REDBRIDGE VERSION 2014

Year 2 Block E:Three 3-week units

Securing number facts, calculating, identifying relationships

Objectives / Units
1 / 2 / 3
•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 /  /  / 
•Solve problems involving addition, subtraction, multiplication or division in contexts of numbers, measures or pounds and pence / 
•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 / 
  • Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value; find different combinations of coins that equal the same amounts of money

•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 /  /  / 
•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) /  /  / 
•Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves /  /  / 
•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 /  /  / 
•Find one-half, one-quarter and three-quarters of shapes and sets of objects /  /  / 

Vocabulary

problem, solve, calculate, calculation, inverse, answer, method, explain, predict, pattern, order

place value, partition, ones, tens, hundreds, one-digit number, two-digit number, add, subtract, plus (+), minus (–), sign, equals (=), operation, symbol, number sentence, number line

count on, count back, lots of, groups of, equal groups of, grouping, array, row, column, multiply, multiplication, multiplied by (×), multiple, share equally, divide, division, divided by (÷), remainder, round up, round down, double, halve

fraction, part, equal parts, one whole, parts of a whole, number of parts, left over, fraction, one-half, one-quarter, three-quarters, one whole

Building on previous learning

Check that children can already:

•solve one-step problems involving multiplication and division using concrete objects, pictorial representations and arrays with the support of the teacher

•count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 10.

•recognise, find and name a half as one of two equal parts of an object, shape or quantity.

•recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

Year 2 Block E: Securing number facts, calculating, identifying relationships

Extracts from New National Curriculum

The national curriculum for mathematics aims to ensure that all pupils:
 become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
 can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Number – addition and subtraction
Pupils should be taught to:
 solve problems with addition and subtraction:
using concrete objects and pictorial representations, including those involving numbers, quantities and measures
 applying their increasing knowledge of mental and written methods
 recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
 add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
 a two-digit number and ones
 a two-digit number and tens
 two two-digit numbers
 adding three one-digit numbers
 show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
 recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems. / Notes and guidance (non-statutory)
Pupils extend their understanding of the language of addition and subtraction to include sum and difference.
Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10, 10 - 7 = 3 and 7 = 10 - 3 to calculate 30 + 70 = 100, 100 - 70 = 30 and 70 = 100 - 30. They check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (e.g. 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and associativity of addition.
Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.
Number – multiplication and division
Pupils should be taught to:
 recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
 calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
 show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
 solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. / Notes and guidance (non-statutory)
Pupils use a variety of language to describe multiplication and division.
Pupils are introduced to the multiplication tables. They practise to become fluent in the 2, 5 and 10 multiplication tables and connect them to each other. They connect the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations.
Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, to arrays and to repeated addition. They begin to relate these to fractions and measures (for example, 40 ÷ 2 = 20, 20 is a half of 40). They use commutativity and inverse relations to develop multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 = 4).
Number – fractions
Pupils should be taught to:
 recognise, find, name and write fractions 1/3, ¼, 2/4 and ¾ of a length, shape, set of objects or quantity
 write simple fractions for example, ½ of 6 = 3 and recognise the equivalence of 2/4 and ½ / Notes and guidance (non-statutory)
Pupils use fractions as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet as the first example of a non-unit fraction. 4 3
Pupils should count in fractions up to 10, starting from any number and using the and equivalence on the number line (for example, 1 ,1, 1 (or 1 )1), 1 ,1, 2). This reinforces the concept of fractions as numbers and that they can add up to more than one. 2 1 4 2 4 1 4 2 2 1 4 3

