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Maths Year 6 Summer Revision

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 Areas, perimeters and volume (suggested as 2 days)

Objectives

Understand and calculate areas, perimeters & volume
Unit 1: ID# 6073

National Curriculum
Meas (iv), (v), (vii)
Alg (i)

Hamilton Objectives
36. Use simple formulae, including formulae expressed in words.
42. Measure areas and perimeters. Understand that area is a measurement of covering and is measured in square units, and perimeter is a length, measured in mm, cm, m or km. Recognise that shapes with the same area can have different perimeters and vice versa.
44. Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres and cubic metres; extend to other units [e.g. mm³ and km³].

Teaching and Group Activities for Understanding

Day 1 Teaching
Show a picture of two ponds. Which pond has the greater area? Model counting all the whole squares in one pond, then also count any squares that have half or more shaded. Ignore squares that have less than half shaded. Why is this a valid strategy for estimating the area? Children draw a rectangle with an area of 24cm² then calculate its perimeter. Challenge children to draw a ‘rectilinear’ shape with an area of 24cm², explaining that a rectilinear shape is one made out of rectangles, e.g. an ‘L’ or ‘T’ shape. They find its perimeter. Share some of their shapes. End by creating today’s ‘Top Tip for Tests’.
Group Activities
-- Estimate areas of irregular ‘ponds’ by counting squares. Calculate area and perimeter of rectangles and rectilinear shapes.
-- Draw rectangles and rectilinear shapes with a given area; calculate their perimeters.

Day 2 Teaching
Show a cuboid (3 × 4 × 3) made from 36 centimetre cubes. Observe how many cubes are in each layer, how many layers, and so how many cubes are in the whole cuboid. Remind children how we can use a formula - length × width × height, or l × w × h for short, to find the volume: the amount of space taken up by the shape. Create today’s ‘Top Tip for Tests’. Sketch a 6 × 4 × 5 cuboid, labelling each side in metres. Children calculate its volume in m³.
Group Activities
-- Sketch cuboids; calculate their volumes. Calculate the length of a missing edge in a cuboid of known volume.
-- Investigate the different cuboids that can be made with a volume of 48cm³.

You Will Need

• ‘Ponds’ (see resources)
• ‘Isometric paper’ (see resources)
• A4 cm2 paper
• 100 centimetre cubes
• Mini whiteboards and pens

Mental/Oral Maths Starters

Suggested for Day 1
Convert between mm, cm and m (simmering skills)

Suggested for Day 2

Procedural Fluency

Day 1
Find perimeters and areas of rectilinear shapes, then areas of triangles shown as half rectangles.

Day 2
Find volumes of cuboids, then missing dimensions, given two dimensions and volume.

Mastery: Reasoning and Problem-Solving

• Nell says, ‘If two rectangles have the same perimeter, they must have the same area. Do you agree? Explain your ideas.
• Draw two different quadrilaterals with an area of 20 cm².
• Each side of an equilateral triangle measures 12cm. Each side of a regular hexagon is b cm. The perimeter of the hexagon is 6 centimetres less than the perimeter of the triangle. What number does b represent?
• A square of area 64cm² is cut into quarters to create four smaller squares. What is the perimeter of one of the small squares?
• Ronnie has 36 centimetre cubes. She uses all 36 cubes to make a cuboid with dimensions 9cm, 2cm and 2cm. Write the dimensions of the different cuboids she can make using all 36 cubes.
• A cuboid has a square base. It is three times as tall as it is wide. Its volume is 192 cubic centimetres. Calculate the width of the cuboid.

Extra Support

This unit has no separate Extra Support activities.

Unit 2 Algebra: unknowns and linear sequences (suggested as 2 days)

Objectives

Algebra: finding unknowns, continue and describe linear sequences
Unit 4: ID# 6091

National Curriculum
Alg (ii), (iii), (iv), (v)

Hamilton Objectives
37. Solve missing number problems, including where letters are used to replace constants.
38. Find pairs of numbers that satisfy an equation with two unknowns and list, in order, the possibilities of combinations of two variables.
39. Generate, describe and continue linear sequences.

Teaching and Group Activities for Understanding

Day 1 Teaching
Show the following sequence: 1, 8, 15, 22, 29.... Children write the next three terms. Repeat for: 2, 5, 8, 11…. Children describe the sequence to a partner and write what they think the 10th term will be. Draw a table and explain that n is the number of terms in the sequence. What can we do to 2 to get 5? And to 3 to get 8? It needs to be the same function! Establish that that we can multiply by 3, and subtract 1. Share today’s top tip for tests.
Group Activities
-- Continue linear number sequences. Generalise linear sequences using algebra to define an nth term.

