This is a youcubed favorite which comes from Mark Driscoll. The activity encourages students and teachers to engage in visual, creative thinking. We have coupled Mark’s activity with asking students to reason and be convincing, two important mathematical practices.

## Materials

At least one square piece for each student. 8.5×8.5 is a good size since this is made from a piece of 8.5×11 piece of paper. (Patty paper recommended)

## Task Instructions

Work with a partner. Take turns being the skeptic or the convincer. When you are the convincer your job is to be convincing! Give reasons for all of your statements. Skeptics must be skeptical! Don’t be easily convinced. Require reasons and justifications that make sense to you.

For each of the problems below one person should make the shape and then be convincing. Your partner is the skeptic. When you move to the next question switch roles. Start with a square sheet of paper and make folds to construct a new shape. Explain how you know the shape you constructed has the specified area.

Start with a square sheet of paper and make folds to construct a new shape. Explain how you know the shape you constructed has the specified area.

1. Construct a square with exactly ¼ the area of the original square. Convince yourself and

then your partner that it is a square and has ¼ of the area.

2. Construct a triangle with exactly ¼ the area of the original square. Convince yourself

and then your partner that it has ¼ of the area.

3. Construct another triangle, also with ¼ the area, that is not congruent to the first one

you constructed. Convince yourself and then your partner that it has ¼ of the area.

4. Construct a square with exactly ½ the area of the original square. Convince yourself and

then your partner that it is a square and has ½ of the area.

5. Construct another square, also with ½ the area, that is oriented differently from the

one you constructed in #4. Convince yourself and then your partner that it has ½ of the

area.

## Reference

Adapted from: *Fostering Geometric Thinking: A Guide for Teachers, Grades 5-10, *by Mark Driscoll, 2007, p. 90, http://heinemann.com/products/