• 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 4 Spring 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 Draw circles, study polygons, e.g. triangles (suggested as 3 days)

### Objectives

Draw circles, identify and study polygons, especially triangles
Unit 1: ID# 4421

National Curriculum
PofS Y4(i); Y6(iv)

Hamilton Objectives
39. Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Introduce the terminology for circles: radius, diameter, and circumference. Show children a compass and model how to use it to draw a circle. Discuss drawing circles with specified radii. Observe that the diameter is double the radius.
Group Activities
-- Use compasses to draw circles with measured radii.

Day 2 Teaching
Show a large 50p coin and agree (having noted slightly curved sides and rounded corners) that it is a heptagon. Children draw irregular heptagons. Identify types of angle within it. Explain that all polygons have straight sides and are closed. Discuss what makes a good description of a polygon.

Group Activities
-- Identify the properties of polygons and use this to sort them.
-- Draw 2-D shapes based on given properties.

Day 3 Teaching
Show children five different triangles and discuss their similarities and differences. Look at the number of sides and angles, lines of symmetry, length of sides, sizes of angles. Name the triangles as: equilateral, isosceles, right angled, scalene. Note that a right angled triangle can also be isosceles. Sort triangles according to different properties, e.g. has a right angle or not.
Group Activities
Use the in-depth problem-solving investigation ‘Egyptian Rope’ from NRICH as today’s group activity.
Or, use this activity:
-- Identify right angles and other properties in triangles; classify them.

### You Will Need

• A circle: pre-drawn and annotated (circumference, radius, diameter)
• Compasses, large pieces of paper, glue, sticky notes and rulers
• cm cards (see resources)
• Range of sharp coloured pencils and scissors
• Picture of 50p coin (or large mock 50p coin)
• ‘Polygons to sort’ sheet (see resources)
• Paper equilateral triangle
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
2-D shapes (pre-requisite skills)

Suggested for Day 2
Telling the time (simmering skills)

Suggested for Day 3
Complete symmetrical drawings (simmering skills)

### Procedural Fluency

Day 1
Draw circles of given radii using compasses.

Day 2
Guess the shape game.

Day 3
Name triangles and identify right angles and other properties.

### Mastery: Reasoning and Problem-Solving

• Always true, sometimes true or false?
The circumference of a circle is the distance across the centre from one side to the other.
The radius of a circle is half the diameter.
A circle is a special type of polygon.
A pentagon is a regular five-sided polygon.
A polygon has eight sides.
• Draw triangles to match each description.
With a right angle and the shortest side is 3cm.
Two sides and two angles are equal.
No equal angles; one side twice as long as one other side.

In-depth Investigation: Egyptian Rope
The ancient Egyptians were said to make right-angled triangles using a rope which was knotted to make 12 equal sections. If you have a rope knotted like this, what other triangles can you make? Egyptian Rope from nrich.maths.org.

### Extra Support

Recognising acute, right and obtuse angles

## Unit 2 Identify and explore 3-D shapes (suggested as 2 days)

### Objectives

Identify and explore 3-D shapes
Unit 2: ID# 4441

National Curriculum
PofS (i)

Hamilton Objectives
39. Compare and classify geometric shapes based on their properties and sizes

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show a variety of 3-D shapes. Write the words: face, edge, vertex (plural: vertices) and polyhedron on the board. Revise their meanings and ask children to use these words to describe one of the shapes to a partner. Discuss the properties of different shapes, using these terms.

Group Activities
-- Make and describe 3-D shapes, identifying faces, edges and vertices.
-- Make 3-D models using cubes.

Day 2 Teaching
Show children a selection of 3-D shapes. Explain that we will sort these into prisms and pyramids and those which are neither. Identify the properties of prisms and those of pyramids and ensure children understand that there are different examples of each. Sort using other headings/criteria.
Group Activities
Use the in-depth problem-solving investigation ‘Soma Cube’ as today’s group activity.
Or, use these activities:
-- Make, describe and classify 3-D shapes.

