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Year 3 Block A - Counting, partitioning and calculating Unit 2

Objectives Children's learning outcomes are emphasised	Assessment for learning
Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and diagrams I can explain how I solve problems	Tell me how you solved this problem. Did you make any notes or drawings to help you? Can you describe them to me? Show me how to solve this problem using practical objects. What is the cost of 12 stamps at 5p each? Draw me a picture to show how to solve the problem. Why is this a good mental method for adding 19? What is the difference between adding 19 and subtracting 19 using this method? Show me why this is, using a 100-square.
Partition three-digit numbers into multiples of 100, 10 and 1 in different ways I can split a number into hundreds, tens and ones I can explain how the digits in a number change when I count in 10s or 100s	Start at 93 and count back in tens. What will be the smallest number that you reach on a 100-square? Will 54 be one of the numbers you would say? Why not? What do you look for when finding a number 100 less than (or 100 more than) a given number? Count on in tens from 312. Which digits change? Why does the ones (units) digit not change? When does the hundreds digit change, and what happens to the tens digit in this case? What happens when you count back? If we count in 100s from 1, what is the pattern? Is this the same or different when we count from 11 or 111?
Round two-digit or three-digit numbers to the nearest 10 or 100 and give estimates for their sums and differences I can round numbers to the nearest 10 or 100 and estimate a sum or difference	Why does 76 become 80 when it is rounded to the nearest 10? Why does 249 become 200 when rounded to the nearest 100? Round 249, 243 and 245 to the nearest 10. Explain why you decided to round 249 and 245 up to 250, and 243 down to 240. The answer to 44 + 38 is less than 100. Give me a better estimate. How did you do it? Why is 38 + 24 approximately 60? Why is 51 – 27 approximately 20?
Derive and recall all addition and subtraction facts for each number to 20, sums and differences of multiples of 10 and number pairs that total 100 I know the sum and difference of any pair of numbers to 20 I can add and subtract multiples of 10 or 100 in my head I know number pairs that sum to 100	What is 3 + 4, 30 + 40 and 300 + 400? What is 8 – 5, 80 – 50 and 800 – 500? How do you know? Two numbers add up to 20. They have a difference of 2. What are the numbers? What must you add to 62p to make £ 1? I cut 53 cm off 1 metre of string. How long is the piece that is left?
Add or subtract mentally combinations of one-digit and two-digit numbers I can add or subtract one-digit and two-digit numbers in my head (e.g. 62 + 7, 7 + 45, 48 – 6, 60 – 8)	What is 46 + 8? Explain how you did it. How would you add 18 to 46? What is 73 – 7? Explain how you did it. How would you subtract 17 from 73? Think of two numbers that have a difference of 9. Write a number sentence to show this. Now find and record some more pairs of numbers with a difference of 9. What is 58 + 30? What is 58 + 29? How do you know? What is 58 – 30? What is 58 – 29? How did you work these out? Show me on an empty number line.
Multiply one-digit and two-digit numbers by 10 or 100, and describe the effect I can multiply by 10 or 100 and say what happens to the number I multiply	Multiply 4 by 10. Multiply the answer by 10. What has happened to the value of the digit 4? Can you explain what happens to the 4 when we multiply 4 by 100? What number is 10 times more than 70 tens? What is 10 times bigger than 23?
Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000 I know my tables for 2, 3, 4, 5, 6 and 10	Count on in fours from zero. Now count back to zero.This time, count on seven fours from zero. Show me seven hops of four from zero on the number line.How can you work out the 4 times-table from the 2 times-table? The 6 times-table from the 3 times-table? What is the relationship between 4 × 7 = 28, 6 × 7 = 42 and 10 × 7 = 70?
Follow up others' points and show whether they agree or disagree in a whole-class discussion In a discussion I can share my views with others in the class and follow up their points	Is this calculation correct? John thinks that it is wrong. Do you agree or disagree? Why do you think so? Mary has just told us how she subtracted 39 from 76. Use Mary's method to subtract 59 from 92. What diagram did you draw to help you to solve the problem? Did anyone use a different diagram?

Learning overview

Children continue to count on or back from any number. They know what each digit in a three-digit number is worth and recognise and explain the effect on the digits as they count in 10s or 100s and the impact of crossing boundaries when moving between 10s and 100s, and between 100s and 1000s. Children use their knowledge of the relationship between numbers on a number line to round any two-digit number to the nearest 10 and any three-digit number to the nearest 100.

