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Year 4 Block B - Securing number facts, understanding shape

Objectives

Children's learning outcomes are emphasised 		Assessment for learning
  • Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples

    I can start with a calculation such as 18 minus 3 = 15 and use number patterns to create a family of calculations with the same answer:
    180 minus 30 = 150
    190 minus 40 = 150
    200 minus 50 = 150
    I can draw polygons on triangular grid paper and pick out some of the properties they have in common

Name a multiple of 6 that is also a multiple of 9.
Using the numbers 6, 8 and 48, create some sentences using the vocabulary product, factor, multiplied by and multiple of.
Here are some polygons. Decide on a property and classify them according to your property. Explain your decisions to me.
What colour is each shape? Write it on the shape.
Four squares and two circles
Clues

  • Red is not next to grey.
  • Blue is between white and grey.
  • Green is not a square.
  • Blue is on the right of pink.
  • Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate

    I can work out how to solve problems with one or two steps
    I can decide what calculation to work out and whether a calculator will help me
    I can think about the numbers in a calculation and choose a good way to do the calculation

Sort these problems into those you would do mentally and those you would do with pencil and paper. Explain why.
John wanted to use his calculator to add 463 and 319. He entered 263 plus 319 by mistake. What could he do to correct his mistake?
A Add 200.
B Add 2.
C Subtract 2.
D Subtract 200.

  • Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols

    I can describe how I solved a problem about shapes using mathematical vocabulary

This grid has two shaded shapes.
A net of tessellated triangles with shading to show 2 polygons of different sizes
Leon says: 'Shape A has a larger area than shape B.' Explain how he could have worked this out.

  • Use knowledge of rounding, number operations and inverses to estimate and check calculations

    I can use inverse operations to help me check calculations
    If you give me a number fact, I can tell you some related facts

6 plus 7 = 13. Write three other facts that you can work out from the addition fact.
48 ÷ 8 = 6. Write three other facts that you can work out from the division fact.
Write a calculation that you could do to check that the answer to 53 × 4 is 212.

  • Use knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000

    Because I know number facts such as 8 - 3 = 5, I know that
    80 - 30 = 50. I can use this to work out calculations such as
    86 - 36 = 50
    I can find differences between numbers such as 2993 and 3000 because I know facts such as 3 plus 7 = 10

Which three numbers in this list have a sum of 190?
10 30 50 70 90
How did you work it out?
Which pairs of these numbers have a difference of 60?
190 30 70 130 90
How did you work it out?

  • Identify the doubles of two-digit numbers; use to calculate doubles of multiples of 10 and 100 and derive the corresponding halves

    I can work out doubles of two-digit numbers
    Because I know that double 9 is 18, I know that double 900 is 1800
    Because I know that double 80 is 160, I know that half of 160 is 80
    I know that doubling and halving are inverse operations

What are the missing numbers in this sequence?
A number line with missing numbers, doubling each time from 17

Complete the number pattern.
A number line with missing numbers, halving from 96

  • Derive and recall multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple

    I can tell you answers to the 9 times-table, even when the questions are not in order
    If you give me a multiplication fact I can give you one or two division facts that go with it
    I know what a factor of a number means. I can find all the factors of 36

If you count in nines from zero, which digits change? How? Why do they change like this? Show me the pattern on the 100-square. How does the pattern help you to work out, say, six nines?
How can you build the 9 times-table from the 3 and 6 times-tables?
If you know 4 × 9 = 36, how does this help you to work out 36 ÷ 9?
What are the missing numbers in this number sentence? Are there any other possibilities?
square × circle = 18
What is the missing number in this number sentence?
9 × square = 54
How do you know?

  • Visualise 3-D objects from 2-D drawings; make nets of common solids

    When I look at a drawing of a 3-D shape I can work out what shapes I need to make its net, such as four triangles and a square to make a square-based pyramid

Match these 3-D shapes to these pictures of them.
There are three shapes in a row. What order are they in and what colour are they?
Clues
The cube is in the middle.

