• 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 5 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 Deepen understanding of 3-D shapes (suggested as 2 days)

### Objectives

Revise and deepen understanding of properties of 3-D shapes
Unit 1: ID# 5477

National Curriculum
PofS (i)

45. Identify 3-D shapes from 2-D representations.

### Teaching and Group Activities for Understanding

Day 1 Teaching
The cube and the cuboid. What is the same about these two shapes and what is different? Discuss how to sort 3-D shapes into the two sets of a Venn diagram. Show how a Carroll diagram can also allow us to sort shapes.
Group Activities
-- Describe and sort 3-D shapes according to a range of properties.

Day 2 Teaching
Look at pictures of 3-D shapes on suggested websites. Can children describe and name each shape? Do they find it easy to visualise shapes from 2-D drawings? Click on shapes to play animations. Explore the many different types of pyramid and prism.
Group Activities
Use the ‘Pharaoh’s rest’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Explore the properties of prisms and pyramids.

### You Will Need

• Models of 3-D shapes including cuboids, cones, cylinders, pyramids and prisms
• Feely bag, sorting hoops & small cards for labels
• Blu-tack & dry-wipe pens
• ‘Prisms’ & 'pyramids' activity sheets (see resources)
• Paper, scissors, tape
• Models of prisms & pyramids

### Mental/Oral Maths Starters

Suggested for Day 1
Find lines of symmetry (simmering skills)

Suggested for Day 2
Bonds to 100 (simmering skills)

### Procedural Fluency

Day 1
Sort 3-D shapes according to number of faces.

Day 2
Sort 3-D shapes according to number of edges.

### Mastery: Reasoning and Problem-Solving

• Always true, sometimes true or false?
A cube is a type of cuboid
Pyramids have 5 faces
Prisms have a cross-section that is always the same, so a cylinder is a prism
Cubes and cuboids have the same number of vertices
• How many edges has a…
-- Cuboid?
-- Square-based pyramid?
-- Cylinder?
-- Triangular prism?

In-depth investigation: Pharaoh’s Rest
By looking at this net for a square-based pyramid, can you visualise and draw other, different nets that fold to give the same pyramid?

### Extra Support

What’s Special?
Identifying and describing properties of triangles; using these properties to sort the triangles.

## Unit 2 Properties of polygons; quadrilaterals (suggested as 3 days)

### Objectives

Describe properties of 2-D shapes and polygons; classify quadrilaterals
Unit 2: ID# 5483

National Curriculum
PofS (v) (vi)

Hamilton Objectives
48. Understand properties of rectangles & triangles; distinguish between regular and irregular polygons based on reasoning about equal sides/angles.
39. (Y4) Compare and classify … quadrilaterals … based on their properties.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display ‘Guess the shape’. Choose a shape. Children work in pairs to write five facts about it. Take feedback. Ensure that children are clear that a polygon only has straight sides, so a circle, oval, semi-circle are 2-D shapes, but are not polygons.

Group Activities
Draw and investigate polygons on isometric paper.
-- Play ‘Guess the shape’ to practise describing 2-D shapes.

Day 2 Teaching
Ask children to draw a polygon. Make sure all children draw a straight-sided closed shape. Ask children to hold up their polygon if it has an acute angle. Continue like this, asking children to hold up their shape if it has a particular property.
Group Activities
-- Draw polygons of 3 to 8 sides, with certain features stipulated.

Day 3 Teaching
Ask children to draw a quadrilateral, then discuss similarities and differences. Repeat, to explore other properties by drawing a quadrilateral with at least one pair of perpendicular sides/ parallel sides, etc. Name and explore the different quadrilaterals using an online activity from www.mathsisfun.com.
Group Activities
Use the in-depth problem-solving investigation ‘Quadrilaterals’ from NRICH as today’s group activity.
Or, use this activity:
-- Draw, describe and classify quadrilaterals.

### You Will Need

• ‘Guess the shape’ sheet (see resources)
• Rulers & squared paper
• ‘Five-triangle polygons’ sheet (see resources)
• Protractors, scissors & glue
• Poster paper (7 sheets)
• ‘Exploring quadrilaterals’ sheet (see resources)

### Mental/Oral Maths Starters

Suggested for Day 1
Times tables (simmering skills)

Suggested for Day 2
Place numbers with 2dp on a line (simmering skills)

Suggested for Day 3
Place value in 4-digit numbers (simmering skills)

### Procedural Fluency

Day 1
Look at properties of 2-D shapes.

Day 2
Look at properties of polygons.

