• Hamilton's Flexible Maths Blocks Explained Open our sample 'Year 5 Autumn Unit 1' to find out how the blocks of units work.

• Go Deeper with Maths Investigations Our Investigations provide the materials to confidently teach problem solving & investigation skills.

• Free Maths Resources on Hamilton Find out which Hamilton maths units you can access for free, including our new slide presentations.

# Maths Year 6 Spring Spring/Summer Revision Menu B

Revision for Year 6 SATs will be driven by the specific needs of the children in your class. We therefore provide a 'Menu' of Revision units for you to choose from, with the option to begin your Revision in the Spring Term. The full 'Menu' is also available in the Summer term. Menu 'A' caters largely for number-based skills; Menu 'B' provides for consolidation of non-number toipcs. Our 'SHORT BLOCKS' provide the same menus of revision teaching.

Each Revision unit has everything you need to revise a set of related skills and concepts. 'Teaching & Group Activities' provides a plan for whole-class teaching; a 'Slide Presentation' brings this teaching to life on the IWB. Fully-differentiated adult-led group activities follow, allowing for small-group personalised learning, where you may deal with children's 'Common Misconceptions'. Fluency can be rehearsed with our 'Practice Sheets', or learning checked with the 'Mastery Activity'.

‘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 the associated documents. These bulk downloads are only available to 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 Shapes, angles, reflections, translations (suggested as 3 days)

### Objectives

Understanding co-ordinates, reflections and translations, calculate angles; properties of 2D and 3D shapes
Unit 2: ID# 6079

National Curriculum
PofS (ii), (iii), (v)
P&D (i), (ii)

Hamilton Objectives
49. Draw 2-D shapes, using given dimensions and angles. Understand terms parallel and perpendicular.
50. Recognise, describe and build 3-D simple shapes, including making nets.
52. Find unknown angles in triangles, quadrilaterals and regular polygons; also find missing angles at a point, vertically opposite or on a straight line.
54. Identify positions on the full co-ordinate grid. Draw and translate simple shapes and reflect them in the x-axis or y-axis.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a point on the board and four equal length lines coming from it. Use an IWB protractor to measure three of the angles; then work out the fourth. Read from the correct scale! Children work out the missing angles in a triangle and angles around two intersecting lines.
Group Activities
-- Solve geometry problems to find missing angles. Investigate general statements about angles in triangles.

Day 2 Teaching
Use the online Transformation game. Children write the co-ordinates of the house. Share today’s top tip for remembering the order to read/ plot co-ordinates. Children discuss, in pairs, which mirror line is correct, and where it needs to go on the grid. Click on ‘Reflect’ to check. What are the new co-ordinates of the house? Repeat for translation. Is there a pattern in the way the x and y co-ordinates changed each time?
Group Activities
-- Place and transform a shape on a co-ordinate grid. Give instructions to the rest of the group to make their shapes finish in the same position.

Day 3 Teaching
Children work in groups to write a description of a given 3-D shape, e.g. number and shape of faces it has, number of vertices and edges. They then draw a net of the shape. The rest of the class guess their shape from the description, confirming by looking at the net.
Group Activities
-- Visualise 2-D representations of 3-D shapes. Make nets to test whether they form open cubes.

### You Will Need

• ‘Missing angles’ activity sheets 1 and 2 (see resources)
• ‘Reflections and Translations Sets A and B’ (see resources)
• IWB protractor (2-directional)
• Protractors and scissors
• Transformation game from www.kidsmathgamesonline.com
• ‘L-shaped’ pieces of card
• Interlocking 2-D shapes (e.g. ‘Polydron’)
• Bag of polyhedra (e.g. tetrahedron, square-based pyramid, etc)
• Flipchart paper, marker pens, mini-whiteboards and coloured pencils
• 3-D shapes: cuboid, tetrahedron, triangular prism, square-based pyramid

### Mental/Oral Maths Starters

Day 1
Draw 2-D shapes using given dimensions and angles (pre-requisite skills)

Day 2
Find lines of symmetry (pre-requisite skills)

Day 3
Parts of circles and describing regular and irregular polygons (pre-requisite skills)

### Procedural Fluency

Day 1
Children measure some angles in a pattern, then use angle relationships (in a triangle, on a straight line, round a point, opposite angles) to deduce all the angles in the pattern. Then, they use a protractor to check.

