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Year 5 Block B - Securing number facts, understanding shape Unit 1

Learning overview

In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils’ Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and on 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 children. When you make a periodic assessment of children’s learning, this accumulating evidence will help you to determine the level at which they are working.

To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children 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, Communicating
  • Ma2, Numbers and the number system
  • Ma3, Properties of shapes.

Children rehearse multiplication facts to 10 × 10 and the related division facts. They discuss the facts that they can recall rapidly and strategies to help them derive those they struggle to recall, for example doubling 4 times-table facts to work out 8 times-table facts. They respond to questions such as: The product of two numbers is 24. What could the numbers be? They record their answers systematically to derive all pairs of factors for the number 24. They use squared paper or peg boards to create all the different arrays possible using 10, 11, 12, ... squares or pegs. They use this to list all of the factors of 10, 11, 12, ... They investigate which numbers can create a square array and learn that these are called square numbers; for example, 16 is a square number because it is equal to 4 × 4.

Children classify numbers according to their properties, recording the classifications in Venn and Carroll diagrams. For example, they place the numbers 1 to 30 on a Venn diagram. They describe patterns in their diagram and respond to questions such as: What do you notice about numbers that are multiples of both 2 and 5? An empty Venn diagram with labels for multiples of 2 and multiples of 5

They learn the vocabulary common multiple and suggest general statements based on similar relationships, for example: All common multiples of 3 and 4 are multiples of 12. They test these statements by finding examples that match them.

Assessment focus: Ma2, Numbers and the number system

Look out for children who can sort and classify numbers according to their properties. Look for evidence of children recognising and describing the relationship between numbers that are all, for example, factors of 36 or all square numbers. Look for children who use this understanding when investigating relationships between numbers and solving problems.

Children use known multiplication facts and place value to find related facts. For example, they use 8 × 4 = 32 to find the answer to 80 × 4, explaining that 80 is ten times as big as 8 so the answer will be ten times 32, or 320. They predict the answer to 80 × 40, explaining how they worked this out, then check their prediction using a calculator. They find related division facts, e.g. recognising that 3200 ÷ 400 = 8 because 8 × 400 = 3200. Children use similar strategies and their understanding of inverse operations to find the missing numbers in calculations such as:

20 × square = 600
2800 ÷ 70 = square
square ÷ 50 = 300

Children use rounding to suggest sensible estimates to addition and subtraction calculations. For example, they predict whether the answer to 3217 - 1682 is (a) 1635, (b) 1535 or (c) 1435. They use efficient written methods for addition and subtraction of whole numbers, estimating first. They use their knowledge of number facts, rounding and inverses to find the missing digits in calculations such as 3square 67 - 192square = 1539.

Children visualise and describe 3-D shapes according to a range of properties including: the shapes of faces, the number of faces, edges and vertices, and whether the number of edges meeting at each vertex is the same (as in a cube) or different (as in a square-based pyramid). They solve problems involving 3-D shapes, for example finding all of the possible nets for an open cube or sorting a set of 3-D shapes using an ICT 'binary tree' program.

Assessment focus: Ma3, Properties of shapes

Look for evidence of children using the properties of shapes to solve problems. For example, look for children who, given a set of 2-D or 3-D shapes and ‘properties cards’, match all relevant properties to shapes. Look for children who select or design a set of properties that defines just one of the shapes in the set. For example, look for evidence of children using the properties of 3-D shapes to match 3-D shapes to an appropriate net from the set of corresponding nets.

Children extend their knowledge of the properties of 2-D shapes. For example, they investigate the properties of rectangles. They measure the length of the two diagonals, commenting on what they notice. They measure the distance from the point where the diagonals cross each other to each of the four vertices. Children predict and test which other shapes have diagonals of equal length or diagonals that bisect each other.

Assessment focus: Ma1, Communicating

Look for evidence of children’s use of mathematical vocabulary, and for children who refine their use of vocabulary to be more precise or accurate. Look for children using terms such as side or edge, diagonal and vertex, for example, to draw attention to a particular line in their drawing of a 2-D shape.

Objectives


Children's learning outcomes are emphasised

Assessment for learning
  • Explore patterns, properties and relationships and propose a general statement involving numbers or shapes; identify examples for which the statement is true or false

    I can sort numbers or shapes according to their properties and explain how I sorted them
 What is the same about these two numbers (or shapes)? What is different?
Look at this shape (or a shape that is drawn on a square grid). Tell me whether each of these statements is true or false.
  • The shape has exactly two right angles.
  • The shape has two pairs of parallel lines.
  • The shape has one line of symmetry.
  • The shape is a quadrilateral.
Look at these four numbers (or shapes). Think of a property which is true for two of them and false for the other two. Now think of some different properties.
  • Recall quickly multiplication facts up to 10 × 10 and use them to multiply pairs of multiples of 10 and 100; derive quickly corresponding division facts

