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| Objectives Children's learning outcomes are emphasised | Assessment for learning |
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Tell me how you solved this problem What does the answer to this calculation tell you? Asim and Mike both buy 12 cans of lemonade.
Asim buys 3 packs of 4 cans at
Mike buys 2 packs of 6 cans at Mike says to Asim: 'You paid 50p more than me.' Is Mike correct? Circle Yes or No. Explain how you know. On Sports Day children get points for how far they jump. Joe jumped 138cm. How many points does he get? Sam said: 'I jumped 1.5 metres. I get 4 points.' Give a reason why Sam is correct
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A fruit pie costs 55 pence. What is the cost of three fruit pies?
Some children go camping. It costs How much will each child have to pay for the 6 nights? There are 70 children. Each tent takes up to 6 children. What is the least number of tents they will need? The table shows the cost of coach tickets to different cities.
What is the total cost for a return journey to York for one adult and two children? How much more does it cost for two adults to make a single journey to Hull than to Leeds? |
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Write a decimal that contains 3 units and 7 hundredths I started with a number and rounded it to the nearest whole number. The answer was 13. What number could I have started with? Write a number that is bigger than 0.3 but smaller than 0.4. Some children run a 100 metres race on Sports Day. Here are their times in seconds.
What is the winner's time? Who has the time nearest to 16 seconds? |
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Write the next number in this counting sequence: 8.7, 8.8, 8.9, ... Create a sequence that includes the number 1.6. Describe your sequence.
Here is part of a sequence: 3, 2.7, 2.4, How can you find the missing numbers? |
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Multiply 60 by 50. |
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Look at these calculations with two-digit decimals. Tell me how you could work them out in your head. What other method could you use? |
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There are 12 pencils in a box. A school buys 24 boxes. How many pencils does the school buy? Talk me through your method. Write in the missing digits to make this correct.
Calculate 847 ÷ 7. Roughly, what answer do you expect to get? How did you arrive at that estimate? Do you expect your answer to be less than or greater than your estimate? Why? Look at these worked examples. Is this one correct? How do you know? How could we put it right? |
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Find the total of 1.58m, 79cm and 1.23cm using a calculator. Did you key in the numbers as 1.58, 79 and 1.23? Why not? What answer does the calculator give? What is the total of the three lengths? |
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Roughly, what answer do you expect to get? How did you arrive at that estimate? Is this calculation correct? How do you know? |
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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? |
Children describe how to find or place decimals to two decimal places on a number line; for example, they explain that 3.72 is between 3 and 4 and that it lies 2 hundredths along from 3.7. They round decimals to the nearest whole number, recognising that 3.72 is closer to 4 than to 3, so 3.72 rounded to the nearest whole number is 4. They order a set of decimals such as 5.51, 3.75, 7.35, 5.73, 3.77, appreciating that the most significant digit defines the size of a number and is the leftmost non-zero digit.
They appreciate the role of zero as a placeholder; for example, they write the number 'one and four hundredths' as 1.04 and can place it appropriately on a number line from 1 to 2. They use number lines to solve problems such as:
State a number that lies between 4.1 and 4.2.
Which number lies exactly halfway between 8.2 and 8.8? 6.35 and 6.75? 1.2 and 1.5?
Place a digit in the box so that the number 3. 
4, when rounded to the nearest whole number, is 3. How many possibilities are there?
Children count in decimal steps, for example in steps of 0.4 or 0.09. They compare these sequences to those involving whole numbers, comparing, for example, the count 0.4, 0.8, 1.2... to the count 4, 8, 12... They use this relationship to answer related questions such as 0.4 × 7 (Where do we land after 7 hops of 0.4?) or 3.2 ÷ 0.4 (How many hops of 0.4 are needed to reach 3.2?). They count using measures, for example in steps of 0.2 kg.
This allows for the opportunity to assess fractions, decimals, percentages and ratio, and in particular the ability to order decimals. Look for children being able to order decimals to three decimal places.
