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Display Boards

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

 

The challenge: arranging the display boards in the hall 

A Year 5 class wants to display the results of their problem solving in the school hall. 
They need 32 display boards - one each - and they are wondering how to arrange them.

Rules for setting up the boards: 
  • The boards can be joined in a straight line or at right angles.
  • The boards will fall if there are five or more in a straight line.
  • The final arrangement of the 32 display boards has to be a closed shape so that people can walk around the outside and view all the problem solving results displayed.
  • The hall floor has square tiles.  Each board, which is as long as the square tiles, needs to be placed on the edge of one of these squares so that it stands up.
See if you can work out how to arrange the boards to satisfy each of the following people. 
This means you will need to find three different arrangements. 

A/ The kitchen staff would like to use the hall for school dinners. They would like the display to be as long and narrow as possible, and at one end of the hall.

B/ Teachers would like to use the hall for PE. They would like the display to fit in a corner, and be as long and narrow as possible so that it leaves as much space as possible for PE.
Are the teachers right that the corner design takes up less space than the one at the end of the hall? Give reasons for your answer.

C/ The Year 5 teacher thinks that the best viewing shape is the one that has as many long straight lines of four display boards in it as possible and doesn't mind where it is in the room.

Further challenge 
The Head would like the display to be very visible from whatever door people enter the hall. S/he would like the display to be as square as possible and in the middle of the hall.

a. Design a display for the headteacher that is as square as possible.
Explain how you have decided it is as square as possible.

b. Design a display for the headteacher that is as square as possible and has four lines of symmetry.

c. Design a display for headteacher that is as square as possible, has four lines of symmetry and has an internal area of 40 square tiles.

See if you can find three different answers for a, b and c.
Can you find any other arrangements that fit either b or c?

This problem featured in a preliminary round of the Young Mathematicians' Award 2014.