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

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 I know what I need to do to help me solve a problem and then I can work out the answer I can show how I solved a problem or puzzle and explain steps in my working	What do you need to find out? How do you know that you need to add/multiply/double/halve? What helped you to decide how to do this calculation? Could you do it another way? Tell me how you solved the puzzle. Why did you write that number sentence? Is there another way you could write it? Write as many different ways as you can of making 12. Record your working so that a friend can follow it. How could you check that you have found all the possibilities?
Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence I can use calculations to solve problems and I know which calculation to use	How did you know it was a multiplication/division? How did you work it out? If you had three 5p coins, how much money would you have? How could you write that down? What sort of calculation is it? What if, instead of three 5p coins, you had four 5p coins. How would your number sentence change? How would the answer change? Make up a story that would mean that you need to work out: 15 + 24, 18 ÷ 3, 9 × 5.
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 sharing to work out divisions and can explain what I did	Suppose 15 pencils were to be shared out between three children. How many pencils would each child get? Explain to me how you could work it out. Explain to me how you would work out 20p divided equally among five people. How could you write it down? What about 18 sweets between two people? How many more sweets would you need to give them 10 sweets each? How many £ 2 coins do you get for £ 20? 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 know how to write number sentences for multiplication and for division I can explain what different number sentences mean	Show me on the number line what 3 × 8 would look like. What about 5 × 8? How different would 8 × 5 look on a number line? I have 20 counters here. Show me what 20 ÷ 5 means with these counters. Explain how you worked out the missing number in this number sentence: 24 ÷ = 6 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 know some of my doubles up to 20 I can work out the rest and some others too	Which doubles do you just know? What number must I double to get 10? 16? 22? I double a number and get 20. What number did I start with? You know that double 15 is 30. How could you use this to work out double 16? What about double 17? What about double 14?
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 some of my times-tables for 2, 5 and 10 I can use counting or other strategies for those I don't know I know that multiples of 5 end in 5 or 0	What tips would you give someone who had forgotten the 10 times-table? How could you use a 10 times-table fact such as 10 × 6 = 60 to work out a 5 times-table fact such as 5 × 6 = 30?
Find one half, one quarter and three quarters of shapes and sets of objects I can find a half or a quarter of a set of objects I can fold a piece of paper into halves or quarters	How could you find one quarter of a piece of string? What about a quarter of two pieces of string? Here is a set of 12 pencils. How many is a quarter of the set? Shade one quarter of this shape.
Listen to a talk by an adult, remember some specific points and identify what they have learned I can remember how to work out a sharing problem	When we share a number of cherries equally among several people, we give out the cherries one by one, saying 'one for you, one for you', and so on, until the cherries are all used up. Sometimes there are some cherries left over, because there are not enough to go round once more. Explain to your partner how you would share 13 cherries equally among four people. How many cherries would be left over?

Learning overview

Children know doubles of numbers to 10 and the related halves. They record calculations using × 2 and ÷ 2. They use these facts to find doubles of numbers to 20 using partitioning. For example, they double 15p, using 10p and 5p coins, and matching each coin with an identical coin.

15p in coins with double matching coins

They halve amounts of money in a similar way, replacing two coins of the same kind by one coin. If there is only one coin of a particular type, they replace it with smaller coins of equivalent value, for example replacing a 20p coin with two 10p coins.

Children recognise and write the fraction notation for ¹/₂ and ¹/₄. They fold shapes in half and then in half again to make quarters. They know that four quarters make one whole and that each quarter must be the same size.

Children consolidate finding half of a set of objects and recognise that finding half of a number is the same as dividing it by 2. They find a quarter of a set of objects by sharing them equally among four. For example, they share a set of objects equally among four children and establish that each child has one quarter, or they share 12 'tomatoes' equally onto the quarters of a 'pizza' and count what one quarter of 12 is. They use the appropriate vocabulary related to halves and quarters.

Children establish multiplication and division facts for the 2, 5 and 10 times-tables by counting in twos, fives and tens. If necessary, they use practical apparatus, counting or drawing to support them. They respond to questions such as:

Count on seven twos. Where do you finish?
What are eight fives?

They use patterns and relationships to support their learning of these facts. For example, they remember that all numbers in the 2 times-table are even and that numbers in the 5 times-table must end in 0 or 5. Children chant the tables in unison, using rhythm and the patterns of words to help them to commit facts to memory. They say:

One five is five.
Two fives are ten.
Three fives are fifteen ...

so that the answer to How many 5s make 30? relates closely to the wording.

Chanting of tables is supported with a counting stick or number line. This helps to establish the relationship between the increasing steps and corresponding products.

A number line with 0-10 on the top and 0-50 on the bottom in multiples of 5

Occasional chanting of division tables can help to establish both the knowledge of division facts in their own right and the use of the phrase 'divided by'. For example:

Five divided by five is one.
Ten divided by five is two ...

Children relate division to multiplication. For example, they recognise that one way to understand 30 ÷ 5 is as: How many 5s make 30? and use the 5 times-table to answer this.
Children use their knowledge of multiplication and division facts to answer simple word problems such as

Seven pairs of socks go in the wash. How many socks is this?
How many 5p coins are needed to make 45p?
What is the next multiple of 5 after 25?

They record the necessary calculation using the appropriate symbols.

Children use sharing to answer division questions; for example, they find 24 ÷ 3 by sharing 24 counters equally into 3 pots. They experience divisions that give rise to remainders, such as:

Three friends share 16 marbles equally. How many marbles does each friend get? How many marbles are left over?

Children tell division and multiplication stories to accompany calculations such as 20 ÷ 5, 4 × 10.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 645KB
Activity 23 - At the toy shop

Intervention programmes

Springboard unit

None currently available

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

Diagnostic focus	Resource
Does not use partitioning to find double twelve or double thirty five	4b Y2 ×/÷ DfES 1146-2005 (PDF 68KB)
Does not use knowledge of doubles to finding half of a number	5 Y2 ×/÷ DfES 1147-2005 (PDF 86KB)
Is not systematic when sharing into equal groups using a 'one for you' approach	6 Y2 ×/÷ DfES 1148-2005 (PDF 96KB)

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