# Maths Year 3/4 Autumn Shape

Each unit has everything you need to teach a set of related skills and concepts.

First time using Hamilton Maths?

The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Symmetry and 2D shapes (suggested as 3 days)

### Objectives

Symmetry and 2D shapes
Unit 1: ID# 34348

Y3: Recognise symmetry and complete symmetrical drawings; Describe, name and sort 2-D shapes.
Y4: Recognise symmetry in a variety of diagrams; draw symmetrical patterns; draw different polygons and identify their properties; identify properties of triangles and sort them using diagrams.

National Curriculum
Y3: Properties of shapes (i) (ii)
Y4: Properties of shapes (i) (iii) (iv)

Y3 Hamilton objectives
37. Draw 2-D and make 3-D shapes, recognising both in different orientations, and describe them.
38. Identify right angles as 90° in shapes.

Y4 Hamilton objectives
39. Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.
41. Identify lines of symmetry in 2-D shapes presented in different orientations; complete a simple symmetrical figure with respect to one line of symmetry.

### Planning and Activities

Day 1 Teaching
Define and explore lines of symmetry using online animations/examples.
Further Teaching with Y4
Explore symmetrical patterns on a square grid.
Group Activities: T with Y4
Use the ‘Tremendous tiles’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Complete symmetrical pictures, either pre-drawn or self-drawn.
Y4 -- Create patterns with horizontal or vertical lines of symmetry.

Day 2 Teaching
Explore regular and irregular heptagons and their properties.
Further Teaching with Y3
Identify properties of polygons and use associated vocabulary.
Group Activities: T with Y3
Y3 -- Introduce the Venn diagram; use it for sorting 2-D shapes.
Y4 -- Sort polygons into a Carroll or Venn diagram.

Day 3 Teaching
Describe and sort irregular polygons.
Further Teaching with Y4
Classify types of triangles, learning associated vocabulary.
Group Activities: T with Y4
Y3 -- Sort a wide range of 2-D shapes into a Venn diagram.
Y4 -- Identify, classify and sort a range of triangles.

### You Will Need

• ‘Symmetrical patterns’ sheets 1 and 2 (see resources)
• ‘Folding houses 1 and 2’ (see resources)
• Small pieces of paper, scissors and squared paper
• Glue sticks
• Sticky notes and rulers
• Large 50p and 20p coins
• A wide selection of 2-D shapes (regular and irregular: ideally paper, card or very thin plastic)
• ‘Pentagons, hexagons and octagons’ sheet (see resources)
• Additional activity sheets (see resources)
• Sorting hoops and A3+ pieces of paper

### Short Mental Workouts

Day 1
Lines of symmetry

Day 2
Feely bag 2-D shapes

Day 3
Odd one out 2-D shapes

### Procedural Fluency

Day 1
Y3: Identify symmetry on drawings and complete symmetrical drawings.
Y4: Grid symmetry patterns.

Day 2
Y3: Find and describe the odd one out of sets of shapes.
Y4: Properties of regular and irregular polygons: Draw a shape to match each description.

Day 3
Y3: Sort 2-D shapes.
Y4: Classify and describe triangles.

### Mastery: Reasoning and Problem-Solving

Y3

• 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?

Y4

• How many lines of symmetry in a regular pentagon? Hexagon? Heptagon? Make a generalisation based on your answer.
• 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: 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 symmetry.
Adapt for Y3 by challenging them in the first instance to simply create a symmetrical pattern.

### Extra Support

Y3 and Y4: Making Squares
Investigate the different squares you can make on a 5 × 5 pegboard. (Rather than find out the areas of the squares made, as suggested) Use the same pegboard to practise making other polygons. Are any of them symmetrical? Making Squares from nrich.maths.org.

## Unit 2 Understanding 3D shapes (suggested as 2 days)

### Objectives

Understanding 3D shapes
Unit 2: ID# 34364

Y3: Describe, name and sort 3-D shapes (cube, cuboid, cylinder, sphere, cone, pyramid).
Y4: Describe, name and sort 3-D shapes (cube, cuboid, cylinder, sphere, cone, pyramid, prisms).

National Curriculum
Y3: Properties of shapes (i) (ii)
Y4: Properties of shapes (i) (ii)

Y3 Hamilton objectives
37. Draw 2-D and make 3-D shapes, recognising both in different orientations, and describe them.

Y4 Hamilton objectives
39. Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.

### Planning and Activities

Day 1 Teaching
Identify key properties of polyhedrons: faces, vertices, edges; describe them using appropriate vocabulary in a guessing game.
Group Activities: T with Y3
Y3 -- Name and describe the shape of packaging then use this to make a display. Other children will list properties of given 3-D shapes, then sort into a Venn diagram.
Y4 -- Make models of 3-D shapes, using straws and modelling clay OR Make 3-D models using cubes and draw these on isometric paper.