Day 2 Teaching
Write on the board: 24 + a =. Remind children that this is called an equation and ‘a’ stands for a mystery number. We could write an empty box instead! Share today’s top tip for tests. Sketch a bar model to show this. What is a? Write 30 – a = 24. What is a? How do you know? Repeat for 6b = 48. List pairs of solutions for x + y = 12; then for m × n = 24.
Group Activities
-- Use bar models to represent equations.
-- Solve equations with one or two unknowns, with a range of operations.

You Will Need

• Mini whiteboards and pens
• ‘Sequences’ activity sheets (see resources)
• Flipchart and pens
• ‘Solve these equations’ practice sheet (see practice worksheets)

Mental/Oral Maths Starters

Day 1
Guardian of the rule (pre-requisite skills).

Day 2
Equivalence (pre-requisite skills).

Procedural Fluency

Day 1
Children write the missing terms in sequences. They choose four to describe.

Day 2
Solve equations and list possible pairs of number for equations with two unknowns.

Mastery: Reasoning and Problem-Solving

• Here is a pattern of number pairs:
 n m 1 8 2 13 3 18 4 23

Complete the rule for the number pattern:
m = [_] × n + [_]

• The rule for a number sequence is
s = 1/2t + 5
What is the value of s when t = 12?
What is the value of t when s = 9?

• Work out the value of each shape in this puzzle:
 ■ ■ ● ● ■ Total 72 ■ Total 63

Extra Support

This unit has no separate Extra Support activities.

Unit 3 Problem solving (suggested as 2 days)

Objectives

Problem solving
Unit 4: ID# 6043

National Curriculum

Hamilton Objectives
8. Solve addition and subtraction multi-step problems in context, deciding which operations to use and why.
20. Solve problems involving all 4 operations.

Teaching and Group Activities for Understanding

Day 1 Teaching
Anna chooses 2 numbers, adds them together, and then divides by 2. Her answer is 19. One of the numbers she chose was 14. What was the other number? Discuss how this puzzle could be solved using inverse operations, i.e. multiplying 19 by 2 to give 38, then subtracting 14 to give 24. Check. Repeat with a similar problem. Display the Arithmagon. Explain how it works, and together try out numbers to work out a solution. Share ‘Top Tip for Tests’.
Group Activities
-- Use reasoning skills to solve - then create - number puzzles and problems with all operations.

Day 2 Teaching
Sapna buys 2 CDs for £4.79 each, a DVD for £11.50 and a pack of batteries for £4.25. Find the change from £30. Demonstrate using a bar model to represent this problem. Show some workings out, with errors. Discuss. Explain that this child got a mark for method even though the answer is wrong. Stress the need for clear working out. Share ‘Top Tip for Tests’.
Group Activities
-- Interpret and solve problems with more than more 1 calculation step.

You Will Need

• ‘Multiplication arithmagon’ (see resources)
• ‘Solving number puzzles’ Sheets 1 and 2 (see resources)
• Mini-whiteboards and pens
• Flipchart and pens
• ‘Multi-step problems’ Sheet 1 (see resources)
• ‘Multi-step problems’ Sheet 2 (see resources)

Mental/Oral Maths Starters

Suggested for Day 1
Find a mean (simmering skills).
or
12 times table and division facts (simmering skills).

Day 2
Order of operations (pre-requisite skills).

Procedural Fluency

Day 1
Solve mystery number puzzles, multiplication arithmagons and addition grids.

Day 2
Practise solving multi-step problems.

Mastery: Reasoning and Problem-Solving

• Here are the heights of some British mountains:
Ben Macdui (Scotland): 1309m
Snaefell (Isle of Man): 621m
Maumtrasna (Ireland): 682m
How much higher is Ben Macdui than the combined height of the 2 smaller mountains?
• There are 2,200 pencils in a box.
Class 6 take 450 pencils. Class 1, 2, 3, 4 and 5 share the rest of the pencils equally.
How many pencils does Class 3 get?
• Rita and Sapna each buy a book. Rita pays with a £10 note and gets £2.31 change. Sapna’s book costs £8.40.
How much more does Sapna’s book cost than Rita’s book?

Extra Support

This unit has no separate Extra Support activities.