Maths Year 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.

Unit 1 2-D shapes (circles and quadrilaterals) (suggested as 2 days)

Objectives

2-D shapes, including circles and quadrilaterals
Unit 1: ID# 6229

National Curriculum
PofS (iii) (iv)

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
Pairs discuss how to explain the radius, circumference and diameter to someone with no diagram. Agree the definitions. Describe relationship of diameter and radius as a ratio (2 to 1, 2:1). We will explore whether there is a similar relationship between the circumference and diameter.
Group Activities
Use the ‘Ellipse in a Circle’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Children draw circles, measure diameters and circumferences with string and work out ratio. Pi is introduced.

Day 2 Teaching
Children draw different quadrilaterals and describe them. Together identify their features then name the different types of quadrilateral. Classify these according to their properties.
Group Activities
-- Children make a range of quadrilaterals using art straws. Copy into books and identify features. Sort with sorting tree or Venn diagram.

You Will Need

  • Diagram with parts of a circle labelled
  • Compasses
  • Rulers
  • String
  • Internet access (PCs/laptops/tablets)
  • Art straws
  • ‘Quadrilateral sorting tree’ sheet (see resources)

Procedural Fluency

Day 1
Investigating circle relationships.
Children interpret a table of data to try to discover any relationship between a circle’s circumference and its diameter.

Day 2
Identify and classify Quadrilaterals.
Discuss with partner what is possible and not possible in a quadrilateral. Write down reasoning with diagrams.

Mastery: Reasoning and Problem-Solving

  • 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 close 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: Ellipse in a Circle
Children draw a circle and then use straight lines and angles to construct an ellipse within it.

Extra Support

This unit has no separate Extra Support activities.

Unit 2 Draw, translate, reflect polygons (suggested as 3 days)

Objectives

Draw polygons in all quadrants; translate and reflect these
Unit 2: ID# 6247

National Curriculum
P&D (i) (ii)

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
Show children how to draw a co-ordinate grid. Remind them that of the x- and y- axes, and the mnemonic ‘walk before you fly’ for plotting co-ordinates. Draw simple polygons, using all 4 quadrants.
Group Activities
-- Plot polygon on a coordinate grid; can their partner replicate it when given coordinates?
-- Plot some rectangles/squares where only 3/two vertices are given.

Day 2 Teaching
Join points (-4, 3), (3, 3), (-6, -3) and (1, -3) to form a parallelogram. Translate this by adding 3 to each x-coordinate. Notice new position. Repeat to translate downwards.
Group Activities
Use the ‘Cycling Co-ordinates’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Children plot and translate rectangles/polygons on a coordinate grid.

Day 3 Teaching
Draw a parallelogram in 1st quadrant, write co-ordinates by each vertex. Reflect this in the y-axis. A child draws the reflected shape. Emphasise how the new shape must be the same distance away from the y-axis as before. Rest of class find new co-ordinates. Now reflect shape in x-axis.
Group Activities
-- Children plot rectangles/polygons on a coordinate grid and reflect them.

You Will Need

  • Grid with axis from –10 to 10 (see resources)
  • Rulers
  • Squared paper
  • Whiteboards and pens
  • Crayons (optional)
  • PCs/tablets/laptops and internet access

Mental/Oral Starters

Day 1
Coordinates in 4 quadrants (1) (pre-requisite skills).

Day 2
Coordinates in 4 quadrants (2) (pre-requisite skills).

Suggested for Day 3
Find lines of symmetry (simmering skills).

Procedural Fluency

Day 1
Children find coordinates of missing vertices for various quadrilaterals.

Day 2
Children translate quadrilaterals.
Find x and y changes.

Day 3
Children reflect quadrilaterals.
Answer true or false questions.
Children identify coordinates after reflection.

Mastery: Reasoning and Problem-Solving

  • 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) is 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.
The PowerPoint can be used to guide your class through this investigation.

