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Objectives |
Assessment for learning |
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What are the important things to remember when you solve a word problem? |
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Count back in twos from six. |
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What numbers could go in the boxes to make these correct?
Write a statement using two negative numbers and the 'greater than' symbol. Write a statement using a positive number and a negative number and the 'less than' symbol. |
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What does the digit 7 represent in each of these numbers: 3.7, 7.3, 0.37, 3.07?
What if I put a pound sign in front of each of these numbers? |
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Work out 56 |
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Show me how you would calculate 257  47 35.Give an example of a calculation where it is helpful to change pounds into pence before you work out the calculation. |
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The product is 36. What two numbers have been multiplied together? If 7 × 8  56, what is 7 × 9?
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Give me an example of a two-digit by one-digit multiplication you could do mentally. Give me an example of a similar multiplication where you would use a written method. Describe a problem that will give you a remainder that you will need to round up. What is the largest remainder you can have when you divide by 6? |
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Use a calculator to add these amounts of money: 62p,  1.50, 550p, 15, 8p. What will you have to do before you can add them using a calculator?What does the answer in the display, 22.7, mean? My calculator display says 1.2. What was the question? What other possibilities are there? What would the display of 1.2 mean if you were working with pounds? With metres? |
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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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What was the main difference between Jyoti's method and your method? These two displays which children have made show all the ways of making 50p using only silver coins. Which display is organised in a better way? Why? |
Children rehearse counting forwards and backwards and developing number sequences involving positive and negative numbers. They start their own sequence and challenge others to continue it, describing the rule and pattern. They extend number sequences, including those involving decimals in the context of money and length. For example, they count in steps of 50p in a sequence such as £0.50, £1.00, £1.50, £2.00, or in steps of 25 cm in a sequence like 1.25 m, 1.5 m, 1.75 m. They predict numbers that will occur in the sequence and ask What if? questions, such as:
What would my sequence look like if I counted in steps of 20p from £1.10?
They recognise that to enter £1.10 in a calculator they enter 1.1. They use the constant function to check their predictions (e.g. by entering 1.1 [+] [+] 0.2 the calculator counts in steps of 0.2 every time the [=] key is pressed). They relate this back to counting in steps of 20p in the context of money.
This offers an opportunity to assess children's understanding of numbers and the number system and their ability to recognise a wide range of sequences, such as being able to write in the missing numbers in the sequence: 480, 240, 
, 60, , 15
In particular, look for children being able to continue sequences with decimals.
Children continue to derive pairs of numbers that total 100. They extend this to find pairs of multiples of 50 that total 1000, such as 150 + 850. They continue to add and subtract two-digit numbers mentally, choosing their strategy based on the numbers involved. They investigate how many different ways they can complete an equation such as - 47 = 9, and they find the largest and smallest possible differences.
This offers an opportunity to assess mental methods as well as offering an opportunity to show reasoning skills. In particular, look for children being able to calculate the complements of 100 and being able to add and subtract two-digit numbers. In reasoning, look for children being able to review what they have achieved and suggesting a similar problem to investigate.
They solve mathematical problems and puzzles, such as:
Lisa went on holiday. In 5 days she made 80 sandcastles. Each day she made 4 fewer castles than the day before. How many sandcastles did she make each day?
Children continue to refine their written methods of calculation to make them more efficient. Those who can confidently explain how an expanded method works move on to a more compact method of recording, while others continue with an expanded method. They tackle calculations with different numbers of digits: for example, they find 754 + 86 and 518 - 46. They begin to add two or more three-digit sums of money, first adjusting them from pounds to pence and then moving on to using decimal notation: for example, they find the total of £4.21 and £3.87. They also begin to find the difference between amounts of money, such as £7.50 - £2.84. Before they begin a calculation they use rounding to estimate the answer.
This offers an opportunity to assess written methods for addition and subtraction by asking children to evaluate the efficiency of the written methods that are being used. Look for children having an efficient written method for addition and subtraction with three-digit numbers.
Children continue to develop written methods to multiply and divide TU by U. They estimate the answer before calculating, and recognise how partitioning helps to break down the calculation into manageable parts. They give a remainder as a whole number, recognising that it represents what is left over after a division and is always smaller than the divisor. They make sensible decisions about rounding up or down after division according to the context. They recognise the need to round up with a problem such as:
A box holds 6 cakes. How many boxes will be needed for 80 cakes?
They recognise the need to round down with:
I have £62. Tickets cost £8 each. How many tickets can I buy?
This offers an opportunity to assess children's ability to solve numerical problems. In particular, look for children being able to use both multiplication and division. Also look for children being able to interpret a remainder in a division problem.
Children solve one-step and two-step word problems involving all four operations, some in the context of money, measures or time. For each problem they select relevant information and the calculations they need to do. They also decide whether to calculate mentally, use jottings to keep track of the calculation, use a written method or use a calculator. They learn how to set out a solution to a word problem by recording the calculation they have done. They communicate the main points of their solutions to each other, comparing their approaches and explaining their decisions.
This offers an opportunity to assess the ability to solve numerical problems by seeing whether children are able to explain that their results are reasonable. Look for children being able to solve two-step problems that involve addition and subtraction.
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Activities |
PDF 923KB |
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Activity 42 - Stickers |
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Activty 45 - Sandcastles |
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Objectives for Springboard intervention unit |
Springboard unit |
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Choose and use appropriate operations (including multiplication and division) to solve word problems |
Springboard 4 Unit 6 (PDF 196KB) |
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Understand and use £.p notation |
Springboard 4 Unit 10 (PDF 231KB) |
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Diagnostic focus |
Resource |
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Does not apply partitioning and recombining when multiplying and confuses the value of two digit numbers |
4 Y4 ×/÷ |
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Interprets division as sharing but not grouping |
3 Y6 ×/÷ |
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Does not recognise when a remainder is significant in the decision about whether to round up or down |
6c Y4 ×/÷ |
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Discards the remainder: does not understand its significance |
6b Y4 ×/÷ |
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Writes a remainder that is larger than the divisor |
6a Y4 ×/÷ |
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Does not make sensible decisions about when to use calculations laid out in columns |
3 Y4 |
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Has difficulty with adding three numbers in a column |
4 Y4 |
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