Children use the vocabulary of estimation and approximation. They estimate the number of items in a container with up to 100 items, for example saying that the number of items is about 35 or that there are between 30 and 40. They use rounding to work out, for example, that to buy four 22p oranges the cost will be a bit more than 80p and count up in 20s and 2s to get the answer.

Children recognise the significance of each digit when adding and subtracting. They continue to add and subtract multiples of 10 and 100 and extend this to adding and subtracting near-multiples .

They work out, for example, 632 + 200 and 632 – 200, and then use their answers to find 632 + 199 and 632 – 201, making notes or identifying the steps on an empty number line.

Children derive sequences in calculations such as 32 – 1 = 31, 32 – 2 = 30, 32 – 3 = 29, ... and corresponding sequences such as 320 – 10 = 310, 320 – 20 = 300, 320 – 30 = 290, ... They describe the patterns they observe and apply them to other sequences.

Children understand that when a one- or two digit-number is multiplied by 10 the digits move one place to the left and that doing this twice is equivalent to multiplying by 100. Children begin to multiply a one-digit number by a multiple of 10, for example working out 7 × 50 by finding 7 × 5 then multiplying the answer by 10. They use their knowledge of inverse operations to work out, for example, 350 ÷ 50 and 350 ÷ 7.

Children partition two-digit numbers in different ways; for example, they recognise that 75 can be partitioned into 70 + 5 or 60 + 15. They use partitioning flexibly to support calculation strategies, for example partitioning 75 into 60 + 15 in order to subtract 28 by subtracting 20 from 60 and 8 from 15. They solve problem involving partitioning, such as: If two people share £ 38 and one person gets £10 more than the other, how much do they each get?

They use diagrams to help them solve these problems and record their solutions.

Children understand the term difference .They appreciate that Find the difference between 38 and 52 is equivalent to the question How much greater is 52 than 38? and relate these to the subtraction 52 – 38. They find the difference by counting up from 38 to 52. Children use partitioning to add or subtract mentally one- and two-digit numbers. For example, they calculate 37 + 26 by using 37 + 20 + 6 and 37 – 26 by working out 37 – 20 – 6, recording the steps on a number line. Children begin to check their addition and subtraction with a calculation that uses the inverse operation . They know that subtracting 18 from 34 to get 16 can be checked by adding 18 to 16.

Children solve puzzles and problems that involve all four operations. They use their knowledge of multiplication and division to find the cost of boxes of six items where each item costs 40p or the number of boxes of four items that can be filled from 30 items. They develop strategies to solve 'think of a number' problems that involve halving and doubling. They explore numbers, looking for pairs that total 30 and have a difference of 12, by listing possible pairs and testing to see if the second criterion holds. Children discuss and explain their methods orally and begin to record using pictures or diagrams. They follow the explanations of others, for example how they solved 'think of a number' problems. They compare different approaches and suggest possible modifications.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 923KB
Activity 28 - Dan the detective

Intervention programmes

Objectives for Springboard intervention unit	Springboard unit
Count on and back in ones and tens Say the number that is 1 or 10 more/less than any given two-digit number Say the number 20, 30 more/less than any given number	Springboard 3 Unit 3 lessons 1 and 2 (PDF 170KB)
Use knowledge that addition can be done in any order Know to start with the larger number when adding Know whether to count on in ones or tens Use known number facts and place value to add/subtract mentally	Springboard 3 unit 5 sessions 1 and 2 (PDF 170KB)
Find a small difference by counting on from the smaller to the larger number Measure and compare lengths using standard units	Springboard 3 unit 6 sessions 1 and 2 (PDF 149KB)

Supporting children with gaps in their mathematical understanding (Wave 3)

Diagnostic focus	Resource
Makes mistakes when counting using teen numbers and/or crossing boundaries Spotlights 2, 3, 4 and 5	1 Y2/- DfES 1122-2005 (PDF 67KB)
Does not relate finding a difference and complementary addition to the operation of subtraction	4 Y2/- DfES 1125-2005 (PDF 78KB)
Has difficulty in partitioning, for example, 208 into 190 and 18 and 31 into 20 and 11	2 Y4/- DfES 1129-2005 (PDF 108KB)
Describes the operation of multiplying by ten as 'adding a nought'	3 Y4×/÷ DfES 1152-2005 (PDF 71KB)

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