  • The pink shape is not on the right.
  • The red shape is next to the pyramid.
  • The cone is not blue.
  • Draw polygons and classify them by identifying their properties, including their line symmetry

    I can pick out 2-D shapes that have more than one line of symmetry
    I can draw lots of different polygons on squared paper and tell you their mathematical names
    I can draw all the shapes made from squares placed edge to edge and tell you what sort of polygon each one is

A shape has four right angles. It has four sides which are not all the same length. What is the name of this shape?
Sort a set of polygons using this sorting diagram.
A three by four table with properties of shapes along the top and right side: no sides equal, only 2 sides equal and more than 2 sides equal across the top, 3 sides and more than 3 sides along the left

Here are five shapes on a square grid.
A square grid with 5 different polygons
Which two shapes have a line of symmetry?

  • Use time, resources and group members efficiently by distributing tasks, checking progress, making back-up plans

    I can work with a group of other children to discuss and plan how we will solve a problem

I want you to work in a group to solve this problem. You have 45 minutes. Decide how you will work together and share the tasks. Make sure you ask someone to be the timekeeper to keep a check on your progress.

Learning overview

Children extend their knowledge of multiplication facts to the 9 times-table. They recognise how multiplication facts previously learned, such as multiples of 3 and 6, can help to derive multiples of 9. They use a range of vocabulary associated with multiplication and division including multiple, factor and product. They use arrays to recognise connections between multiplication facts and division facts and identify factors of a number by creating arrays for that number. They extend their knowledge of number properties to solve problems and puzzles. They find a pair of numbers with a sum of 15 and a product of 54. They use knowledge of inverses to solve problems such as: I think of a number, add 2 and multiply by 3. The answer is 15. What was my number?

Children continue to double one- and two-digit numbers and find the corresponding halves. This is extended to calculating doubles and halves of multiples of 10 and 100; for example, if double 9 is 18, then double 90 is 180, and half of 180 is 90. Children discuss their work and explain patterns and rules using mathematical language and symbols. They explore a number sequence arising from a given rule, for example 'double the last number and subtract 1' (2, 3, 5, 9, ...). They discuss the resulting sequence by asking and answering questions such as: What are the gaps between the numbers? and What if the rule were double and add 1?

Children continue to improve their knowledge of number facts, recalling them quickly and applying them accurately. They know all addition and subtraction facts to 20 and use these facts to add and subtract multiples of 10, 100 and 1000. They work out mentally calculations such as 387 minus 50 or 3000 minus 2993. Given one number statement, they use number patterns and their knowledge of place value to record related statements. For example, they start with 18 minus 3 = 15 and use number patterns to create a family of equations each with the same answer, such as 180 minus 30, 190 minus 40, 200 minus 50, etc. They explain the connection between the original and related calculations.

Children solve one- and two-step problems, choosing and carrying out appropriate calculations. They identify stages in a problem. They decide what calculations to do and how best to do them: mentally, on paper or using a calculator. They identify how the result of the calculation fits with the context of the original problem. They continue to use their knowledge of rounding, number operations and inverses to check calculations.

Children extend their knowledge of properties of shapes. They draw polygons on triangular grid paper. They identify properties such as number of sides, types of angle, lines of symmetry. They draw closed straight-sided shapes with their vertices on the intersections of a squared grid. They recognise these shapes as polygons. They assign the correct mathematical names to each one.

They apply their knowledge of properties of shapes to solve mathematical problems or puzzles. They collaborate in groups to investigate the different shapes that can be made by fitting two identical right-angled triangles together edge to edge. They distribute tasks between themselves, think creatively, and regularly check progress to see what new shapes have been discovered.

They continue to visualise shapes. Starting with a rectangular sheet of paper they try to fold it and then make one straight cut to make this hexagon.

A hexagon

Children continue to use their experience of 3-D shapes to enable them to visualise solids. They construct a model using cubes, take a digital photograph of it, then challenge others to recreate it. They put 72 interlocking cubes together to make a 2 by 3 by 12 cuboid, and then work out what other cuboids they can make using 72 cubes. They create nets of a closed cube, a square-based pyramid and a triangular prism.

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

Is not confident when recalling multiplication facts

1 Y4 ×/÷
DfES 1150-2005 (PDF 104KB)

Is muddled about the correspondence between multiplication and division facts

2 Y4 ×/÷
DfES 1151-2005 (PDF 93KB)

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

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
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