Extra Support

Walk Then Fly
Plotting points in the first quadrant

Unit 3 Draw 2-D shapes; find missing angles (suggested as 3 days)

Objectives

Draw 2-D shapes; find missing angles
Unit 3: ID# 6257

National Curriculum
PofS (vii) (x)

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
Measure an obtuse angle using IWB 360° protractor. Point out the numbers going round the protractor the other way. This tells us the reflex angle which goes with the acute angle to make a full turn. Remind children that angles round a point always add up to 360°.
Group Activities
-- Find by measuring that angles around a point sum to 360°.
-- Consider combinations of acute/obtuse/reflex.

Day 2 Teaching
Model how to draw a triangle with sides 7cm and 5cm and a 45 degree angle between them. Children then draw different triangles – show that angles in triangles = 180 and in quadrilaterals = 360.
Group Activities
-- Find by measuring that angles of a quadrilateral sum to 360° and for triangle 180°. To test, cut out and reassemble.

Day 3 Teaching
Draw 2 straight lines crossing each other on the board. Demonstrate that opposite angles are equal. Go on to use angles round a point to find missing angles in polygons.
Group Activities
Use the in-depth problem-solving investigation ‘Baravelle’ from NRICH as today’s group activity.
Or, use these activities:
-- Find by measuring that opposite angles are equal. Calculate missing angles.
-- Partition polygons into triangles and calculate internal angles.

You Will Need

  • IWB protractor
  • PCs/laptops/tablets with internet access
  • Protractors
  • Gummed coloured paper
  • Coloured paper
  • Set of regular polygons (see resources)

Mental/Oral Starters

Day 1
Recognise acute, obtuse, reflex angles (pre-requisite skills)

Suggested for Day 2
Times tables (simmering skills)

Suggested for Day 3
Division facts (simmering skills)

Procedural Fluency

Day 1
Find sets of angles that do not sum to 360°.

Day 2
Find the missing angles in triangles and quadrilaterals.

Day 3
Find the missing angles around a point formed by intersecting lines, including by calculation.

Mastery: Reasoning and Problem-Solving

  • 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 1 of the sides of the new triangle. What shape have you drawn?
  • Write the missing angles.
    A triangle with angles: 45°+ 100° + ☐
    A pentagon with 2 angles of 105° and 2 angles of 90°. What is the fifth?
  • Write the total of angles in:
    A hexagon
    An octagon
    A dodecagon

In-depth Investigation: Baravelle
Can you say some mathematical things about the geometric image? What questions can you ask? Baravelle from nrich.maths.org.

Extra Support

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 4 Construct 3-D shapes using nets (suggested as 2 days)

Objectives

Construct 3-D shapes using nets
Unit 4: ID# 6263

National Curriculum
PofS (vii) (x)

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

Teaching and Group Activities for Understanding

Day 1 Teaching
Show net of a cube. Children sketch it. Point to 1 face. Ask which face will be opposite this when we make it? Repeat this. Then each child makes their cube.
Group Activities
-- Study cubes, describe; draw nets and assemble.
-- Identify which arrangements of squares are correct nets for cubes. Work out principles.

Day 2 Teaching
Remind children that there are lots of sorts of pyramids, with different 2-D shapes on their bases, and there are lots of different prisms, with different 2-D shapes at each end. Show animations of different prisms and pyramids.
Group Activities
Use the in-depth problem-solving investigation ‘Experiment with Patterns’ from STEM as today’s group activity.
Or, use these activities:
-- Study example of a prism and a pyramid. Describe key features. Draw nets and make up. Look at polyhedra website to find a simple one to make and describe.
-- Investigate number of faces and vertices in different prisms and pyramids.

You Will Need

  • Square templates to draw around
  • Cube nets
  • Cubic wooden blocks
  • ‘Nets’ sheet (see resources)
  • Prisms & pyramids

Mental/Oral Starters

Day 1
Properties of 3-D shapes (pre-requisite skills)

Suggested for Day 2
Lowest common multiples (simmering skills).

Procedural Fluency

Day 1
Identify nets and properties of cubes.

Day 2
Identify prisms and pyramids that could be made, and listing faces.

Mastery: Reasoning and Problem-Solving

  • What do we call 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.