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# Maths Year 6 Summer More 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 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
• ‘Properties of 3-D’ shapes practice sheet (see Practice Worksheets download)
• 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 2 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.

### Mastery: Reasoning and Problem-Solving

Refer to the Mastery: Reasoning and Problem-Solving download.

### Extra Support

This unit has no separate Extra Support activities.