Maths Year 5/6 Autumn 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 Quadrilaterals, other polygons and circles (suggested as 2 days)

Objectives

Quadrilaterals, other polygons and circles
Unit 1: ID# 56356

Y5: Quadrilaterals and other polygons
Y6: Quadrilaterals and circles

National Curriculum
Y5: PofS (v) (vi)
Y6: PofS (iii) (iv)

Y5 Hamilton Objectives
48. Understand properties of rectangles and triangles; distinguish between regular and irregular polygons based on reasoning about equal sides/angles.
39. (Y4) Compare and classify … quadrilaterals … based on their properties ...

Y6 Hamilton Objectives
51. Compare and classify geometric shapes based on their properties; classify and name types of triangle and angle (acute, obtuse, reflex).
53. Identify, illustrate and name parts of circles, including diameter, circumference and radius, understanding that the radius is half the diameter.

Teaching and Group Activities for Understanding

Day 1 Teaching
Children each draw a quadrilateral, then discuss similarities and differences. Name and explore properties of quadrilaterals using an online activity.
Group Activities: T with Y5
Y5 -- Tear the four vertices from a quadrilateral and arrange around a point to find the total angle. Investigate diagonals of quadrilaterals;
Y6 -- Use a sorting tree, Carroll or Venn diagram to sort quadrilaterals. Make a range of quadrilaterals using art straws and identify features.

Day 2 Teaching
Children write facts about shapes, then use facts to guess a mystery shape.
Further Teaching with Y6
Discuss radius, circumference and diameter. Describe relationship of diameter and radius as a ratio (2 to 1, 2:1).
Group Activities: T with Y6
Use the in-depth problem-solving investigation for this unit ‘Polygon dissections’ as today’s group activity.
Or, use these activities:
Y5 -- Investigate how many different polygons can be made by drawing five equilateral triangles next to one another.
Y6 -- Draw circles, measure diameters and circumferences with string and work out ratio (Pi is introduced).

You Will Need

  • Mini-whiteboards and pens
  • Internet access
  • Rulers, protractors, scissors and glue sticks
  • ‘Quadrilateral sort’ (see Day 1 Practice sheets)
  • ‘Quadrilateral sorting tree’ (see resources)
  • Art straws
  • ‘Shape game board’ (see resources)
  • Additional activity sheets (see resources)
  • Calculators, lengths of string and pairs of compasses

Short Mental Workouts

Day 1
Find lines of symmetry

Day 2
Time intervals

Procedural Fluency

Day 1
Y5: Measure and reason about angles in quadrilaterals. Sort quadrilaterals using a sorting tree.
Y6:
Identify and classify quadrilaterals. Discuss the geometric properties possible and not possible in a quadrilateral. Write down reasoning with diagrams.

Day 2
Y5: Identify polygons. Identify properties of polygons.
Y6: Look for relationships between radius, diameter and circumference. Calculate using the formula C = p x d.

Mastery: Reasoning and Problem-Solving

Y5

  • Is a semicircle a polygon?
  • Draw a polygon and list five of its properties.
  • Which of these shapes are quadrilaterals? (see download)

Y6

  • Draw a circle and label the radius and diameter. Explain how you could find the diameter.
  • Use damp string to measure the circumference of a small plate. Now measure its diameter and calculate the circumference. How accurate was your damp string measurement?
  • Mystery quadrilaterals:
    I have 2 non-equal parallel sides. The 2 non-parallel sides are equal. What am I?
    I have 2 pairs of equal sides, but no sides are parallel. 2 opposite angles are equal but not the other 2. What am I?

In-depth Investigation: Polygon Dissections
Children cut squares, rectangles and regular polygons into two parts. They see what new shapes they can make by putting the two parts together in different ways.

Extra Support

Y5: What’s Special?
Identifying and describing properties of triangles; using these properties to sort the triangles.

Y6: Sorting Logic Blocks
Using an on-screen interactivity to practise describing and sorting 2-D shapes; Sorting Logic Blocks from nrich.maths.org.

Unit 2 Find missing angles and draw 2D shapes (suggested as 4 days)

Objectives

Find missing angles and draw 2D shapes
Unit 2: ID# 56364

Y5: Find missing angles and draw 2-D shapes
Y6: Find missing angles and draw 2-D shapes

National Curriculum
Y5: PofS (ii), (iii), (iv)
Y6: PofS (vii) (x)

Y5 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.

Y6 Hamilton Objectives
49. Draw 2-D shapes, using given dimensions and angles; understand terms parallel and perpendicular.
52. Find unknown angles in triangles, quadrilaterals and regular polygons; also find missing angles at a point, vertically opposite or on a straight line.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use a protractor to show that angles around a point add up to 360°. Use an interactive online tool to rehearse finding missing angles around a point.
Group Activities: T with 6
Y5 -- Calculate missing angles around a point.
Y6 -- Calculate missing angles around a point; Identify angles. Some children will investigate combinations of acute/obtuse/reflex angles around a point.

