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

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 explain how I solved a problem and say why I did it that way	What information did you use to solve the problem? How did you decide which calculations to do? Could you have solved it in a different way? How is your method different from Judi's method?
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 know which numbers are odd and which are even	Give the children three digit cards, including 0, for example: 3 6 0 What numbers can you make using two or three of these digits? Write down each number you make. Read those numbers to me. Can you write the largest of the numbers in words? Which of your numbers are odd and which are even? 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 explain what each digit in a two-digit number stands for I can partition numbers in different ways	[Show number cards for 19 and 91.] Which of these numbers is nineteen? How do you know? What does the other one say? How are they the same/different? How many tens are there in 60? Use this to partition the number 67. Show me two other ways you might partition this number.
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 some numbers in my head I can add and subtract bigger numbers using practical equipment or by writing notes to help me	What is 48 + 5? How did you work it out? What is 48 + 50? How did you work this out? How do you know that the answer is not 53? Could you write something or use apparatus to help you explain?
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 know how to write number sentences using the symbols + , –, × , ÷ and = I can explain what different number sentences mean	What number goes in the box to make this calculation correct? ÷ 2 = 7 How do you know? Can you make three different number sentences using 16, 7 and 23 with = and any of the four operation symbols? Can you change the three numbers to make this into a different problem for someone else to solve? How will you know if their answer is correct?
Speak with clarity and intonation when reading and reciting I can speak clearly to the class or group when showing and explaining how I solved a problem or my method for a calculation	Can you explain your method clearly so that someone else in the class could use it to solve another problem like this?

Learning Overview

Children build on their knowledge of reading and writing two- and three-digit numbers. They know that 300, for example, has a zero in the tens and units columns. They understand that when they write two hundred and sixty-five the zeros are replaced: in the tens column by 6, to give sixty; and in the units column by 5, giving 265.

Cards showing a three digit number partitioned

They use practical equipment such as 100-squares and arrow cards to develop and support their understanding. For example they select arrow cards for the numbers 10, 50, 90 and explain why there is only one card for each of these two-digit numbers.

They partition two-digit numbers in different ways, for example:

25 = 20 + 5

25 = 10 + 10 + 5

25 = 10 + 9 + 6

25 = 19 + 6

They find missing numbers in calculations such as 37 = 30 + 30 + square + 2.

Based on their experience of counting objects, children estimate the number of objects in a set. For example, having counted how many counters fill a cup, they estimate the number of counters in a cup that is about half full. They discuss and compare estimates and explain how the estimate was reached.

Children count on from and back to any number in ones, including across tens and hundreds boundaries. They count in tens across hundreds boundaries, using equipment such as base-ten apparatus, coins or a calculator to secure their understanding. Children use their understanding of partitioning and place value to explain the effect on the digits of adding or subtracting 10 to or from a number. They explain that we can add or subtract 9 to or from a two-digit number by adding or subtracting 10 then adjusting. They illustrate why this works, for example using a 100-square or number line to demonstrate their understanding.

Children understand and use the term difference and find or describe the difference between two numbers practically. They count how many more cubes there are, say, in a tower of 15 cubes than a tower of 11 cubes to find the difference between 15 and 11. They find how much they need to count on from 29 to reach 34 to find the difference between 29 and 34. Children learn that finding the difference involves comparing two numbers and either counting on from the smaller number or subtracting the smaller number from the larger number. They demonstrate this on a number line. They record these calculations as addition or subtraction statements, for example:

29 + square = 34

34 – 29 = square

Children identify how much to add to any two-digit number to reach the next multiple of 10, using their knowledge of number bonds to 10; for example, they solve 32 + square = 40. They find as many ways as possible to complete a missing-digit calculation such as square 1 + square = square 0, recording their results in a logical way and explaining the patterns and relationships in their results.

Children add or subtract multiples of 10 by counting in tens. For example they work out 84 – 30 by counting back in tens: 74, 64, 54. Children use a 100-square or jottings on an empty number line to support their method; they then visualise the numbers and dispense with the support. Children recognise patterns in examples such as 90 – 20 = 70 and 9 – 7 = 2 and use their knowledge of number bonds to remember and recall the sums and differences of multiples of 10.

Children solve word problems using any one of the four operations. Given the problem of sharing 15 grapes equally among three people, for example, they identify an appropriate operation and record the solution as a number sentence. They use equipment, jottings, drawings or symbols to support their method. They record their work, describe their own method and compare it with others' methods.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities
None currently available

Intervention programmes

Springboard unit

None currently available

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

Diagnostic focus	Resource
Does not relate finding the difference and complementary addition to the operation of subtraction	4 Y2 /- DfES 1125-2005 (PDF 78KB)
Does not readily use pattern to support calculating	6 Y2 /- DfES 1127-2005 (PDF 81KB)
Makes mistakes when counting using teen numbers and/or crossing boundaries	1 Y2 /- DfES 1122-2005 (PDF 67KB)

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