Teaching Algebra with Manipulatives

Chapter 5 Teaching Notes and Overview
Answers
1. 4, 2; 9, 3; 16, 4; 25, 5
2. See students’ models.
3. x 2, (x 2) 2 ,(x 2)(x 2);
2x x, (2x x) 2 ,(2x x)(2x x);
3xy xy, (3xy xy) 2 ,(3xy xy)(3xy xy);
b 3, (b 3) 2 ,(b 3)(b 3)
4. 10 5. 9
3
6. 0.2 7.
1 1
8. 2x 9. 2x 2 6
10. 4x 2 y 2 14y 11. 27x 3 y 3 y
Algebra Activity
Recording Sheet
Adding Radicals
(p. 238 of this booklet)
when graphing in the complex plane, ordered
pairs are in the form (real, imaginary). As soon
as students have completed Exercises 1–4,
Exercises 5–7, and Exercise 8, you may want to
stop and go over their answers and answer any
questions they may have. Some students may
be interested in investigating, solving, and
graphing other similar equations. Encourage
them to pursue these interests and to share
their findings with the class.
Answers
1–3. See students’ work.
4. square
5–6. See students’ work.
7. triangle
8. See students’ work.
9. regular hexagon
Algebra 2—Chapter 5
Use With the activity on page 252 in Lesson
5-6 of the Student Edition.
Objective Use dot paper to add radicals.
Materials
isometric dot paper
Students will use the Pythagorean Theorem to
construct a right triangle with hypotenuse of
length 2 units on dot paper. They will extend
the hypotenuse to twice its length and use the
models to add the radicals. Students will also
model other irrational numbers using the same
method.
Answers
See Teacher Wraparound Edition p. 252.
Mini-Project
nth Roots of Negative Numbers
(p. 239 of this booklet)
Use With Lesson 5-9.
Objective Find nth roots of negative numbers.
Have students work in groups of two or three to
complete the Exercises 1 through 9. Require
students to do and show their work for
Exercises 1, 5, and 8. Remind students that
Algebra Activity
Recording Sheet
Adding Complex Numbers
(p. 240 of this booklet)
Use With the activity on page 272 in Lesson
5-9 of the Student Edition.
Objective Add complex numbers by modeling
them on a coordinate plane.
Materials
grid paper
straightedge
Students will graph the first complex number
from an addition equation on a coordinate grid.
They will then move accordingly on the grid to
add the next complex number. The new point
represents the complex number that is the
solution to the equation. Using the coordinate
grid, students will also model the difference and
absolute value of other complex numbers.
Answers
See Teacher Wraparound Edition p. 272.
© Glencoe/McGraw-Hill 233 Teaching Algebra with Manipulatives