Maths Year 5/6 Autumn Shape

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).

• 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

Day 1
Find lines of symmetry

Day 2
Time intervals

Day 1
Y5: Sort quadrilaterals using a sorting tree.
Y6: Identify and classify quadrilaterals. Discuss what is 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.

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.

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.

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.

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

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

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.

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.

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).

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.

• 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

Day 1
3-D shapes

Day 2
Balancing calculations

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.

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.

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.

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.

• 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)

Day 1
Co-ordinates

Day 2
Factors

Day 3
Multiples

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

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

Day 3
Y5: Make patterns using reflections.
Y6: Reflect quadrilaterals.

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.

Y5/6: Walk then Fly
Plotting points in the first quadrant