Construct two open boxes from a 3 x 5 and a 5 x 8 index card. To do this, you need to draw lines on the card as indicated by the dotted lines in the picture above. The darkened lines are where you need to cut the card; the rest of the dotted lines indicate where you will fold. The four corners of the card will become flaps once you do the folding and cutting.
Two things you need to take into account in order to determine where to draw the dotted lines are (i) the level of the box should be the same all around and (ii) the flaps on a side should just touch.
As an aid to constructing your box, run the sharp point of a compass lightly across the lines to help in folding across the line. Use tape to make the box rigid.
Calculate the volume of each of your boxes; do your calculation by hand instead of on a calculator.
Task 2:
Make two more boxes with 3 x 5 cards, one with the flaps overlapping and one where they do not meet. Calculate the volume of these two boxes.
Homework:
Write a brief (but clear and complete) description of the first task of making the two boxes, including how you figured out where to draw the lines, what are their dimensions, and what are the volumes of the two boxes. Mention how you calculated these volumes.
Also, describe how you built the other two boxes you made with 3 x 5 cards, what are their dimensions, and what are the volumes of these boxes.
Drawing pictures is a very good way to illustrate ideas. Think about what pictures might help your explanations, and then draw them.
