Shapes on the playground
Problem
Sally and Ben went outside the school to draw some very large shapes on the tarmac. None of the shapes they drew shared any sides with any other shape - they were all drawn separately although some small shapes were inside larger shapes. The children each had a box of ten sticks of chalk. Each stick drew 10 metres before it was completely worn away. They both drew shapes with all sides one metre long.
Sally drew squares and octagons, sixteen shapes altogether, and used up all her chalk.
How many of each shape did she draw?
Ben drew triangles, hexagons and squares. He drew $20$ shapes and still had two sticks of chalk left. How many of each shape did he draw?
Getting Started
Student Solutions
Classmates from Moorfield Junior School, Thomas and Robert , explain their strategy for solving some of the challenges of Shapes on the Playground :
To find the shapes that Sally drew they explain:
"We listed all the numbers that add up to 100 and then starting
multiplying them by 4 and 8.
The answer we got gave us the solution, 7 squares and 9
octagons.
We then worked Ben's out the same way.
The answer we got gave us the solution 20 squares, 0 triangles and
0 hexagons!!!"
Why do you think Thomas and Robert multiplied by 4 and 8? Do you agree with their answer for the shapes that Ben drew? The problem told us that, "Ben drew triangles, hexagons and squares".
The pupils from St. Aldhelm's C.E. Combined School agree with the solution for Sally, but for Ben they have some other thoughts. They made tables showing the amount of chalk used for each shape and then by completing the tables they discovered how many of each shape Ben would have drawn if he drew 20 shapes in total.
The answer they arrived at was that Ben drew 10 triangles (30 metres), 5 squares (20 metres) and 5 hexagons (30 metres). This used 8 sticks of chalk, as each stick drew 10 metres, leaving two unused sticks. Well done St. Aldhelm's! Can you recognise your initials? LM, ED, RD, HS, KT, DF, LH, NT, AND DR.
Mel and Katie from Loretto Junior School also worked out that Ben could have drawn these shapes:
- 17 squares, 2 triangles, and 1 hexagon
- 8 squares, 8 triangles and 4 hexagons
Very well done!