Teaching Algebra with Manipulatives

Chapter
6
Quadratic Functions and Inequalities
Teaching Notes and Overview
Mini-Project
Parabolas
(p. 243 of this booklet)
Use With Lesson 6-1.
Objective Write equations for parabolas.
Materials
clear acetate sheet for each group
Have students work in small groups to complete
this Mini-Project. Give each group a clear
acetate sheet. This sheet will be used to trace
the parabola on the worksheet. Using 1 4 -inch
grid paper, place the acetate on a coordinate
plane with the vertex at the given point. Then
have students align the axis with a vertical line
of the grid paper. Next, they list five points that
the graph contains, and write the equation for
the graph. This activity shows students that
parabolas with the same shape will have
different equations depending on the vertex.
Allow students to share and discuss their
answers for Exercises 3 and 4.
Some students may become interested in
investigating parabolas that face downward.
These students may use the same parabola that
they traced on acetate paper. Encourage them
to write about their findings and share their
work with the other students by making a
presentation.
Answers
1. See students’ trace of graph.
2a. (2, 9), (1, 4), (0, 1), (2, 1), (3, 4), (4, 9);
(x 1) 2
2b. (1, 9), (0, 4), (1, 1), (3, 1), (4, 4), (5, 9);
(x 2) 2
2c. (0, 9), (1, 4), (2, 1), (4, 1), (5, 4), (6, 9); (x 3) 2
2d. (4, 9), (3, 4), (2, 1), (0, 1), (1, 4), (2, 9);
(x 1) 2
2e. (3, 11), (2, 6), (1, 3), (1, 3), (2, 6), (3, 11);
x 2 2
2f. (3, 5), (2, 0), (1, 3), (1, 3), (2, 0),
(3, 5); x 2 4
2g. (0, 10), (1, 5), (2, 2), (4, 2), (5, 5), (6, 10);
(x 3) 2 1
2h. (2, 7), (1, 2), (0, 1), (2, 1), (3, 2), (4, 7);
(x 1) 2 2
3. y (x h) 2 k
4. y (x 2) 2 3
Algebra Activity
Recording Sheet
Completing the Square
(p. 244 of this booklet)
Use With the activity on page 308 in Lesson
6-4 of the Student Edition.
Objective Solve quadratic equations by
completing the square.
Materials
algebra tiles*
equation mats*
* available in Overhead Manipulative Resources
You may need to review how to represent a
quadratic equation with tiles on the equation
mat. Have students follow along as you go over
using the mat to complete the square for a
quadratic equation. Ask students to work in
pairs to complete the square for Exercises 1
through 4.
Answers
See Teacher Wraparound Edition p. 308.
Algebra Activity
Completing the Square
(pp. 245–246 of this booklet)
Use With Lesson 6-4.
Objective Solve quadratic equations by
completing the square.
Materials
algebra tiles*
classroom set of Algebra Activity worksheets
transparency master of Algebra Activity
grid paper*
* available in Overhead Manipulative Resources
© Glencoe/McGraw-Hill 241 Teaching Algebra with Manipulatives
Algebra 2—Chapter x 6