### You Will Need

• A collection of 3-D shapes: cubes, cuboids, cylinders, spheres, cones, prisms, pyramids and tetrahedra
• Shape construction equipment
• Interlocking cubes
• ‘Cube Models’ sheet (see resources)
• Isometric paper (see resources)
• Straws and modelling clay
• ‘Skeletons’ sheets 1 and 2 (see resources)
• Two hoops and card or paper for labels

### Mental/Oral Maths Starters

Day 1
Use clues to identify 3-D shapes (pre-requisite skills)

Suggested for Day 2
Counting on and back in ones from 4-digit numbers through 1000s and 100s (simmering skills)

### Procedural Fluency

Day 1
List the properties of 3-D shapes.

Day 2
Sort 3-D shapes into given Venn diagrams.

### Mastery: Reasoning and Problem-Solving

• Create a net for a tetrahedron. Fold it up to ensure that it 'works'. Is this the only way to draw a net for a tetrahedron?
• Imagine a 3 by 3 by 3 cube hanging in front of you with just one face facing you.
The cube is made up of three 3 by 3 layers, that is 27, small cubes.
You drill a hole through the four corner cubes that are facing you, all the way through to the back.
A friend looks down on the cube, from above, and they also drill four holes through their four corner cubes all the way through to the bottom.
You and your friend then examine all the 27 small cubes.
How many small cubes will then have holes drilled in them?
• Find out what a dodecahedron is. Build one using a construction kit, then write a description of it for someone who has never seen one, using all your best mathematical shape language.

In-depth Investigation: Soma Cube
Children create specified 3-D shapes using 2-D representations and then combine these to create other 3-D shapes including a cube.

### Extra Support

Solid Specials
Looking at the relationship between 2-D and 3-D shapes

## Unit 3 Co-ordinates: draw polygons (suggested as 3 days)

### Objectives

Use x, y co-ordinates on a grid to draw and complete polygons in the 1st quadrant
Unit 3: ID# 4447

National Curriculum
PofS Y4(i); Y6(iv)

Hamilton Objectives
39. Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw horizontal and vertical axes from 0 to 10 on a square background on the Interactive Whiteboard. The x-axis goes across. Ring 2 points: (2, 5) and (6, 1). Show children how we write these as co-ordinates. Children give more co-ordinates to make a square. Repeat with co-ordinates for another square and a triangle.
Group activities
Use the in-depth problem-solving investigation ‘Coordinate Challenge’ from NRICH as today’s group activity.
Or, use this activity:
-- Plot (x, y) co-ordinates and use them to construct 2-D shapes (in the first quadrant) of a co-ordinate grid.

Day 2 Teaching
Draw a triangle on a grid. Children write co-ordinates for each corner. Move the triangle 2 squares to the right and discuss how each vertex has moved 2 squares. Explain that this shape has been translated. Repeat with other shapes moving up, down, left or right. Children sketch and label the new co-ordinates.
Group Activities
-- Translate 2-D shapes up, down, left or right in the first quadrant of a co-ordinate grid.

Day 3 Teaching
Launch the Coordinates ITP. Stress that the x co-ordinate comes before the y one. Use the grid to show the co-ordinates of vertices of different polygons, including a ‘house-shaped’ pentagon.
Group Activities
-- Plot co-ordinates in the first quadrant and describe translations.
-- Apply knowledge of co-ordinates in the first quadrant.

### You Will Need

• Interactive Whiteboard
• Squared paper and 0-9 cards
• ‘Co-ordinates’ sheet, including one enlarged copy (see resources)
• ITP: Co-ordinates
• Counters, two 1-6 dice and coloured pencils
• Coin with T (translation) labelled on one side and D (destination) labelled on the other
• Cali and the Co-ordinate System game from www.math10.com

### Mental/Oral Maths Starters

Suggested for Day 1
Convert from 24-hour clock to 12-hour am/pm (simmering skills)

Suggested for Day 2
Roman numeral clocks (simmering skills)

Suggested for Day 3
Roman numerals (simmering skills)

### Procedural Fluency

Day 1
Plot x and y coordinates in one quadrant on a graph to draw 2-D shapes, including missing co-ordinate points.

