1. Suppose that two lines in a plane meet at a point. Label the angles around the two intersecting lines as a, b, c, d (in order). Use the fact that the angle formed by a straight line is 180° to explain why a = c and b = d
2. Discuss the types of angles that can be formed.
3. Explain why the sum of the angles in every triangle must always be 180°.
4. Discuss types of triangles by a) angles and b) sides.
5. Informally, we might describe a circle as a perfectly round shape. What is the
mathematical definition of a circle? How would you show a student what that means?
6. Give the (short) definitions of square, rectangle, and parallelogram. Describe in words how the sets of squares, rectangles, and parallelograms are related. Explain how you know these sets of shapes are related the way they are.
7. State the meaning of each of the prefixes, which are used in the metric system.
8. Give examples of two units in the metric system that use the prefix milli. State the attributes that the units are used to measure. For each unit, give an example of some actual thing whose size could be appropriately described using that unit.
9. Sue is confused about why we multiply by 3 to convert 9 yards to feet. Sue thinks we should divide by 3 because feet are smaller than yards. Address Sue’s misconception and explain in a clear, simple, no-technical way why we multiply by 3 to convert 9 yards to feet.
10. One yard is 3 feet. Does it therefore follow that one cubic yard is 3 cubic feet: Explain.
11. Using the area formula for rectangles and principles about area that we have studied, give a clear and thorough explanation for why the area of a triangle is 1/2 b h square units. Your explanation should be general, in the sense that we could see why it would work for any triangle.
12. A student in your class wants to know why we multiply only two of the lengths of the sides of a rectangle in order to determine the rectangle’s area. When we calculate the perimeter of a rectangle we add the lengths of the four sides in order to find the area? Explain to the student what perimeter and are mean and explain why we carry out the perimeter and ara calculations for a rectangle the way we do.
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