Day 2 Teaching
Sort 3-D shapes into a Carroll diagram.
Further Teaching with Y4
Explore the similarities and differences between pyramids and prisms, classify and sort.
Group Activities: T with Y4
Use the ‘Soma cube’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Sort 3-D shapes onto a Carroll diagram. Some children will use logic to deduce headings in a Carroll diagram.
Y4 -- Make 3-D shapes using construction equipment; describe and classify them.

### You Will Need

• A wide selection of 3-D shapes including cubes, cuboids, cylinders, spheres, cones, pyramids, prisms, tetrahedra
• Feely bag
• Selection of packaging
• Sticky notes, hoops and straws
• Modelling clay and rulers
• ‘Skeletons’ sheets 1 and 2 (see resources)
• Interlocking cubes
• ‘Cube models’ (see resources)
• ‘Isometric paper’ (see resources)
• Large sheet of paper
• 2-D construction shapes, e.g. Polydron

### Short Mental Workouts

Day 1
Naming 3-D shapes

Day 2
Complete a symmetrical drawing

### Procedural Fluency

Day 1
Y3: Describe 3-D shapes.
Y4: 3-D shape facts: faces, edges and vertices.

Day 2
Y3: Sort 3-D shapes into Carroll diagrams.
Y4: Sort 3-D shapes into Venn diagrams.

### Mastery: Reasoning and Problem-Solving

Y3

• 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
cylinder
triangle-based pyramid
cuboid

Y4

• 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 × 3 × 3 cube hanging in front of you with just one face facing you.
The cube is made up of three 3 × 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

Y3 and Y4: Solid Specials
Exploring the relationship between 2-D and 3-D shapes

## Unit 3 Co-ordinates in the first quadrant (suggested as 3 days)

### Objectives

Unit 3: ID# 34380

Y4: Read and plot co-ordinates in the first quadrant; use x, y co-ordinates to draw and translate shapes in the first quadrant.

National Curriculum
Y3: n/a
Y4: P&D (i) (ii) (iii)

Y3 Hamilton objectives
42. Draw 2-D shapes and describe them.

Y4 Hamilton objectives
42. Describe positions on a 2-D grid as coordinates in the first quadrant, plot specified points and draw sides to complete a given polygon.
43. Describe movements between positions as translations of a given unit to the left/right, up/down.

### Planning and Activities

Day 1 Teaching
Introduce key vocabulary relating to drawing co-ordinate axes. Model how to read and plot co-ordinates on the grid, suggesting ways for the children to remember how to do so.
Further Teaching with Y4
Finding the missing co-ordinates needed to complete a polygon.
Group Activities: T with Y4
Y3 -- Read and plot co-ordinates on a 0–6 or 0–10 grid.
Y4 -- Plot (x, y) co-ordinates and use them to construct 2-D shapes. Determine missing co-ordinate(s).

Day 2 Teaching
Draw shapes on a co-ordinate grid and model how to translate them; find new co-ordinates.
Group Activities: T with Y3
Y3 -- Plot shapes or capital letters on a co-ordinate grid; challenge children to write words with plotted letters.
Y4 -- Translate shapes horizontally or vertically on a co-ordinate grid. Read co-ordinates and describe the translation.

Day 3 Teaching
Quick revision of reading and plotting co-ordinates.
Further Teaching with Y3
Play the Hit the co-ordinate online game to practise plotting co-ordinates in the first quadrant.
Group Activities: T with Y4
Use the in-depth problem-solving investigation ‘Co-ordinate Challenge’ from NRICH as today’s group activity.
Or, use these activities:
Y3 -- Play ‘Hit the Co-ordinate’ or create an alien mask by following a set of instructions to plot sequences of co-ordinates (both online activities).
Y4 -- Play ‘Translation or destination’ game from NCETM.

### You Will Need

• Whiteboard and pens
• Number cards 0–10
• ‘Co-ordinates grid’ sheet 1 (see resources)
• ‘Co-ordinates grid’ sheet 2 (see resources)
• ITP: Co-ordinates
• Hit the Co-ordinate from www.mathsisfun.com
• 1–6 dice, counters and coloured pencils
• Squared paper, A4 card and glue
• Pens or paints and sticky tape
• Coins, with sides labelled T and D
• ITP: Tell the Time

### Short Mental Workouts

Day 1
Identify 3-D shapes

Day 2
Tell the time

Day 3
Clock face Roman numerals

### Procedural Fluency

Day 1
Y3: Identify co-ordinates of shapes.
Y4: Plot shapes from given co-ordinates; identify missing co-ordinates.

Day 2
Y3: Plot shapes from given co-ordinates.
Y4: Plot and translate shapes.

Day 3
Y3: Name shapes; identify their co-ordinates.
Y4: Translate shapes; identify new co-ordinates.

### Mastery: Reasoning and Problem-Solving

Y3 & Y4

• Draw a 6 × 6 grid and 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 point 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’s starting position.

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

Y3: The Lily Pond
Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go? The Lily Pond from nrich.maths.org

Y4: Treasure Island
Write what you can see at the co-ordinates of the treasure island map. The words can be used in a special way to find the buried treasure. Can you work out where it is? Treasure Island from nrich.maths.org