Day 2 Teaching
Children tear corners off triangles, arrange vertices together to form a straight line to show that angles in triangles add up to 180°. Repeat for quadrilaterals, arranging around a point to show that angles add up to 360°.
Group Activities: T with Y5
Y5 -- Calculate missing angles in different types of triangles.
Y6 -- Calculate missing angles in different types of triangles, then quadrilaterals.

Day 3 Teaching
Draw polygons with some given lengths and angles. Measure other dimensions and compare with others.
Group Activities: T with Y5 or 6
Use the in-depth problem-solving investigation for this unit ‘Olympic Turns’ from NRICH as today’s group activity.
Or, use these activities:
Y5/Y6 -- Draw a 2-D shape, then give instructions to another child to draw the exact same shape.

Day 4 Teaching
Draw two straight intersecting lines. Demonstrate that opposite angles are equal. Children then use what they have learnt in this unit to find missing angles in a geometrical figure.
Group Activities: T with Y6
Y5 -- Find by measuring that opposite angles are equal using an online tool. Calculate missing angles.
Y6 -- Find by measuring that opposite angles are equal. Calculate missing angles. Some children will partition polygons into triangles and calculate internal angles.

You Will Need

  • Interactive Whiteboard 360° protractor
  • Internet access
  • Rulers
  • 180° and 360° protractors
  • Paper
  • ‘Regular polygons’ (see resources)

Short Mental Workouts

Day 1
Find the complement to 180

Day 2
Division facts for the 6 times table

Day 3
Shape facts

Day 4
2-place decimals

Procedural Fluency

Day 1
Y5: Measure and calculate angles around a point on roundabouts.
Y6: Find sets of angles that do not sum to 360°.

Day 2
Y5: Measure and calculate angles in triangular sandwiches.
Y6: Find the missing angles in a triangular jigsaw.

Day 3
Y5: Draw polygons to given dimensions.
Y6: Draw polygons to given dimensions. Some angles need to be calculated first.

Day 4
Y5: Calculate missing angles between intersection lines, in triangles and quadrilaterals.
Y6: Find the missing angles around a point formed by intersecting lines, including by calculation.

Mastery: Reasoning and Problem-Solving

Y5

  • A capital Y is symmetrical. Write two different possibilities for the three angles.

Y5/Y6

  • Draw a triangle with 2 sides of 8cm and an angle of 60° between them. Now draw an identical triangle using the base of your first triangle as one of the sides of the new triangle. What shape have you drawn?
  • Calculate the missing angles:
    Y5/Y6: A triangle with angles: 43°+ 100° + ☐
    Y6: A kite with two angles of 105°, 1 angle of 84°. What is the fourth angle?

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

Y5: One Hundred and Eighty!
Measuring angles using a protractor; Understanding that angles on a straight line add to 180°.

Y6: Helpful Frog
Using frog to find how much to add to make 180 or 360 (to help to calculate angles in triangles, quadrilaterals or around a point).

Unit 3 Sort 3D shapes; nets and 3D shapes (suggested as 2 days)

Objectives

Describe and sort 3D shapes; use nets to construct 3D shapes
Unit 3: ID# 56380

Y5: Describe and sort 3-D shapes
Y6: Construct 3-D shapes using nets

National Curriculum
Y5: PofS (i)
Y6: PofS (ii)

Y5 Hamilton Objectives
45. Identify 3-D shapes from 2-D representations.

Y6 Hamilton Objectives
50. Recognise, describe and build 3-D simple shapes, including making nets.

Teaching and Group Activities for Understanding

Day 1 Teaching
Discuss what is the same and what is different about 3-D shapes. Sort shapes using a Carroll diagram.
Further Teaching with Y6
Show a net of a cube. Discuss which faces are parallel and which are perpendicular to a particular face.
Group Activities: T with Y6
Y5 -- Describe and sort 3-D shapes according to a range of properties.
Y6 -- Identify which arrangements of squares are correct nets for cubes.

Day 2 Teaching
Look at pictures of 3-D shapes on websites. Show animations of 3-D shapes that children find difficult to visualise. Explore different types of pyramid and prism.
Group Activities: T with Y5
Use the in-depth problem-solving investigation for this unit ‘Experiment with Patterns’ from NCETM as today’s group activity.
Or, use these activities:
Y5 -- Explore the properties of pyramids and prisms.
Y6 -- Make nets for a triangle prism and cuboid. Look at a polyhedral website and choose one to make and describe.

You Will Need

  • A collection of 3-D shapes including cuboids, cones, cylinders, pyramids and prisms
  • Feely bag, sorting hoops and small cards for labels
  • Camera/camera function on mobile device
  • ‘Cube nets’ and 'Two nets' (see resources)
  • Internet access
  • ‘Pyramids’ activity sheet (see resources)
  • Models of pyramids (only if required)
  • ‘Prisms’ activity sheet (see resources)
  • Models of prisms (only if required)
  • Paper/thin card, scissors, tape and glue

Procedural Fluency

Day 1
Y5: Sort 3-D shapes according to number of faces.
Y6: Identify nets and properties of cubes.

Day 2
Y5: Sort 3-D shapes according to number of edges.
Y6: Identify prisms and pyramids that could be made, and list faces.