Day 2
Give the x and y coordinates of shapes on a grid after moving them up, down, left or right.

Day 3
Imagine translating shapes and finding new co-ordinates.

### Mastery: Reasoning and Problem-Solving

• Draw a 6 by 6 grid; label the x and y axes. Mark these co-ordinates:
A (1, 1) B (1, 4) C (4, 1).
Join these and name the shape created.
Add another co-ordinate so that if you join all four vertices you create a 4-sided shape that is not a square.
• Sam says that if she draws a square on a co-ordinate grid, then two of its corners will always have the same ‘x’ co-ordinate and two will have the same ‘y’ co-ordinate.
Is she correct? Explain how you know.
• Bill draws a triangle on his grid. He moves it two spaces ‘down’ the grid. The new co-ordinates of its vertices are:
(2,1) (6, 1) (3, 5)
Write the co-ordinates of the triangle before its translation.

In-depth Investigation: Co-ordinate Challenge
Use clues about the symmetrical properties of capital letters to place them on the coordinate grid. Co-ordinate Challenge from nrich.maths.org.

### Extra Support

The Lily Pond
Describe a route for Frog to jump across all the leaves to visit Snail. The Lily Pond from nrich.maths.org.

## Unit 4 Line of symmetry: identify and construct (suggested as 2 days)

### Objectives

Identify a line of symmetry; complete shapes with respect to this
Unit 4: ID# 4457

National Curriculum
PofS (iii) (iv)

Hamilton Objectives
41. Identify lines of symmetry in 2-D shapes presented in different orientations; complete a simple symmetric figure with respect to one line of symmetry.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display a pattern drawn on one side of a line of symmetry (see resources). Discuss the concept of ‘line of symmetry’ and begin to complete each pattern. Provide copies for children who complete each symmetrical pattern. Children create their own symmetrical patterns, colouring just 12 squares lines of symmetry.
Group Activities
-- Create symmetrical patterns across one or two lines of symmetry.

Day 2 Teaching
Draw an irregular but symmetrical hexagon. Ask children to say whether it has a line of symmetry. Then draw half of an irregular but symmetrical octagon. Children need to draw the other half. Discuss shapes with two lines of symmetry and draw one, identifying the two lines. Model how to use a mirror to check for symmetry, perhaps using the Symmetry ITP.
Group Activities
Use the in-depth problem-solving investigation ‘Tremendous Tiles’ as today’s group activity.
Or, use these activities:
-- Identify the lines of symmetry on 2-D shapes; draw shapes with a given number of lines of symmetry.
-- Identify whether shapes are symmetrical. Draw the lines of symmetry on 2-D shapes.

### You Will Need

• ‘Symmetrical patterns’ sheets 1 and 2 (see resources)
• Squared paper
• ITP: Symmetry
• ‘Shapes for sorting’ sheet (see resources)
• Mirrors, rulers and a set of 2D shapes (regular, irregular, symmetrical, not symmetrical)

### Mental/Oral Maths Starters

Suggested for Day 1
Draw irregular polygons (simmering skills)

Suggested for Day 2
Compare pairs of numbers with 2 decimal places (simmering skills)

Or

Suggested for Day 2
Count on or back in steps of 50 and 100 (simmering skills)

### Procedural Fluency

Day 1
Complete patterns across one or two lines of symmetry.

Day 2
Complete drawings of 2-D shapes to make them symmetrical.

### Mastery: Reasoning and Problem-Solving

• Shade 4 more spaces on this grid (see download) to create a pattern with two lines of symmetry.
• Draw a shape with exactly four lines of symmetry. It does not need to be a polygon.
• By shading just one ‘cell’ on a 3 by 3 square grid, how many different symmetrical patterns can you make? Be careful not to count reflections or rotations of patterns already made…
How many different patterns can you make if you are allowed to shade 2, 3, 4 or 5 cells?
Can you make a prediction about how the number of patterns with 6 cells shaded will relate to the number with 3 cells shaded?

