 'three times seven', although the relationship to 3× 7 should be stressed). |
Children use the multiplication and division facts that they know to find factors of numbers, for example, determining that 35 has a factor pair of 7 and 5, so 350 has a factor pair of 70 and 5 or 7 and 50. They use their knowledge of factors for special cases of multiplication and division calculations. For example, to multiply 15 by 6, they work out 15 × 3 × 2 = 4 × 2 = 90, and to divide 72 by 6 they halve it to get 36, then divide by 3. They find common multiples, investigating questions such as:
Children solve a range of one- and two-step word problems, choosing whether to use mental, written or calculator methods. They record their method in a clear and logical way, using jottings and diagrams where appropriate. They compare their methods with others, recognising where another method is more efficient than the one that they chose. They solve inverse operation problems such as 3.42 +What is the smallest whole number that is divisible by 5 and by 3?
Tell me a number that is both a multiple of 4 and a multiple of 6. Are there any other possibilities?
= 10, and word problems such as:Emma saves £3.50 each week. How much has she saved after 16 weeks?
I buy presents costing £9.63, £5.27 and £3.72. How much change do I have from £20?
One bag of sugar weighs 2.2 pounds. How much will 10 bags of sugar weigh?
Zak saves half of his pocket money each month. In one year he saves £51. How much pocket money does he get each month?
Assessment focus: Ma2, Mental methods
As they solve problems and choose the calculation methods to use, look for evidence of the calculations that children perform mentally. Look for children drawing a number line to support their thinking, or jotting down some numbers or interim results to keep track of the calculation. Look out for the addition and multiplication facts that children recall and use to quickly derive subtraction and division facts. Look for children who use their knowledge of place value to work with multiples of ten or with decimal numbers. For example, look for children who use complements to 20 to work out how much to add to 1.3 to make 2, and for children who can use 6 × 4 = 24 to work out 24 ÷ 6 = 4, 240 ÷ 6 = 40 or 240 ÷ 60 = 4.
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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Tell me how you solved this problem |
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Would you use a mental, written or calculator method to solve each of these? Explain your choice. |
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What is the next number in this sequence: 0, 0.2, 0.4, 0.6, 0.8?
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What decimal is equal to 25 hundredths?
Write a number in the box to make this correct: |
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Look at these calculations with two-digit decimals. Tell me how you could work them out in your head. |
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Find two numbers between 3 and 4 that total 7.36. Use a written method to check your answer. |
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Divide 90 by 3. |
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What is the smallest whole number that is divisible by 5 and by 3? |
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Write in the missing number: 3400 ÷ |
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One orange costs 15 pence. How much would five oranges cost? How did you work it out? Could you do it differently? Four bananas cost 68 pence. How much is one banana? Is there another way to do it? Which of these calculations would you work out mentally, using jottings if you wish? 9 × 25 3456 + 1999 6007 – 1995 14 × 6 96 ÷ 8 Why is it possible to solve these mentally? What clues did you look for? Explain your methods. Suggest a subtraction calculation involving four-digit numbers that you would answer by counting on. |
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What calculation can you key into your calculator to solve this problem? A piece of ribbon 2.1 metres long is cut into six equal pieces. How long is each piece? What is the answer? |
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Roughly, what answer do you expect to get? How did you arrive at that estimate? Do you expect your answer to be greater or less than your estimate? Why? Find two different ways to check the accuracy of this answer. |
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Are all the steps of your explanation in the right order? Would your description of your method be more persuasive if you explained why it is particularly suitable for those numbers? Look at this list of the steps to take to solve this problem: A pack of plums costs 68p. Mark bought three packs of plums. How much change did he get from a £5 note? Could the list be improved? How? |
| Activities | PDF 1MB |
| Activity 54 - Joins | |
| Activity 60 - Three digits | |
| Activity 61 - Make five numbers | |
| Activity 62 - Maze | |
| Activity 65 - Age old problems | |
| Activity 66 - Zids and Zods |
| Objectives for Springboard intervention unit | Springboard unit |
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Read, write and order whole numbers to at least 1000 |
Springboard 5 Unit 2 (PDF 305KB) |
| Springboard 5 Unit 2 supplementary (PDF 86KB) | |
| 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) | |
| Calculate a difference mentally by counting up from the smaller to the larger number | Springboard 5 Unit 7 (PDF 305KB) |
| Springboard 5 Unit 7 supplementary (PDF 77KB) | |
| Develop and refine written methods for subtraction, building on mental methods. Reinforce the fact that subtraction is the inverse of addition |
Springboard 5 Unit 8 (PDF 245KB) |
| Springboard 5 Unit 8a Part 1 supplementary (PDF 77KB) | |
| Springboard 5 Unit 8a Part 2 supplementary (PDF 75KB) | |
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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 |
| None currently available |
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