Mastery: Reasoning and Problem-Solving

Y5

  • 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?

Y6

  • What common name do we give a ‘circular-based pyramid’ ?
  • How many vertices does a pyramid with a pentagon base have?
  • How many edges does a prism with pentagon ends have?
  • True or false?
    A prism always has 2 parallel faces.
    A pyramid cannot have any parallel faces.
  • Sketch the net of a cuboid with no ‘lid’.

In-depth Investigation: Experiment with Patterns
Exploring nets for 3-D shapes including the Platonic solids and 'flexagons'; construction with straws. Experiment with Patterns from stem.org.uk.

Extra Support

This unit has no separate Extra Support activities. You might, however, like to explore nets for cubes using the All Wrapped Up activity from NRICH.

Unit 4 Coordinates: polygons & transformations (suggested as 3 days)

Objectives

Co-ordinates: plot polygons, translations and reflections
Unit 4: ID# 56396

Y5: Co-ordinates – plot polygons, translations and reflections (two quadrants)
Y6: Co-ordinates – plot polygons, translations and reflections (four quadrants)

National Curriculum
Y5: P&D (i)
Y6: P&D (i) (ii)

Y5 Hamilton Objectives
49. Identify, describe, represent position of a shape following a reflection or translation, use appropriate language; know that the shape is unchanged.

Y6 Hamilton Objectives
54. Identify positions on the full co-ordinate grid; draw and translate simple shapes and reflect them in the x-axis or y-axis.
55. Begin to reason mathematically making simple generalisations, using mathematical language and making connections between mathematical ideas.

Teaching and Group Activities for Understanding

Day 1 Teaching
Plot points in the first two quadrants, then all four quadrants.
Group Activities: T with Y5
Y5 -- Plot co-ordinates and draw polygons and quadrilaterals in two quadrants.
Y6 -- Plot a polygon on a co-ordinate grid. See if a partner can replicate it when given co-ordinates. Some children will plot rectangles/squares where only three/two vertices are given.

Day 2 Teaching
Translate shapes in two quadrants. Children write the co-ordinates of the new vertices.
Further Teaching with Y6
Translate shapes in four quadrants. Children write the co-ordinates of the new vertices.
Group Activities: T with Y6
Y5 -- Translate squares, rectangles and polygons on a grid; Identify how co-ordinates change.
Y6 -- Plot and translate rectangles/polygons on a co-ordinate grid.

Day 3 Teaching
Children reflect shapes across the y-axis and write co-ordinates of new vertices.
Further Teaching with Y5 or 6
Children reflect shapes in the x-axis and y-axis and write co-ordinates of new vertices, then translate back to the 1st quadrant.
Group Activities:
Use the in-depth problem-solving investigation for this unit ‘Cycling co-ordinates’ as today’s group activity.
Or, use this activity:
Y5/Y6 -- Whole class investigation: Plot rectangles/polygons on a co-ordinate grid and reflect them. Observe and describe the effect on the co-ordinates.

You Will Need

  • Square background on the Interactive Whiteboard
  • ‘Two quadrants’ (see resources)
  • ‘Four quadrants’ (see resources)
  • Rulers
  • Crayons (optional)
  • Mini-whiteboards and pens
  • Internet access
  • Squared paper
  • ‘Translations’ sheet (see resources)
  • Mirrors (optional)
  • Paper/tracing paper (optional)

Short Mental Workouts

Day 1
Co-ordinates

Day 2
Factors

Day 3
Multiples

Procedural Fluency

Day 1
Y5: Plot co-ordinates in 2 quadrants to make polygons.
Y6: Find coordinates of missing vertices for a range of quadrilaterals.

Day 2
Y5: Translate shapes, make patterns; describe translations.
Y6: Translate quadrilaterals. Find x and y changes.

Day 3
Y5: Make patterns using reflections (1st quadrant). Reason about co-ordinates and their reflections (2 quadrants).
Y6: Reflect quadrilaterals. Reason about co-ordinates and their reflections.

Mastery: Reasoning and Problem-Solving

Y5

  • What shape will you get if you plot, then join these points (in order) on a co-ordinate grid ?
    (0, 3) (2, 5) (6, 5) (6, 1) (2, 1) (0,3)
  • 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.

Y6

  • Without drawing a co-ordinate grid and plotting the points, say what each of these shapes are. Be as specific as you can.
    (a) (2, 1) (2, 5) (6, 1) (6, 5)
    (b) (1, 1) (5, 1) (3, 6)
    (c) (–1, –1) (–1, –3) (–3, 0) (–5, –2) (–3, –4)
    Now plot each set of co-ordinates and join to create each shape to check your answers.
  • A triangle is translated so that it has moved 4 squares up the grid. Its co-ordinates are now: (2, 0) (5, 2) and (3, 7) Draw it in its original position.
  • (0 ,0) (5, 0) (5, 5) (0, 5) are the vertices of a shape. When it is reflected in the y-axis, 2 pairs of co-ordinates do not change. Why not? Sketch it to explain.

In-depth Investigation: Cycling Co-ordinates
Children use a sequence of co-ordinates to create quadrilaterals.