• 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 3 Summer Shape

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 available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

## Unit 1 Line symmetry; name/sort 2-D shapes (suggested as 3 days)

### Objectives

Recognise line symmetry; name/sort 2-D shapes
Unit 1: ID #3803

National Curriculum
PofS (i)

Hamilton Objectives
37. Draw 2-D and make 3-D shapes, recognising both in different orientations, and describe them.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Watch a short BBC action clip about line symmetry. Establish a definition for a line of symmetry. Place 2-D shapes in centre of the class, along with long thin strips of paper. Choose a child to pretend to karate chop a shape to find the line(s) of symmetry, placing a strip of paper to show it. Do all of these shapes have a line of symmetry?
Group Activities
-- Fold a picture along a line of symmetry; complete symmetrical pictures.
-- Children draw one half of a picture for a partner to complete symmetrically. Begin to explore shapes with two lines of symmetry.

Day 2 Teaching
Show and carefully describe a square, modelling appropriate vocabulary. Note that it is a polygon. Show and define regular polygons, e.g. with a pentagon, hexagon and octagon. Children choose and describe a shape for a partner to guess. Swap and repeat. Record key vocabulary. Show, define and name irregular shapes.
Group Activities
-- Sort 2-D shapes in Venn diagrams according to children’s criteria.

Day 3 Teaching
What words can we use to name and describe 2-D shapes? Which have ‘square corners’? Remind children that these are called right angles. Draw more shapes, children describe them to a partner. Sort shapes using a Venn diagram.
Group Activities
Use the ‘Don’t make a triangle’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Children sort 2-D shapes into a Venn diagram according to two ‘secret’ criteria, with one shape placed as an ‘odd one out’. The rest of the group try to guess the sorting criteria and the odd one out.

### You Will Need

• Finding lines of symmetry from www.bbc.com
• Paper and mirror
• Selection of large 2-D shapes: most with lines of symmetry; some without
• Long straight thin strips of paper
• ‘Folding houses 1 and 2’ (see resources)
• Small pieces of paper, scissors and a timer
• Selection of 2-D shapes (regular and irregular)
• ‘Pentagons, hexagons and octagons’ (see resources)
• ‘Shapes to sort’ sheet on A3 paper (see resources)
• 2 hoops, roughly A3 size (e.g. made of wire/string)
• Sticky notes and PE hoops
• ITP: Tell the Time

### Mental/Oral Maths Starters

Day 1
Find lines of symmetry (pre-requisite skills).

Day 2
2-D shapes (pre-requisite skills).

Suggested for Day 3
Telling the time (simmering skills).

### Procedural Fluency

Day 1
Draw lines of symmetry on shapes and complete symmetrical drawings.

Day 2
Apply knowledge of shape properties to select and describe an odd one out.

Day 3
Draw shapes in four different Venn diagrams, according to their properties.

### Mastery: Reasoning and Problem-Solving

• Draw a 2-D shape with at least 1 curved side and 2 lines of symmetry.
• How many lines of symmetry in a regular pentagon?
• Can you draw a…
-- 4-sided shape with exactly 2 right angles?
-- Hexagon with every side a different length?
-- Regular octagon?

In-depth Investigation: Don’t Make a Triangle
Game for 2 where strategy and identifying triangles are both crucial.

### Extra Support

Transformations on a Pegboard
Explore the properties of 2-D shapes using an interactive pegboard. Transformations on a Pegboard from nrich.maths.org.

## Unit 2 Identify, describe and sort 3-D shapes (suggested as 3 days)

### Objectives

Identify, describe and sort 3-D shapes
Unit 2: ID #3821

National Curriculum
PofS (i)

Hamilton Objectives
37. Draw 2-D and make 3-D shapes, recognising both in different orientations, and describe them.
39. Identify horizontal and vertical lines, and pairs of parallel and perpendicular lines.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Hold up a cube. How many edges, vertices and faces does it have? Children feedback. Introduce the word polyhedron. Explain that it is a solid shape with flat faces and no curved faces. Hide a 3-D shape (a cube, cuboid, cylinder, sphere, cone or pyramid) in a feely bag. A succession of children describes the shape to their classmates. Discuss which shape it could/ couldn’t be from their clues.
Group Activities
-- Name and describe the shape of packaging. Use to make a display.
-- List properties of given 3-D shapes, then sort.

Day 2 Teaching
Draw a labelled Carroll diagram. Ask a child to pick a 3-D shape from a box and show it. What’s the name of this shape? Where should it go on the diagram? Children discuss properties and feedback. Talk children through the criteria that fit. Place/ draw the shape in. Repeat with other shapes.
Group Activities
-- Sort 3-D shapes in a Carroll diagram.
-- Children guess headings in a Carroll diagram as you sort shapes.

Day 3 Teaching
Show an Egyptian pyramid. Here is a smaller version of the shape… Pass several square-based pyramids round class. Children share descriptions; draw out type and number of faces, numbers of vertices (corners) and edges. Draw a table to record this and fill it in. Look at (but don’t describe in detail) other pyramids.
Group Activities
-- Whole class investigation: Make pyramids with different shaped bases. Count faces, vertices and edges; discuss patterns; make generalisations.

### You Will Need

• Selection of 3-D shapes - cube, cuboid, cylinder, sphere, cone and pyramid and feely bag
• Selection of packaging in as many different shapes as possible
• Sticky notes, hoops, flipchart and pens
• Selection of at least six 3-D shapes including a triangular-based pyramid (tetrahedron), a square-based pyramid and a cube
• Large sheet of paper, scissors and tape
• Several different square-based pyramids, pyramids with differently-shaped bases
• ‘Nets of pyramids’ sheets (see resources)
• Net for a square-based pyramid
• ‘Pyramid properties’ (see resources)

### Mental/Oral Maths Starters

Day 1
Naming 3-D shapes (pre-requisite skills).