In-depth Investigation: Tremendous Tiles
Children explore creating patterns of tiles with three asymmetrical blocks. They look for and identify lines of symmetry, creating patterns with at least two lines of reflective symmetry.

### Extra Support

Colouring Triangles
Make symmetrical patterns by colouring the set of triangles. Colouring Triangles from nrich.maths.org.

## Unit 5 Angle types; properties of polygons (suggested as 4 days)

### Objectives

Identify types of angle; use these in exploring properties of polygons
Unit 5: ID# 4463

National Curriculum
PofS (i) (ii)

Hamilton Objectives
39. Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.
40. Identify acute and obtuse angles, compare and order angles up to 180⁰.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a succession of given angles (see Teaching and Activities document). Ask children which are larger/smaller than 90°. Identify acute (sharp) angles as less than 90° and obtuse (blunt) angles as being between 90° and 180°. Compare angles by placing them on top of one another.
Group Activities
-- Compare and classify angles.

Day 2 Teaching
Show a number of different triangles. Discuss what they have in common and how they are different. Remind children of the previous learning on triangles of different types and identify these. Then focus on the types of angles in each.
Group Activities
-- Explore the angle properties of different types of triangles.

Day 3 Teaching
Remind children of the definition of a quadrilateral. Ask children to draw a quadrilateral (different to their neighbour’s), then to mark right angles with a little square, acute angles with ‘a’ and obtuse angles with ‘o’. Did their neighbour’s shape have the same number of each type of angle?
Group Activities
Use the in-depth problem-solving investigation ‘Rabbit Run’ from NRICH as today’s group activity.
Or, use this activity:
-- Investigate the angle properties of quadrilaterals.

Day 4 Teaching
Draw a parallelogram and a trapezium. Both are quadrilaterals. Children describe each, including what is the same and different. Both have 2 parallel sides (same distance away from each other, like train tracks). Move on to sort other quadrilaterals by properties, including a square, rhombus and oblong.
Group Activities
-- Draw quadrilaterals, based on properties including types of angles.
-- Compare and classify quadrilaterals, based on properties including types of angles.

### You Will Need

• Interactive Whiteboard set square
• ‘Comparing and ordering angles’ sheet (see resources)
• Set squares, scissors, protractors and coloured card
• Flipchart, whiteboards and pens
• Paper copy of triangle 2 (equilateral triangle) from Day 2
• Elastic bands and geoboards
• Rulers
• ‘Sorting quadrilaterals’ sheet (see resources)
• Venn rings (or hoops)
• Sticky notes

### Mental/Oral Maths Starters

Suggested for Day 1
Count on and back in steps of 0.01 through multiples of 0.1 and 1 (simmering skills)

Suggested for Day 2
Multiply and divide numbers by 10 and 100 (simmering skills)

Suggested for Day 3
Division fact bingo for 8 times table (simmering skills)

Suggested for Day 4
Division facts for 7 times table (simmering skills)

### Procedural Fluency

Day 1
Compare and order angles, and identify if they are acute or obtuse.

Day 2
Identify acute, obtuse and right angles in triangles.

Day 3
Identify acute, obtuse and right angles in quadrilaterals.

Day 4
Sort quadrilaterals into Venn diagrams based on their properties.

### Mastery: Reasoning and Problem-Solving

• True or false?
A triangle cannot have two right angles.
A triangle with one right angle cannot be isosceles.
A quadrilateral cannot have exactly three right angles.
A quadrilateral can always be divided into two triangles by drawing just one straight line.
• Sketch the following:
A triangle with one obtuse angle.
A quadrilateral with two obtuse angles.
A triangle with three sides of identical length.
A quadrilateral that has two lines of symmetry but no right angles.
A quadrilateral with two pairs of parallel lines but no right angles.

In-depth Investigation: Rabbit Run
Help Ahmed to build a run for his rabbit using planks of different lengths. Rabbit Run from nrich.maths.org.

### Extra Support

Jig Shapes
Complete the shape jigsaw and describe the shapes for a partner. Can they guess which shape you are describing? Jig Shapes from nrich.maths.org.