Day 2
Children practise making and describing reflections and translations, initially in the first quadrant, then in other quadrants.

Day 3
Answer 3-D shape questions about faces, vertices and edges. Identify nets of open cubes.

### Mastery: Reasoning and Problem-Solving

• A right-angled triangle has an angle measuring 63°. How big is its third angle?
• An isosceles triangle has an angle measuring 34°. How big could its other two angles be?
• The centre of a square has co-ordinates (3, 1) and one vertex at (−1, 5). What are the co-ordinates of its other three vertices?
• Shade two more boxes on this grid to make a design that has a line of symmetry:
 ## ## ## ## ##
• A triangle with co-ordinates (−2, −2), (−2, 3) and (1, −2) is translated 6 grid squares to the right and 5 up. What are the co-ordinates of its new position?

### Extra Support

This unit has no separate Extra Support activities.

## Unit 3 Bar charts, pie charts, line graphs, means (suggested as 3 days)

### Objectives

Draw and interpret bar charts, pie charts and line graphs and find a mean
Unit 3: ID# 6089

National Curriculum
Stats (i), (ii)

Hamilton Objectives
47. Interpret and construct pie charts and line graphs and use these to solve problems.
48. Find and interpret the mean (average) of several quantities.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show and explain the graph of pets. How many children chose a rabbit? Discuss the scale of the graph. Draw a line down to the horizontal axis, and label it 50. Repeat with similar questions. Share today’s top tip. Show a line graph of a dog’s growth in weight over time and ask questions, including intermediate points.
Group Activities
-- Interpret data presented on pictograms, bar charts and line graphs. Write questions for others to answer.

Day 2 Teaching
Show children the graph of pets from day 1. Label each bar with the numbers: 50, 150 and 100. How many children were surveyed in total? 50 out of 300 children chose a rabbit, what fraction is this? (1/6). What fraction chose a dog? (1/2). What fraction chose a cat? (1/3). Children sketch a pie chart to show the results.
Group Activities
-- Interpret data presented on pie charts.
-- Create a pie chart.

Day 3 Teaching
Remind children what the word average means and how the mean is one type of average. A sprinter ran 100m in times of 12s, 15s, 13s, and 16s; then calculated her mean time to be 18s. Does this sound right? Share today’s top tip for tests. Children add the 4 times together and divide by 4 to find her mean time. Take feedback. Challenge children to write three different numbers with a mean of 10.
Group Activities
-- Calculate the mean of a data set. Manipulate data to create given mean values.

### You Will Need

• ‘A graph to show children’s choice of pet’ (see resources)
• ‘A line graph to show the increase in weight of a dog’ (see resources)
• Interpreting graphs’ question sheets 1 to 7 (see resources)
• ‘Interpreting pie charts’ sheets (see Practice Worksheets)
• Flipchart and pens
• Mini whiteboards and pens
• ‘Find a mean’ sheet 1 (see Practice Worksheets)
• 0–9 digit cards

### Mental/Oral Maths Starters

Day 1
Reading scales on bar charts (pre-requisite skills).

Day 2
Find non-unit fractions of amounts (pre-requisite skills).

Day 3
Add five numbers together (pre-requisite skills).

### Procedural Fluency

Day 1
Interpretation of a range of graphs, including bar charts, line graphs and pictograms.

Day 2
Interpretation of pie charts.

Day 3
Find a mean; solve problems involving finding a mean.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 4 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 5 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.