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Year 2 Block E - Securing number facts, relationships and calculating

Objectives Children's learning outcomes are emphasised	Assessment for learning
Identify and record the information or calculation needed to solve a puzzle or problem; carry out the steps or calculations and check the solution in the context of the problem When I have worked out the answer to a problem I can look again at the problem and then check that the answer makes sense	Sam goes to the shop for some buttons. There are two red buttons and four blue buttons on each card of buttons. How many buttons are there on ten cards? What do you need to find out? What was the question that you were asked? So does your answer make sense? How do you know? Could 20 be the answer? Or 40? How do you know? There are 15 apples in a tray. Ling has 4 trays of apples. How many apples does Ling have altogether? Show how you work it out.
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 worked out the answer to a problem and can show the working I did	Kiz worked out the answer to 7×3 on a number line. Show how Kiz could have worked out the answer on this number line. Mr Bell had three pots with four crayons in each pot. How many crayons did he have altogether? Which one of these would you use to work out the answer to the question? A 4 4 B 33 C 4 × 3 D 3 4 Sita worked out the correct answer to 9 × 5. Her answer was 45. Show how she could have worked out her answer. Harry worked out the correct answer to 20 ÷ 5. His answer was 4. Show how he could have worked out his answer.
Represent repeated addition and arrays as multiplication, and sharing and repeated subtraction (grouping) as division; use practical and informal written methods and related vocabulary to support multiplication and division, including calculations with remainders I can use arrays to help me work out multiplication I can do multiplication and division in different ways and show how I do them	Explain how you work out how many dots there are without counting them all. Here are 20 counters. How could you arrange them in equal rows? How could you use a number sentence to show your arrangement? 4 4 4 4 4 =20 Write this addition fact as a multiplication fact. × =
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 numbers in number sentences When I think I have the answer, I can put it in the number sentence and check whether it is correct	What could the missing numbers be? × = 20 ÷ = 5 How can you record the solution to this problem? I am thinking of a number. I divide it by 5 and the answer is 3. What is my number? Make up some 'missing-number' problems for others to solve.
Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves I can double all numbers up to 20 and can find matching halves	I'm thinking of a number. I've halved it and the answer is 15. What number was I thinking of? I'm thinking of a number. I doubled it and the answer is 28. What number was I thinking of? Explain how you know. Write the missing numbers. 5 double and add 3 8 double and add 3 There are 30 children in a classroom. Half of them are girls. How many are boys? Mina has 32 stickers. She gives half to her brother. How many stickers does she give him?
Derive and recall multiplication facts for the 2, 5 and 10 times-tables and the related division facts; recognise multiples of 2, 5 and 10 I know my 2, 5 and 10 times-tables I can work out divisions that go with the tables	Write the missing numbers in the boxes. 5 × 4 = 10 × × 5 = 50 Write the answer: 45 ÷ 5 = Draw rings around all the multiples of 5. 45 20 54 17 40
Find one half, one quarter and three quarters of shapes and sets of objects I can find three quarters of a set of objects or of a shape	Take 20 counters. Can you show me one quarter? Two quarters? Three quarters? Four quarters? What do you notice? Can you write that down in some way? Here is a set of 12 pencils. How many is a quarter of the set? How many is three quarters? Find three quarters of 20 biscuits. Three quarters of 24 buttons. How will you find one quarter of that rectangle? Three quarters? If one quarter of a set of shells is 2, how many shells are in the set? Here is a pizza cut into eight equal pieces. How many pieces are needed for three quarters of the pizza? What is half of this amount?
Adopt appropriate roles in small or large groups and consider alternative courses of action I can work in a group and help the group to think about different ways to do things	There is plenty of squared dotty paper. In your group, discuss how divide this shape into four equal parts.

Learning overview

Children understand and use arrays to represent repeated addition/multiplication. They use counters on a grid to represent '7 lots of 2' and use this to find the answer of 14.

2 rows of 7 counters

They use pegboards to create arrays where rows/columns are in different colours. They record the calculation this represents using repeated addition and multiplication. They explain how an array helps to show multiplication, pointing to the rows and/or columns to describe how they work out the total number of dots/counters to find the answer to the multiplication.

Children derive and learn to recall multiplication and division facts for the 2, 5 and 10 times-tables. They use these facts to respond to oral and written questions such as

40 ÷ 5
What is double 8?
How many 10s make 90?
Half of a number is 6. What is the number?

They become more proficient with using multiplication and division facts to calculate the missing number in number sentences such as:

× 2 = 18

3 × = 15

20 ÷ = 10

Children find doubles of numbers to 20 and corresponding halves and explain their method. They secure their understanding of finding half and quarter of shapes and sets of objects. They count the quarters 'one quarter, two quarters, three quarters, four quarters', and use this to recognise that four quarters are the same as one whole and that two quarters are the same as one half. They shade three quarters of shapes, recognising and recording the fraction notation 3 quarters .

Children find halves and quarters of groups of objects using practical apparatus or diagrams or using knowledge of doubling/halving facts. They find quarters of groups of objects by, for example, sharing objects fairly into the quarters of a circle and use this to find the number of objects in three quarters.

Children solve problems involving multiplication and division, representing the information using apparatus or diagrams. They record the calculation using appropriate symbols. For example:

Patti bought five stickers and paid 30p. The stickers were all the same price. How much did each sticker cost?
A bus ticket costs 25p. How much will five of these tickets cost?
It costs 75p for a child to go swimming. How much does it cost for two children?
Ella's dad washes some cars. He uses 12 buckets of water. Each bucket has 5 litres of water.
How many litres of water does he use altogether?
Ten children can sit at one table. There are 43 children. How many tables are needed so that each child can sit at a table?
A carton of orange fills 6 cups. Mrs Green wants to fill 50 cups with orange. How many cartons of orange does she need to buy?

They also solve puzzles such as:

I have only one sort of coin in my purse. I have 20p. Find different ways that this is possible.
What is the least number of coins that you need to make 97p?

Children identify the operation(s) needed to solve the problem and explain reasoning. They relate the answer found back to the situation and check that it makes sense.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 645KB
Activity 21 - Birthdays

Intervention programmes

Springboard unit

None currently available

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

Diagnostic focus	Resource
Does not focus on 'rows of' or 'columns of', but only sees an array as a collection of ones	3 Y2 ×/÷ DfES 1145-2005 (PDF 81KB)
Does not use partitioning to find double twelve or double thirty-five	4b Y2 ×/÷ DfES 1146-2005 (PDF 68KB)

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