Day 3

### Mastery: Reasoning and Problem-Solving

• Is a semicircle a polygon?
Draw a polygon and list five of its properties.

How many different quadrilaterals can be made by joining four of the dots on a circle with eight evenly-spaced dots? Quadrilaterals from nrich.maths.org.

### Extra Support

Sorting Logic Blocks
Use an on-screen interactivity to practise describing and sorting 2-D shapes.
Could you make some more shapes to add to the set? What would you make and why? Sorting Logic Blocks from nrich.maths.org.

## Unit 3 Draw/reflect shapes on co-ordinate grids (suggested as 3 days)

### Objectives

Using a co-ordinate grid to draw and reflect 2-D shapes
Unit 3: ID# 5501

National Curriculum
P&D (i)

Hamilton Objectives
49. Identify, describe, represent position of a shape following a reflection or translation, use appropriate language; know that the shape is unchanged [use a 2-D grid and co-ordinates in two quadrants].

### Teaching and Group Activities for Understanding

Day 1 Teaching
Support children in drawing a co-ordinate using ‘across’, and ‘walk before you fly’. Draw all but the last point of some recognisable polygons and ask children to draw in the last point and record its co-ordinates. Draw a pentagon straddling both quadrants. Children sketch the shape, then label the co-ordinates.
Group Activities
Use the ‘Cycling co-ordinates’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Plot co-ordinates and draw polygons in two quadrants.

Day 2 Teaching
Join points (-3, 1), (4, 1), (-1, 5) and (6, 5) for a parallelogram.
Children write the co-ordinates of each point. This parallelogram moves two squares to the right. What are the co-ordinates of its new position? Draw the new position and discuss how each x- value has been increased by 2, but the y-values have stayed the same. Repeat with other polygons.
Group Activities
-- Translate polygons on a grid; identify how co-ordinates change.

Day 3 Teaching
Draw a right-angled triangle in the right quadrant. Children pretend there is a mirror on the y-axis. We will reflect this triangle in the y-axis. Draw the reflected triangle in the left quadrant. Check each point is the same distance away from the y-axis as it was originally, and that it looks to be the same shape. Children label the co-ordinates.
Group Activities
-- Reflecting shapes and points in positive y-axis and predicting new co-ordinates

### You Will Need

• Whiteboards & pens
• ‘Two quadrants’ image (see resources)
• Squared paper or maths exercise books
• Rulers
• ‘Two quadrants – blank’ sheets (see resources)
• ‘Translations’ sheet (see resources)
• Mirrors

### Mental/Oral Maths Starters

Suggested for Day 1
Revise finding lines of symmetry (simmering skills)

Suggested for Day 2
Pairs to 200 (simmering skills)

Suggested for Day 3

### Procedural Fluency

Day 1
Plot points to make polygons.

Day 2
Translate shapes, make translation patterns.

Day 3
Make patterns using reflections.

### Mastery: Reasoning and Problem-Solving

• What shape will you get if you join these points on a co-ordinate grid?
(0, 3) (2, 5) (6, 5) (6, 1) (2, 1)
• A square has vertices at (0, 2) and (0, 6). What are the co-ordinates of its two other vertices?
• A triangle is moved 3 spaces to the right on the co-ordinate grid. Its new co-ordinates are: (2, 5), (–1, 2) and (5, 2).
What were its original co-ordinates?
• Draw a rhombus and then reflect it in the y-axis.

In-depth investigation: Cycling Co-ordinates
Children use a sequence of co-ordinates to create quadrilaterals, investigating a conjecture around predicting shape types.

### Extra Support

Walk then Fly
Plotting points in the first quadrant

## Unit 4 Recognise, measure and draw angles (suggested as 2 days)

### Objectives

Recognise, measure and draw angles
Unit 4: ID# 5507

National Curriculum
PofS
(ii) (iii)

Hamilton Objectives
47. Know angles are measured in degrees, estimate and compare acute, obtuse and reflex angles, draw and measure given angles.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Using an online protractor, show how to align the protractor to read the angle. Point out how the numbers of degrees go both anticlockwise and clockwise; this is the case on many protractors! Measure angles of 90°, 180°, 270°. Show different angles for children to estimate then measure.
Group Activities
Use the in-depth problem-solving investigation ‘Nine-pin triangles’ from NRICH as today’s group activity.
Or, use this activity:
-- Accurately draw and measure angles.

