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

Objectives Children's learning outcomes are emphasised	Assessment for learning
Present solutions to puzzles and problems in an organised way; explain decisions, methods and results in pictorial, spoken or written form, using mathematical language and number sentences I can show and explain clearly how I solved a problem	How did you know what information to use? Where did you decide to start? Is there a pattern in your results? Could you record your results in order to help you see patterns? Have you found all of the ways? Is there a different way to solve the problem?
Read and write two-digit and three-digit numbers in figures and words; describe and extend number sequences and recognise odd and even numbers I can read and write numbers up to 1000 in figures and in words I can explain the pattern for a sequence of numbers and work out the next few numbers in the list	What is the largest number you know how to write in figures? I know a secret sequence. It has the numbers 13, 15, 17, 19 in it. What numbers come next in my sequence? What numbers come before? What clues did you use to work this out? Give me a number greater than 40 that is in my secret sequence. How do you know this number is in my sequence? How could you check? If you count in tens from 32, which digit changes? Why doesn't the ones digit change? If you start with 84 and count back in tens, what would be the smallest number you reach on a 100-square? Would 13 be one of the numbers you say? How do you know?
Count up to 100 objects by grouping them and counting in tens, fives or twos; explain what each digit in a two-digit number represents, including numbers where 0 is a place holder; partition two-digit numbers in different ways, including into multiples of 10 and 1 I can use partitioning to help me to carry out calculations	What numbers go into the boxes? 53 = 30 + 67 – 30 = Can you find two different ways to work out the answer to each of these calculations? 27 + 40 23 – 18
Order two-digit numbers and position them on a number line; use the greater than (>) and less than (<) signs I can write numbers in order and position them on a number line I can use the greater than and less than symbols to show that one number is larger or smaller than another	Give the children six digit cards, including 0 and at least one digit repeated twice, for example: 0 4 5 5 7 8 Make three 2-digit numbers using these cards. Where would they go on a number line? Now make three different numbers using the same cards. Position these on a number line. Look at this number sentence: + = 20 What could the missing numbers be? What is different about this number sentence? + < 20 How would you choose numbers to make it correct? Can you choose numbers to make this correct? 30 > –
Estimate a number of objects; round two-digit numbers to the nearest 10 I can say roughly how many there are in a group of objects	I think of a number and round it to the nearest 10. The answer is 70. What could my number be?
Add or subtract mentally a one-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to add and subtract two-digit numbers I can add and subtract two-digit numbers using practical equipment or written notes to help me	Show me how you could use a number line/bead-string/written notes to work out the answer to these calculations: 38 + 20 49 – 27 58 + 34 72 – 14 Can you work out the answer a different way? Which way do you find most helpful? Why?
Understand that subtraction is the inverse of addition and vice versa; use this to derive and record related addition and subtraction number sentences I know when it is easier to use addition to work out a subtraction	Look at this number sentence: 74 – 13 = 61 Write three more number sentences using these numbers. How do you know, without calculating, that they are correct? What addition facts can you use to help you calculate these? 12 – 5 , 19 – 8 Explain how the addition facts helped you. I think of a number, I subtract 19 and the answer is 30. What is my number? How do you know?
Use the symbols + , – , × , ÷ and = to record and interpret number sentences involving all four operations; calculate the value of an unknown in a number sentence (e.g. ÷ 2 = 6 , 30 – = 24) I can work out the missing number in a number sentence such as 14 + = 35	14 + = 35. What is the missing number? How do you know? What subtraction could you do to find the answer? How many different ways can you find of adding three numbers to make 11? Choose three numbers for the square boxes and use + or – in the circles to make this number sentence correct. = 11
Respond to presentations by describing characters, repeating some highlights and commenting constructively I can listen carefully to someone explaining how they solved a problem, and ask a question or suggest another method	Listen to how the problem was solved. Was your method the same in some way? Did you do something differently? Could you use this method to solve a similar problem? Could you teach someone else to use your method? Which method takes the fewest steps? Which method is easiest to follow?

Learning overview

Children use their knowledge of counting on from or back to zero in steps of 2, 5 and 10 to answer multiplication and division questions such as 7 × 2 and 40 ÷ 5. They understand that one way to work out 40 ÷5, for example, is to find out how many fives make 40. They know that this can be done by counting in fives from zero.
Children describe patterns in the sequences they generate when they count on or back from any two- or three-digit number in steps of 1, 2, 3, 5 and 10. For example, they recognise that when they count in twos the numbers are all odd or all even, whereas when they count in fives the numbers are odd, even, odd etc. They find missing numbers in simple sequences, for example:

square , 48 , 51 ,854 , square , 60, ...

Children count a set of objects by grouping them into twos, fives or tens. They build on this experience to make sensible estimates of sets of objects, explaining their decisions. They round two-digit numbers to the nearest 10 and state, for example, that a pot containing 27 pencils contains about 30 pencils.

Children order a set of two-digit numbers, such as 52, 25, 5, 22, 2, 55. They explain their decisions. They understand and use the < and > symbols; for example, they write a two-digit number to make the statement 56 < square true. They partition two-digit numbers in different ways.

Children use partitioning, counting strategies and knowledge of number bonds to add or subtract a one-digit number or a multiple of 10 to any two-digit number. To work out 86 minus 50, for example, they might partition and calculate:

86 – 50 = 80 + 6 – 50 = 80 – 50 + 6 = 30 + 6 = 36

Similarly, to find the total number of people on a bus with 14 people on the top deck and 8 below, they might use:

14 + 8 = 14 + 6 + 2 = 20 + 2 = 22

Children add or subtract two-digit numbers using practical and informal methods and their knowledge of the relationships between operations. For example, they count back along a number line to find 64 – 25 or count up from 67 to find the answer to 94 – 67. They represent such calculations as number sentences. They calculate the value of an unknown in a number sentence such as square ÷ 2 = 6 or 85 – square = 29. They recognise, for example, that to answer 85 – square = 29 they could use the related addition 29 + square = 85

Children apply their knowledge to solve problems using any of the four operations such as:

Amit spent 24p. He spent 8p more than Amy. How much did Amy spend?Class 2 has the same number of boys and girls. There are 30 children in Class 2. How many girls are there?
Emma went into a shop at 10:30. She came out at 11:15. How long was she in the shop?

Children identify appropriate operations and explain and record their calculations in number sentences. They write their own word problems to match a given calculation such as 72-45. They work individually and in pairs to solve problems and puzzles involving understanding of numbers and operations, for example:

Use 1 , 4 , 5 and + , – , = .
How many different answers can you make?

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 645KB
Activity 20 - Ones and twos

Intervention programmes

Springboard unit

None currently available

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

Diagnostic focus	Resource
Has difficulty in remembering number pairs totalling between ten and twenty, resulting in calculation errors	2 Y2 /- DfES 1123-2005 (PDF 75KB)
Does not link counting in equal steps to the operation of multiplication	2 Y2 ×/÷ DfES 1144-2005 (PDF 71KB)

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