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Year 2 Block E - Securing number facts, relationships and calculating Unit 1

Learning overview

In this learning overview are suggested assessment opportunities linked to the Assessment focuses within the Assessing Pupils’ Progress guidelines. As you plan your teaching for this Unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of pupils. When you make a periodic assessment of pupils’ learning, this accumulating evidence will help you to determine the level at which the pupils are working.

To gather evidence against the three Ma1 Assessment focuses (problem solving, reasoning and communicating) it is important that children are given space and time to develop their own approaches and strategies throughout the mathematics curriculum as well as through the application of skills across the curriculum.

In this Unit the illustrated Assessment focuses are:

  • Ma1, Problem solving
  • Ma2, Numbers and the number system
  • Ma2, Fractions

Children extend their understanding of counting on and back in steps of 1, 2, 5 and 10 from various start numbers. They record sequences and describe patterns in the numbers, including recognising odd and even numbers. In particular, they explain the patterns from counting in twos, fives and tens when starting from zero. They find missing numbers from sequences such as:

30, 40, italic square, 60, italic square and 55, 50, £, 40, 35, £, 25, 20

Assessment focus: Ma2, Numbers and the number system 

Look for the range of sequences for which children can find missing numbers or can continue forwards and backwards. Look for children working out how much the numbers increase or decrease with each step or recognising familiar sequences, for example from counting in tens. 

Children work with others to explain their reasoning and to listen to the reasoning of others. They consolidate counting on from zero in steps of 2, 5 and 10 and build up these times-tables, describing what they notice about numbers in the tables. They use this to predict some other numbers that would be in the count and to answer questions such as:

What are four fives? How many twos make 18?

They use counting, practical equipment, diagrams or a number line to support, record or explain their answers.

Using practical equipment or objects as a starting point, children understand that repeated addition can be represented using the multiplication symbol. For example, they record four lots of five fingers as 5 + 5 + 5 + 5 and use the multiplication sentence 5 × 4 to record this. They understand that 'multiplied by 4' or '× 4' means 'add the number four times'.

hey use a number line to support repeated addition, recording the equal jumps on the line and writing the repeated addition statement and the matching multiplication statement. They become familiar with different ways of describing a multiplication:

A number line showing counting in fives

5 + 5 + 5 + 5 + 5 + 5 = 30

5 × 6 = 30

5 multiplied by 6 equals 30

6 groups of 5 make 30

6 hops of 5 make 30

For a given multiplication such as 2 × 6, children explain how jumps can be made on a number line. They point to the numbers as they make the jumps and provide a 'commentary' of what they are doing as they go along, explaining why this shows 2 × 6. They use arrays of pegs in pegboards, patterns on squared paper or hops on a number line to show that 3 × 5 = 5 × 3 or that 4 × 2 = 2 × 4.

Two tables, one showing blocks arranged in columns of three by five, the other showing rows of five by three

A number line with two hops of four equalling eight and four hops of two equalling eight

Assessment focus: Ma1, Problem solving

Look for children engaging with practical mathematical activities and beginning to represent problems in different ways. For example look for children gaining insights into multiplication by representing it as counting, repeated addition as jumps along a number line, sets of objects and arrays of linking cubes. Look for children who represent a problem in one way but can suggest and use a different way. Look for children beginning to make connections, for example between arrays representing 2 fives and 5 twos or between arrays and corresponding jumps on a number line. 

Children experience division as grouping. They use practical equipment or objects to answer questions such as: How many 2s make 12? They relate this to the division 12 ÷ 2. They use objects or a number line to support, record or explain this. For example, starting from 12, they jump back in steps of 2, or starting with 12 counters, they keep on taking away 2 counters. They record this as repeated subtraction and as division:

12 – 2 – 2 – 2 – 2 – 2 – 2 = 0

12 ÷ 2 = 6

12 divided by 2 equals 6

Children explain how they use equipment, objects or a number line to carry out division.

Throughout the unit, children find doubles of numbers to 10 using practical resources or drawings to consolidate their understanding of doubling. They record using repeated addition and multiplication and find inverse operations, knowing, for example, that if double 7 is 14 then half of 14 is 7.

Children find halves of shapes by folding. They recognise that each part of the shape on either side of the fold line is one half so that the whole shape is made up of two identical halves. They explore different ways of finding half of shapes, for example folding squares in half in as many different ways as possible. They reinforce their understanding that the halves must be of equal size. They relate this to line symmetry.

Children fold shapes in half and then half again to make quarters. They know that four quarters make one whole and that each quarter must be the same size.

Assessment focus: Ma2, Fractions

Look for evidence of children understanding halves and quarters in a range of contexts. For example, look for children finding different ways to fold and cut a square in half or into quarters. Notice if children can re-assemble the square using the smaller squares or the triangles that are its quarters. Look for children using the strategy of halving and halving again in the context of finding a quarter of a set of objects that they can move. Notice how children solve the problem of finding a quarter of a number of objects in a picture. Look for children using cubes to represent the objects in the picture. Look for those children who draw a line through the picture so that the same number of objects appears on either side of it, and repeat the process to find one quarter. 

Children consolidate finding halves and quarters of a group of objects, by giving an equal number of objects to each of two or four people by sharing out the objects equally among the people. They reinforce this idea in practical situations such as:

Placing 14 dots on a ladybird so that the same number of dots is on each half

Placing 12 'tomatoes' on four plates so that each plate has the same number of tomatoes.

In a group, children sort a set of numbers into those that can be halved exactly and those that cannot. They discuss their findings and discover that when they halve a set of objects there may be one left over. They relate this finding to even and odd numbers, noticing that the numbers that can be halved exactly are those that they land on when they count in twos from zero along the number.

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 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, including calculations with remainders

    I can use a number line to do multiplication and division and can work out remainders if there are any

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:
Two identical tables each showing two by four cells, one with four along the bottom and one with two
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. italic square ÷ 2 = 6, 30 - italic square = 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?

  • Find one half, one quarter and three quarters of shapes and sets of objects

    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.
A table with two by six cells, two cells are 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.

  • Listen to a talk by an adult, remember some specific points and identify what they have learned

    I can remember how to work out one quarter by halving one half

Tell me how to find one quarter of a piece of paper.
Listen carefully while I show you how to find one quarter of these cubes.

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

Has difficulty relating multiplying by two to known facts about doubles

4a Y2 ×/÷
DfES 1146-2005 (PDF 78KB)

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 understand 'groups of' need to be subtracted

7 Y2 ×/÷
DfES 1149-2005 (PDF 104KB)

Click here for information on different file formats and their usage.

Year 2 Securing number facts, relationships and calculating - Unit 1

PDF 56KB RTF 455KB Word 70KB

Wave 3 addition and subtraction tracking children's learning charts

PDF 161KB RTF 930KB Word 315KB

Wave 3 multiplication and division tracking children's learning charts

PDF 195KB RTF 1.3MB Word 430KB

Wave 3 Resource sheets and index of games booklet

PDF 500KB
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