Teaching Algebra with Manipulatives

Chapter
9
Mini-Project
Interpreting Powers of a Binomial
Geometrically
(p. 272 of this booklet)
Use With Lesson 9-1.
Objective Interpret and analyze powers of a
binomial geometrically.
This activity requires students to work in small
groups to interpret and analyze two geometric
models. Students are then asked to make other
geometric models of their choosing to represent
the products of binomials, and then, write an
analysis of the models. As soon as the groups
have completed Exercises 1–2, discuss their
answers. In Exercise 1, take the opportunity to
show that (x 4) 2 x 2 16. Also, in Exercise 2,
that (a b) 3 a 3 b 3 .After completing
Exercise 3, have the groups exchange models
with one another and analyze them.
Answers
Rational Expressions and Equations
Teaching Notes and Overview
1. The area of the large square is (x 4) 2 .The
areas of the component rectangles are x 2 ,4x,
4x, and 16. Since the areas are equal,
(x 4) 2 x 2 8x 16.
2. The volume of the large cube is (a b) 3 . This
cube consists of 8 rectangular prisms with
the following volumes: a 3 , b 3 ,3ab 2 , and 3a 2 b.
Thus, (a b) 3 a 3 b 3 3ab 2 3a 2 b.
3. See students’ models and analyses.
Algebra Activity
Recording Sheet
Rational Functions
(p. 273 of this booklet)
Use With the activity on page 487 in Lesson
9-3 of the Student Edition.
Objective Use rational functions to graph
real-life data.
Materials
balance
metric measuring cups
several various kinds of liquids
grid paper
Students use a balance to find the volumes of
200 grams of different liquids such as water,
cooking oil, isopropyl alcohol, sugar water, and
salt water. Then they find the density of each
liquid and graph the data by plotting the points
(volume, density) on a graph.
Answers
See Teacher Wraparound Edition p. 487.
Algebra 2—Chapter x 9
© Glencoe/McGraw-Hill 271 Teaching Algebra with Manipulatives