Day 2 Teaching
Introduce acute, obtuse and reflex angles.
Launch ‘Angles’ from www.mathsisfun.com. Scroll down to 'Try it yourself' and move the top line of the angle anticlockwise to gradually increase it from 1° to 360°, asking children to watch the angle titles at the side. Draw some angles, and children classify them as acute, obtuse or reflex.
Group Activities
-- Classify angles as acute, obtuse or reflex through shape investigation.

### You Will Need

• IWB and internet access
• Whiteboards
• Rulers
• Protractors
• 1–6 dice

### Mental/Oral Maths Starters

Suggested for Day 1
24-hour time tease (simmering skills)

Suggested for Day 2
Quickly find complements to 100 (simmering skills)

### Procedural Fluency

Day 1
Estimate and measure angles.

Day 2
Identify acute, obtuse and reflex angles.

### Mastery: Reasoning and Problem-Solving

• Draw an acute angle, estimate its size. Write your estimate. Then measure it. How close were you?
Repeat this for an obtuse angle.
• Draw a pentagon with two right angles and two obtuse angles. Can you draw a pentagon with three acute angles?
• True or False?
A quadrilateral could have two reflex angles.

In-depth investigation: Nine-pin Triangles
Draw triangles; measure and classify the angles of each triangle. Nine-pins Triangles from nrich.maths.org.

### Extra Support

Recognising acute, right and obtuse angles.

## Unit 5 Angle theorems; draw angles in polygons (suggested as 3 days)

### Objectives

Use angle theorems and draw polygons with specified angles
Unit 5: ID# 5521

National Curriculum
PofS (iii) (v)

Hamilton Objectives
46. Find unknown angles in triangles and rectangles; identify angles round a point and on a straight line, finding missing angles.
47. Know angles are measured in degrees, estimate and compare acute, obtuse and reflex angles, draw and measure given angles.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Place two corners from an A4 page on a line, and then show that four right angles make a complete turn. Next, draw a straight line, then draw two straight lines to divide the 180° angle into three unequal angles. Measure these and show that they add to 180°.
Group Activities
-- Measure accurately to piece together angles on a straight line.

Day 2 Teaching
Establish that a full turn is 360° by asking children to turn through four right angles. Sketch an acute angle, and measure it with an IWB protractor. With the protractor still in place, ask children how big the reflex angle is that goes with the acute angle. Record, e.g. 75° + 285° = 360°. Repeat with other acute and obtuse angles.
Draw three lines that meet at a point. Ask children to measure two of the angles. Can you calculate the missing angle?
Group Activities
Use the in-depth problem-solving investigation ‘Olympic turns’ from NRICH as today’s group activity.
Or, use this activity:
-- Determine missing angles at point by finding a complement to 360°.

Day 3 Teaching
Agree that a polygon is a shape with straight sides, e.g. a hexagon, but not a circle. Display ‘Polygons’ images (see resources). Children describe each one with reference to their properties and the types or sizes of their angles. Ask children to sketch shapes with a range of angle properties, e.g. a triangle with no right angles and two angles the same, a pentagon with one reflex angle, etc.
Group Activities
-- Construct polygons; use them to create tessellations.

### You Will Need

• Interactive whiteboard and internet access
• ITP Calculating Angles (see resources)
• 180° and 360° protractors
• Semicircle angles (see resources)
• Rulers, scissors, glue, coloured paper (3 colours) & sugar paper
• IWB 360° protractor
• ‘Polygons’ images (see resources)

### Mental/Oral Maths Starters

Day 1
Find the complement to 180 (pre-requisite skills)

Suggested for Day 2
Properties of 2-D shapes (simmering skills)

Day 3
Estimating angles from nrich.maths.org (pre-requisite skills)

### Procedural Fluency

Day 1
Find missing angles on a straight line.

Day 2
Find missing angles around a point.

Day 3
Draw polygons to given specifications.

### Mastery: Reasoning and Problem-Solving

• Draw a straight line divided into three acute angles. Measure two of the angles and calculate the third. Then measure it to check.
• Draw four angles around one point. Make the ‘missing’ angle 90 degrees. Measure and label the other three angles.
• The three angles inside a regular (equilateral) triangle are all 60°, so add to 180°. The four angles inside a regular quadrilateral (square) are all 90°, so add to 360°.
• The sum of the five angles inside a regular pentagon follows a pattern begun by the triangle and square. Can you calculate how big each one is?

In-depth investigation: Olympic Turns
Children explore photos of some Olympic sports that involve turns and angles. Olympic Turns from nrich.maths.org.

### Extra Support

One hundred and eighty!
Measuring angles using a protractor; Understanding that angles on a straight line add to 180°