Suggested for Day 2
Number bonds to 10 and 20 (simmering skills).

Day 3
Describing 3-D shapes (pre-requisite skills).

### Procedural Fluency

Day 1
Name and describe faces of 3-D shapes.

Day 2
Sort 3-D shapes into Carroll diagrams.

Day 3
Fill in missing information about faces, vertices and edges of prisms. Look for and describe patterns.

### Mastery: Reasoning and Problem-Solving

• What shape could I be describing?
It has 6 faces…
It has 12 edges…
4 edges are twice the length of the other 8 edges.
• True or false?
All cubes have eight vertices
A pyramid always has a square base
A cylinder has 3 faces.
There is a shape with just 1 face
A cone has 1 circular face
• Tick the polyhedrons:
-- sphere
-- cube
-- cone
-- triangle based pyramid
-- cuboid
-- cylinder

In-depth Investigation
Use the group activity on Day 3 as the in-depth activity for this unit.

### Extra Support

Solid Specials
Exploring the relationship between 2-D and 3-D shapes

## Unit 3 Right angles as turns; angles in 2-D shapes (suggested as 4 days)

### Objectives

Understand right angles as turns; identify/ compare angles in 2-d shapes
Unit 3: ID #3833

National Curriculum
PofS (ii) (iii) (iv)

Hamilton Objectives
38. Identify right angles as 90⁰ in shapes, and also as turns; recognise angles as less than or greater than 90⁰.
39. Identify horizontal and vertical lines, and pairs of parallel and perpendicular lines.

### Teaching and Group Activities for Understanding

Day 1
Show a clock face on the IWB. Where does the minute hand point at quarter past? At half past. Quarter to? Draw lines to split the clock into quarters. Shade a quarter section. This is a quarter of the clock face. What’s the angle between the lines? [a right angle; 90 degrees; 90°]. Draw a right angle. A right angle is a quarter turn. Repeat to identify a half turn and a three-quarter turn. Note that the clock hands turn clockwise. Turning the other way is anti-clockwise.
Group Activities
-- In the hall or an outdoor space, give instructions to practise making quarter, half and three-quarter turns.

Day 2
Show a picture. Close your eyes. Turn it 90° clockwise. Open eyes, what have I done? You have turned it through a right angle, a quarter of a full turn. Repeat, turning it through 2, then 3 then 4 right angles, both clockwise and anticlockwise. 2 right angles is half a complete turn, 4 right angles a complete turn.
Group Activities
-- Create patterns by rotating an irregular shape through successive right angles.
-- Create patterns by rotating a shaded 3 by 3 grid through successive right angles.

Day 3
Draw a square and a rhombus. Which is a square? All the sides in each shape are the same length. Observe how each angle in a square must be a right angle. Show a large set square and how a ‘square’ corner is a right angle. Compare angles in the square and rhombus against the right angle of the set square.
Group Activities
-- Find examples of different types of angle in the classroom and around the school.
-- Classify angles <90° as ‘acute’ and >90° as ‘obtuse’.

Day 4
Use the range of shapes on ‘Perpendicular and parallel lines’ (see resources) to explore lines that are vertical, horizontal, perpendicular and parallel. Look for examples of these around the classroom.
Group Activities
Use the ‘My square, not yours!’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Sort shapes into a Venn diagram based on their properties.

### You Will Need

• Large Hamilton clock (see resources)
• ‘Animal cards’ (see resources)
• Use of the hall
• A picture
• Squares of card, brass fasteners, sheets of paper
• Cm² paper and coloured pencils
• A large set square and small set squares
• ‘Perpendicular and parallel lines’ (see resources)
• Flipchart paper
• Selection of 2-D shapes (both regular and irregular)
• ‘Sorting shapes’ (see resources)
• Scissors and glue sticks

### Mental/Oral Maths Starters

Suggested for Day 1
Subtraction facts (simmering skills).

Suggested for Day 2
Add multiples of 10 (simmering skills).

Suggested for Day 3
Multiply/divide by 10 (simmering skills).

Suggested for Day 4
Match digital and analogue times; revise am and pm (simmering skills).

### Procedural Fluency

Day 1
Say where an arrow on a spinner will be after stated turns.

Day 2
Respond to true /false statements about angles, then questions about a diver’s turns.

Day 3
Use set squares (or corner of a piece of paper) to check which angles on shapes are right angles, more than a right angle or less than a right angle.

Day 4
Identify vertical, horizontal, perpendicular and parallel lines.

### Mastery: Reasoning and Problem-Solving

• Draw a shape with 2 right angles that is not a square. Identify any angle in this shape that is more than 90 degrees.
• Set a clock to 3 o’clock. Move the minute hand clockwise through 3 right angles. What is the time? What is the angle between the hands of a clock at 6 o’clock?
• Draw a triangle with 1 angle less than 90 degrees and 1 angle more than 90 degrees. Is the third angle more or less than a right angle?
• True or false?
A horizontal line is always at right angles with a vertical line.
All shapes with 2 pairs of parallel lines are rectangles.
A pair of perpendicular lines must be horizontal and vertical.

In-depth Investigation: My Square, Not Yours!
Children draw a succession of perpendicular and parallel lines to create squares.

### Extra Support

Construction Site
Identifying faces, corners and edges on 3-D shapes