Shapes, parts and grids
Describe flat shapes by their boundaries, build figures and copy positions on a grid.
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Look at the boundary
A triangle has three straight sides. A rectangle has four straight sides and four square corners. A square is a rectangle with all four sides equal. A circle has a curved boundary and no corners.
Count sides and notice corners. The turned square still has four equal sides and four square corners.
Turn a square so one corner points up. It is still a square. Its sides and corners have not changed. A triangle can be wide, narrow or upside down and still have three straight sides.
Check your understanding 1 Use sides and corners together
Which of A, B and C have four straight sides and four square corners? There may be more than one. Name or point to every figure that fits.
Show answer
A and C fit. Both are rectangles because each has four straight sides and four square corners. A is also a square: all four sides are equal. B has four equal sides, but its corners are not square corners. Equal sides alone do not make a square.
A whole circle can be split
Fold a paper circle into two matching parts. Each part is a half circle. It has one straight edge and one curved edge.
Fold again into four matching parts of the original circle. Each is a quarter circle. Two quarter circles can make a half circle; four can make a whole circle.
Trace each boundary. A half circle has one straight edge; a quarter circle has two. Each also has a curved edge.
Check your understanding 2 Describe the whole boundary
Compare a whole circle, a half circle and a quarter circle. How many straight edges and unbroken curved parts does each have? Trace the whole boundary before answering.
Show answer
- A whole circle has 0 straight edges and 1 unbroken curve.
- A half circle has 1 straight edge and 1 unbroken curve.
- A quarter circle has 2 straight edges and 1 unbroken curve.
The curve of a whole circle is one unbroken boundary. A half circle adds one straight edge across the circle. A quarter circle has two straight edges meeting at the circle’s centre. Count each continuous curve once, even if a drawing uses several segments to show it.
Use paper shapes or draw them. Put two matching squares side by side, with a full side touching. The outside boundary makes a rectangle. The line inside shows where the parts meet; it is not another outside side.
Check your understanding 3 Build with whole pieces
Make a rectangle from two squares. Keep both pieces whole: move or turn them, then bring their edges together. A gap leaves separate figures. An overlap covers part of a piece twice.
Try the model. You can change your answer or look at the worked model. This activity has no score.
Check that both square pieces join without overlap and the outside is a rectangle. You can also draw on paper and compare with the public answer.
Show solution
Could your rectangle stand upright instead of lying sideways? Try another arrangement before looking at the worked model.
Check your understanding 4 Find the parts of a figure
Look inside the whole figure
Trace the outside first, then the two parts separated by the dashed line.
View figure data
| Feature | Description |
|---|---|
| Lower part | As wide as it is high, with four square corners. |
| Upper part | Two sloping sides meet above the horizontal join. |
| Join | The dashed line is inside the whole figure. |
Name the two shapes that make up this figure. Draw your own copy on paper, then turn the paper sideways. Do the two parts change their names?
Show answer
The parts are a square and a triangle. The square is also a rectangle: it has four square corners. When a question asks for every name that fits, choose both square and rectangle for that part. Turning the drawing changes its orientation, but not the sides or corners of either part.
Check your understanding 5 Name the parts and the whole
Two parts, one outside outline
Trace each part, including the join. Then trace just the outside of the whole figure.
View figure data
| Path | Start | Segment | End | Arc centre |
|---|---|---|---|---|
| Boundary 1 | 50, 50 | Line | 10, 50 | — |
| Boundary 1 | 10, 50 | Quarter arc, clockwise | 50, 10 | 50, 50 |
| Boundary 1 | 50, 10 | Line | 50, 50 | — |
| Boundary 2 | 50, 50 | Line | 50, 10 | — |
| Boundary 2 | 50, 10 | Quarter arc, clockwise | 90, 50 | 50, 50 |
| Boundary 2 | 90, 50 | Line | 50, 50 | — |
Name part A and part B. Then name the whole outside shape. Do all three have the same name?
Show answer
A and B are each a quarter circle. Together they make a half circle. The join is an edge of each small part. It is inside the whole figure, so it is not an edge of the outside outline.
Check your understanding 6 Turn a curved piece
Use two quarter circles to make a half circle. Think about which straight edges should meet. You may need to turn one piece so the curves continue smoothly around the outside.
Try the model. You can change your answer or look at the worked model. This activity has no score.
Check that both quarter-circle pieces join without overlap and the outside is a half circle. You can also draw on paper and compare with the public answer.
Show solution
Now try paper pieces. Use a rectangle with a triangle, or put a half circle against a straight edge of a rectangle. Explain which edges became joins and which are still on the outside.
Copy a figure on a grid
On squared paper, choose a starting dot. Draw a square with sides two grid gaps long. Count gaps, not dots: from the starting dot go two gaps right, two down, two left and two up. You return to the start.
Copy the square from a new starting dot. Keep the same number of gaps and the same turns. The copy should have the same size and shape even though it is in a different place.
Check your understanding 7 Copy a different outline
The outline starts at O. Copy it on squared paper, starting at S in the empty part of the grid. Keep the grid gaps the same size. Count the gaps along each side before drawing that side.
Same shape, new starting point
Start a fresh outline at S. Move each corner by the same amount; keep every side's length and direction.
View figure data
| Feature | Description |
|---|---|
| Original | Start at O and follow these moves in order. |
| Move 1 | 3 gaps right |
| Move 2 | 1 gap down |
| Move 3 | 2 gaps left |
| Move 4 | 3 gaps down |
| Move 5 | 1 gap left |
| Move 6 | 4 gaps up |
Show answer
From S, go three gaps right, one down, two left, three down, one left and four up. You return to S. Check every corner and side, not only the first side: a figure can close and still have the wrong shape.
Check the whole copy
Compare your drawing with this copy. Its position changed; its size and shape did not.
View figure data
| Feature | Description |
|---|---|
| Copy | Start at S and follow the same moves in order. |
| Move 1 | 3 gaps right |
| Move 2 | 1 gap down |
| Move 3 | 2 gaps left |
| Move 4 | 3 gaps down |
| Move 5 | 1 gap left |
| Move 6 | 4 gaps up |
Check your understanding 8 Trace the outside
Your square has four sides. Each side follows two grid gaps. How many gaps do you trace around its outside?
Show answer
Eight gaps: 2 + 2 + 2 + 2 = 8. The four corner dots are meeting points, not extra lengths.
Make a different figure
Put a half circle on top of a rectangle. Draw the join, then trace the outside. Tell someone which part of the boundary is curved. Use the parts to explain your figure rather than only giving it a name.
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