Children use a calculator to solve one-step and two-step word problems involving decimals in the context of money and measures. They solve problems such as:
£1 = 1.8 US dollars
£1 = 1.47 euro
£1 = 210.9 yen
Children clear the calculator display before entering a calculation. They recognise the need to be consistent with units when entering money and measures. They interpret the answer shown on the calculator display appropriately (recognising, for example, that a display of 2.4 in the context of money represents £2.40) and give the answer using correct units where appropriate. They use rounding to estimate and check their answers.
This allows for opportunities to assess the ability to solve numerical problems and in particular checking the reasonableness of results. Look for children being able to justify the reasonableness of an answer through a context and through the size of the numbers.
Children use their understanding of whole number and decimal place value to extend written methods for multiplication and division (including TU×TU, U.t×U and HTU×U).
Extending written methods for multiplication and division
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Process |
Example |
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For TU×TU, estimate first. Start with the grid method. The partial products in each row are added, then the two sums at the end of each row are added to find the total product. The first column becomes an extra top row as a stepping stone to the method below. |
56 × 27 is approximately 60 × 30 = 1800
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When children are confident, reduce the recording, showing the links to the grid method above. |
56 × 27 is approximately 60 × 30 = 1800
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For TU÷U, begin with 'chunking', which is based on subtracting multiples of the divisor. Chunking is useful for reminding children of the link between division and repeated subtraction. However, chunking is inefficient if too many subtractions have to be carried out. When children understand the principles, encourage them to reduce the number of steps and to subtract the largest possible multiples. |
196 ÷ 6
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The key to the efficiency of chunking lies in the estimate that is made before the chunking starts. Estimating for HTU÷U involves multiplying the divisor by multiples of 10 to find the two multiples that 'trap' the HTU dividend.
Estimating has two purposes: to check the answer after the calculation, and to help to choose a starting point for the division.
Children who have a secure knowledge of multiplication facts and place value should be able to move on quickly to more efficient recording.
Efficient recording
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Process |
Example |
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To find 196 ÷ 6, we start by multiplying 6 by 10, 20, 30... to find that 6 × 30 = 180 and 6 × 40 = 240. The multiples of 180 and 240 trap the number 196. So the answer to 196 ÷ 6 is between 30 and 40. We start the division by first subtracting 180, leaving 16, and then subtracting the largest possible multiple of 6, which is 12, leaving 4. |
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Children use written calculations (and work methodically) to solve problems such as:
1 ÷ 7 has no remainder.This offers an opportunity to assess written and calculator methods. Look for children being able to find ways of making their method more efficient and being able to multiply a simple decimal by a single digit.
Children solve word problems and number puzzles using all four operations. They record their methods clearly and logically using jottings or diagrams where appropriate. They explain their method and justify their choices. They solve problems such as:
+ + = 1.Find different ways of doing it, including some that use numbers with two decimal places.This offers an opportunity for children to show their reasoning and in particular to search for solutions by trying out ideas of their own. Look for children being able to justify their answers, and to make statements such as 'finding decimals to make the answer 1 is the same as finding single-digit numbers to make the answer 10'.
| Activities | PDF 1MB |
| Activity 54 - Joins | |
| Activity 60 - Three digits | |
| Activity 61 - Make five numbers | |
| Activity 65 - Age old problems |
| 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) | |
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Use decimal notation for tenths and hundredths |
Springboard 5 Unit 5 (PDF 305KB) |
| Springboard 5 Unit 5 supplementary (PDF 88KB) | |
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Know the three- and four-times tables |
Springboard 5 Unit 9 (PDF 269KB) |
| Springboard 5 Unit 9 supplementary (PDF 110KB) | |
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Develop and refine written methods for multiplication (two- or three-digit x single-digit) |
Springboard 5 Unit 10 (PDF 269KB) |
| Springboard 5 Unit 10 supplementary (PDF 63KB) |
| Diagnostic focus | Resource |
| 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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1.20 for each pack.
, 1.8, 1.5, 
400
2.7, half of 5.6, double 0.34)
of 150g); interpret the display correctly in the context of measurement
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