2 Block E: Securing number facts, calculating, identifying relationshipsUnit 1

Oobjectives Unit 1 / 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 information I need to use to solve a problem and can describe what I did step by step
I can record it in a number sentence and check if my answer makes sense / What do you think the problem or puzzle wants you to do? What information will you use?
Explain how you recorded your solution.
How could you work out the cost of 3 pencils each costing 5p? How could you write this in a number sentence?
What does this mean? 2 + 2 + 2 + 2 + 2 + 2
Is there another way of recording this?
Make up another problem like this and tell me how to work it out.
•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.
I can use a number line to do multiplication and division. / Look at these jumps on a number line. What does it show? How could you record that? Is there another way that you could record it?
Show me on a number line how you could do:
3 × 4, 2 × 6
Show me on a number line how you could do:
14 ÷ 2, 15 ÷ 3, 20 ÷ 5
Look at these diagrams:

Is 2 × 4 the same as 4 × 2? 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 division as well as addition and subtraction
I can explain what my number sentence means / Look at these problems. What number sentences could you write to record them?
How many tens make 80?
Jo's box is 5 cm wide. Mary's box is twice as wide as Jo's box. How wide is Mary's box?
How many wheels are there on 3 cars?
•Understand that halving is the inverse of doubling and derive and recall doubles of all numbers to 20, and the corresponding halves
I know doubles of numbers up to 10 and I can use what I know to work out halves
I understand the connection between doubling and halving / Calculate quickly:
Two fives 8 × 2 Double 7 Half of 20
Roll these two dice and add the numbers together. Now double your number. What score do you get?
I'm thinking of a number. If I halve it my answer is 9. What number was I thinking of? Explain how you know.
Two identical books cost £12. How much does one book cost? Write a number sentence that shows what you did.
Make up some halving or doubling problems yourself.
•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 can recognise some of the 2, 5 and 10 times-tables and can explain the patterns I see
I can use these patterns to see if other numbers belong to the sequence / Look at the numbers in the 5 times-table. What do you notice? If we carried on, what do you think the next number would be? If we carried on, do you think the pattern would continue? How do you know?
Think of a number bigger than 100 that would be in the 5 times-table if we carried on. Why do you think that number would be in the table?
•Recognise, find, name and write fractions – 1/3, ¼, ½, ¾ of a length, shape, set of objects or quantity.
I can use my knowledge of halving numbers to help me to work out half and a quarter of a set of objects or a shape
I can also work out three-quarters / Explain how we could find one quarter of this set of 12 pencils? What about three quarters?
Shade more squares so that exactly half of the shape is shaded.

How could we give someone half of 20p if we had one 20p coin? What about half of 12p if we had one 10p and two 1p coins?
In PE, can you turn through a quarter-turn clockwise and anticlockwise? Now make a three quarter turn.
How could we work out half of three equal strips of paper?
Make up some problems of this sort for your group to solve.
  • Write simple fractions e.g. ½ of 6 = 3 and recognise the equivalence of 2/4 and ½.
I can recognise and write equivalent fractions for ½. / Tell me another fraction that is equivalent to 2/4. Can you shade a shape to show me?

Year 2 Block E: Securing number facts, relationships and calculatingUnit 2

Objectives Unit 2

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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.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?

  • To calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (x), division (÷) and equals (=) signs.
I can make connections between the 2, 5 and 10 times tables /

CThey connect the 10 times table to place value and the 5 times table to the divisions on a clock face.

  • To show that the multiplication of two numbers can be done in any order (commutative) and division on one number by another cannot. To use number facts to check answers to calculations.
I can check answers to calculations involving doubling by halving the answer. / How many multiplication number sentences can you make using these numbers; 7 and 5?
How many division number sentences can you make using 20 and 5?
•Find one-half, one-quarter and three-quarters of shapes and sets of objects
* To recognise, find, name and write fractions – 1/3, ¼, ½, ¾ of a length, shape, set of objects or quantity.
I can find a half or a quarter of a set of objects
I can fold a piece of paper into halves or quarters
I can identify and write 1/3, ½, ¼, ¾ of a length, shape, set of objects or quantity. / 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.

Counting in fractions up to 10 starting from any number and using ½ and 2/4 equivalence on thenumber line (e.g. 1 ¼ , 1 2/4, (or 1 ½ ), 1 ¾ , 2)This reinforces the concept of fractions as numbers and that they can add up to more than 1.