    I can use tables facts to multiply multiples of 10 and 100 and to find linked division facts
 The product is 400. At least one of the numbers is a multiple of 10. What two numbers could have been multiplied together? Are there any other possibilities?
What tips would you give someone who had forgotten the 6 times-table to help them to work it out?
  • Identify pairs of factors of two-digit whole numbers and find common multiples (e.g. for 6 and 9)

    I can find pairs of factors that multiply to make a given number
    I can find a number that is a multiple of two different numbers

Find all the factors of 30. Explain how you know you have found them all.
The area of a rectangle is 32 cm2. What are the lengths of the sides? Are there other possible answers? How did you work it out?
Explain why 81 is a square number.
One number is in the wrong place on the sorting diagram. Which one is it?

A Venn diagram with multiples of 10 and numbers greater than a 100

Choose from these digit cards each time: 7, 5, 2, 1.
Make these two-digit numbers:

  • an even number
  • a multiple of 9
  • a square number
  • a factor of 96
  • a common multiple of 3 and 4
  • Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations

    I can check whether a calculation is correct and explain how I did this
 Which is the best estimate for 2348 plus 4965?
A 6000 B 6300 C 7000 D 7300
Explain your decision.
  • Use efficient written methods to add and subtract whole numbers and decimals with up to two places

    I can explain each step when I write addition and subtraction calculations in columns

What tips would you give to someone to help them with column addition of decimals? What about subtraction?
Which of these decimal additions/subtractions are correct? What has this person done wrong? How could you help them correct it?
What are the missing digits in this calculation?

A 4 digit by 4 digit subtraction with a missing number in each

Explain your reasoning.

  • Identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids; use knowledge of properties to draw 2-D shapes and identify and draw nets of 3-D shapes

    I can describe the important features of shapes such as rectangles I know the important features of a cube. I can use these to draw its net

I am thinking of a 3-D shape. It has a square base. It has four other faces which are triangles. What is the name of the 3-D shape?
Use squared dotty paper. Use the dots to draw a shape that has four straight sides and no right angles.
Here is part of a shape on a square grid. Draw two more lines to make a shape which has a line of symmetry. Use a ruler.

3 lines of a shape on a grid

Look at these diagrams. Which of them are nets of a square-based pyramid? Explain how you know.

4 nets each made up of 4 equilateral triangles and a square

Is this a net for an open cube? Explain why not.

5 squares joined in a row

  • Identify different question types and evaluate impact on audience

    I know that when my teacher asks certain mathematical questions there may be more than one answer. I try to think of all the possible answers
 What is the difference between these two questions?
What is the sum of 1.2 and 0.8?
Tell me two decimals with a sum of 2.

Resource links to existing published material

Mathematical challenges for able pupils in Key Stages 1 and 2
Activities PDF 1MB
Activity 53 - Square it up
Activity 56 - A perfect match
Activity 58 - Spot the shapes 2
Activity 59 - Four by four
Activity 61 - Make five numbers
Activity 65 - Age old problems
Activity 66 - Zids and Zods
Intervention programmes
Objectives for Springboard intervention unit Springboard unit

Identify doubles and also near doubles using doubles already known
Halve numbers where the double is known
Understand and use £.p notation

Springboard 5 Unit 1 (PDF 305KB)
Springboard 5 Unit 1 supplementary (PDF 77KB)
Develop and refine written methods for subtraction, building on mental methods.
Reinforce the fact that subtraction is the inverse of addition		 Springboard 5 Unit 8 (PDF 245KB)
Springboard 5 Unit 8a Part 1 supplementary (PDF 77KB)
Springboard 5 Unit 8a Part 2 supplementary (PDF 75KB)

Know the three- and four-times tables
Begin to know the six-times tables

Springboard 5 Unit 9 (PDF 269KB)
Springboard 5 Unit 9 supplementary (PDF 110KB)
Supporting children with gaps in their mathematical understanding (Wave 3)
Diagnostic focus Resource
Has insecure understanding of the structure of the number system resulting in addition and subtraction errors and difficulty with estimating 1 Y4 plus/-
DfES 1128-2005 (PDF 101KB)
Has difficulty in partitioning 2 Y4 plus/-
DfES 1129-2005 (PDF 78KB)
Is not confident when recalling multiplication facts 1 Y4 ×/÷
DfES 1150-2005 (PDF 104KB)
Does not make sensible decisions about when to use calculations laid out in columns 3 Y4 plus/-
DfES 1130-2005 (PDF 101KB)
Does not use knowledge of doubles to finding half of a number 5 Y2 ×/÷
DfES 1147-2005 (PDF 86B)
Has difficulty adding three numbers in a column 4 Y4 plus/-
DfES 1131-2005 (PDF 95KB)

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

Year 5 Securing number facts, understanding shape - Unit 1

PDF 59KB RTF 560KB Word 77KB

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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