Wrapping presents
Problem
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it's completely covered.
Getting Started
Student Solutions
Colet Court School worked on this problem and came up with a few ideas of what the solution might be.
Thomas and Ken-Ree thought the smallest rectangle can be found by drawing around the net of the box. Here are Ken-Ree's diagrams.
Camille tried something similar but moved parts of the net around to get a smaller rectangle.
I chose a box with 7.8cm length, 5.6 cm width and 3 cm height. Firstly, I started by turning the box on a sheet of white paper drawing around it every time to get a net. Next I cut it out. Then on another piece of paper, using what I cut out, I drew the rectangle just around its borders. On this rectangle I turned the piece of paper to see what I could move to another place to make the rectangle smaller. The final rectangle measured 14.3 cm by 14.5 cm.
Well done to John from Nagoya International School who used algebra to work out this problem.
Teachers' Resources
Wrapping Presents
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it's completely covered.
Why do this problem?
Possible approach
This activity is suitable for working in pairs (which of course will require less special paper at the end). Supply the children with lots of newspaper and a selection of boxes to choose from. Spend a little time in comparing the boxes. Ask them to predict which box they think will need the most wrapping paper, the least paper, two that might need the same amount etc. Encourage them to experiment with wrapping the boxes in various ways and to cut off parts of the sheet of newspaper, keeping it rectangular. Have the pairs demonstrate their solution to others and compare the shapes and areas of their papers. Discuss the predictions they made earlier. The piece of newspaper can then be used as a template for cutting the same rectangle from the special wrapping paper. Perhaps the children could first try to fit the templates together over the special paper in such a way that little is wasted.
Key questions
Possible extension
For more extension work
Go to the Auditorium steps here.
Possible support