© 2015 Elementary Pre-Service Teachers Mathematics Project • School of Education • Boston University •

Boston, MA 02215 • (617) 353-7105 • schapin@bu.edu

Please do not circulate or cite without permission

Parallelograms and Triangles

In this lesson, you will derive and explain the area formulas for parallelograms and triangles using some

of the strategies explored in previous lessons. Work on the following sets of problems with your partner

or group. Be sure to share your ideas. Work to make sense of the ideas together.

1. a) On the attached grid paper draw 5 different parallelograms with a base of 4 units and a height of 3

units. One of these parallelograms should be a rectangle. Determine their areas.

b) Apply some of the strategies you learned in previous lessons to explain how you know for sure

the areas of the parallelograms in Problem 1a. Consider why the area of these parallelograms can

be determined using the formula, A=bh, where b is the length of the base and h is the height.

Whole Class Discussion Question

Provide a convincing argument for why the area of any parallelogram is the product of base

length and height.

Parallelograms and Triangles 2

© 2015 Elementary Pre-Service Teachers Mathematics Project • School of Education • Boston University •

Boston, MA 02215 • (617) 353-7105 • schapin@bu.edu

Please do not circulate or cite without permission

2. Cut out 2 copies of each of the following triangles from the end of this packet:

right triangle

isosceles triangle

scalene triangle

equilateral triangle

Your goal is to explain to others why the formula for the area of a triangle (A = ½bh) makes sense.

Your reasoning must work for any type of triangle. Consider using some of the strategies for

determining area that you learned in prior lessons.

Whole Class Discussion Question

Explain why your formula for the area of a triangle is correct for all triangles.

Parallelograms and Triangles 3

© 2015 Elementary Pre-Service Teachers Mathematics Project • School of Education • Boston University •

Boston, MA 02215 • (617) 353-7105 • schapin@bu.edu

Please do not circulate or cite without permission

Parallelograms and Triangles Homework: Summarize & Connect

1. Explain why the area formula for a parallelogram makes sense.

2. Explain why the area formula for a triangle makes sense.

Parallelograms and Triangles 4

© 2015 Elementary Pre-Service Teachers Mathematics Project • School of Education • Boston University •

Boston, MA 02215 • (617) 353-7105 • schapin@bu.edu

Please do not circulate or cite without permission

Isosceles triangles

Right triangles

R R

I I

Parallelograms and Triangles 5

© 2015 Elementary Pre-Service Teachers Mathematics Project • School of Education • Boston University •

Boston, MA 02215 • (617) 353-7105 • schapin@bu.edu

Please do not circulate or cite without permission

Equilateral triangles

Scalene triangles

S S

E E