Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Which of these shapes tessellates on its own?
Show worked solution
A regular hexagon has 120° angles and 3 × 120 = 360, so the hexagon tessellates.
2 Write how many equilateral triangles meet at a point in a tessellation, and how many squares do.
Show worked solution
6 triangles and 4 squares.
3 On a plan, 1 unit stands for 2 metres. A wall is drawn 7 units long. How many metres long is the real wall?
Show worked solution
7 × 2 = 14 metres.
Level 2 · Core
4 A regular pentagon has angles of 108°. How many fit round a point before a gap is left?
Show worked solution
3 fit, making 324°, and the 36° gap is too small for a fourth.
5 On a map 1 cm stands for 50 m. Write the real length of a path drawn 6 cm long, and the drawn length of a path that is really 400 m.
Show worked solution
6 × 50 = 300 m; 400 ÷ 50 = 8 cm.
6 A regular hexagon has angles of 120°. How many meet at a point in a tessellation?
Show worked solution
3.
Level 3 · Challenge
7 Think about which shapes tessellate.1 Every triangle tessellates.
2 Every quadrilateral tessellates.
3 Every regular shape tessellates.
Which statements are correct?
2 Every quadrilateral tessellates.
3 Every regular shape tessellates.
Which statements are correct?
Show worked solution
A triangle's angles make 180 and two of each corner make 360 (1 ✓); a quadrilateral's make 360 already (2 ✓). The regular pentagon does not tessellate (3 ✗). 1 and 2.
8 A room is drawn 5 units by 4 units on a plan where 1 unit stands for 3 metres. Write its real length and its real area.
Show worked solution
5 × 3 = 15 m and 4 × 3 = 12 m, so the area is 15 × 12 = 180 square metres.
9 On a plan 1 unit stands for 2 metres. A hall is drawn 9 units long. How many metres long is it really?
Show worked solution
18 metres.