Shape patterns and solid shapes

Track a shape pattern’s changing attributes and distinguish flat faces from solid objects.

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Primary 2 Mathematics 2022

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Find what changes and what stays the same

A pattern shows: small triangle pointing up, large triangle pointing down, small triangle pointing up, large triangle pointing down.

Position 1

small blue triangle, up

Position 2

large blue triangle, down

Position 3

small blue triangle, up

Position 4

large blue triangle, down

The small up-pointing triangle and large down-pointing triangle form one repeating pair.

All the shapes are triangles. Size and orientation alternate together. The next shape is a small triangle pointing up. Follow both attributes; choosing any small shape would miss the triangle rule.

A different pattern could change shape and colour while keeping size fixed. Say the rule before continuing it. Colour is one possible attribute, but the pattern must also be describable in words.

Check your understanding 1 Follow two attributes

A repeating block is: small square, large circle, small square, large circle. What are the fifth and sixth shapes? Which two attributes change?

Try the model. You can change your answer or look at the worked model. This activity has no score.

Fill both empty positions. Keep the size and shape in the repeated block; do not change its colour. You can also draw on paper and compare with the public answer.

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Position 1 · given

small blue square

Position 2 · given

large blue circle

Position 3 · given

small blue square

Position 4 · given

large blue circle

Position 5

small blue square

Position 6

large blue circle

The fifth shape is a small square; the sixth is a large circle. Size and shape follow the same repeating pair.

Your answer or drawing on paper

Show answer

The fifth is a small square and the sixth is a large circle. Size and shape change. Nothing in the rule tells you to change orientation or add another shape.

A solid is more than one flat face

A cube has six square faces. A cuboid has six rectangular faces; a cube is a special cuboid with all its edges equal.

A cylinder has two equal flat circular faces joined by a curved surface. A cone has one flat circular face, one curved surface and a pointed vertex. A sphere has one curved surface and no flat face.

A drawing of a circle is flat. A ball is a solid sphere. Looking at only the outline of a solid can hide its other surfaces.

A cube has six square faces. Each square is also a rectangle, so a cube is a special cuboid.

This cuboid has six rectangular faces. Look at its hidden faces too; a drawing does not show every face from the front.

A cylinder has two flat circular faces and one curved surface. Turning it onto its side does not change its shape.

A cone has one flat circular face and one curved surface leading to a point.

A sphere has no flat face and one curved surface. The guide across it is not an edge or a join.

Object to inspect	Useful model	Features to notice
Ordinary dice	cube	six square faces
Shoe box	cuboid	rectangular faces
Straight-sided can	cylinder	two circular ends and a curved side
Cone-shaped party hat with a flat base imagined	cone	one point and one circular base
Smooth ball	sphere	curved all round, no flat face

Real objects can have seams, rounded corners or missing surfaces. Use the mathematical model for the shape features, and explain where the object differs.

Turn the solid

Inspect a box from the front, side and top. A face hidden at the back is still there. Mark each face with a removable label as you count, so you do not count one twice.

Check your understanding 2 A circular view is not enough

One object looks circular from above. It could be a cylinder, a cone or a sphere. What could you look for from the side to decide?

Your answer or drawing on paper

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A cylinder has two flat circular ends and no pointed vertex. A cone has one flat circular base and a point. A sphere curves all round with no flat face. One circular outline alone does not decide the solid.

Check your understanding 3 Sort by surfaces

Sort the cube, cuboid, cone, cylinder and sphere into three groups: only flat faces; both flat and curved surfaces; only a curved surface. Name or point to every solid in each group. Think about the whole solid, including the parts hidden in its drawing.

Your groups, or say them aloud

Show answer

Only flat faces: cube and cuboid. Both flat and curved surfaces: cone and cylinder. Only a curved surface: sphere. A circular outline does not make a flat circular face: the sphere has no flat face, even where a guide is drawn across it.

Check your understanding 4 Name the whole solid and its faces

Hold a cube or look at its drawing above. Give every name that fits the whole solid. Then describe its flat faces. Would turning the cube onto another face change either answer?

Whole-solid names and face shapes, or say them aloud

Show answer

The whole solid is a cube and a cuboid. It is not a square: a square is flat. Each of its six faces is a square, and each square is also a rectangle. The cube has no curved surface. Turning it changes which faces you see, not their shapes or number.

For a cylinder, count both circular ends even when one is hidden. It has two flat circular faces and one curved surface. For a sphere, the circular outline belongs to the drawing of its curved surface; it does not add a flat face.

Build a pattern of your own

Use paper flat shapes or draw them in a row. Choose one or two attributes to change: size, shape, colour or orientation. Keep the other attributes the same. Make a repeating block and show it at least twice. Ask someone to continue it and explain the rule without relying on colour alone.

Check your understanding 5 Check your repeating block

Point to where your block starts again. Which attributes change? What are the next two shapes? Draw or place them before comparing with the example below.

Try the model. You can change your answer or look at the worked model. This activity has no score.

Make a three-shape block and repeat it twice. Size and direction must both change; shape and colour stay the same. You can also draw on paper and compare with the public answer.

Show solution

Position 1

small blue triangle, up

Position 2

large blue triangle, down

Position 3

large blue triangle, down

Position 4

small blue triangle, up

Position 5

large blue triangle, down

Position 6

large blue triangle, down

One valid block is small triangle up, large triangle down, large triangle down. The whole three-shape block repeats. Other blocks can work.

The palette shows two sizes of the same triangle and its direction. Turning it changes its direction, not its size. A circle has no up or down direction; turning a square through a quarter turn also leaves it looking the same. Use shapes whose turns you can see when direction is part of your rule.

Draw on paper; optionally name your changing attributes

Show answer

Many patterns work. One block is small triangle pointing up, large triangle pointing down, large triangle pointing down. Repeat that same three-shape block. Size and orientation change; shape and colour stay the same. After two complete blocks, the next two shapes are a small triangle pointing up and a large triangle pointing down.

Your block may be different. Check that the same block repeats, that only your chosen one or two attributes change, and that your next two shapes follow that rule. If your rule uses colour, name the colours as well as showing them.

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