Teaching Algebra with Manipulatives

Chapter 5 Teaching Notes and Overview
Using Overhead
Manipulatives
Point-Slope and Standard
Form of Equations
(pp. 100–101 of this booklet)
Use With Lesson 5-5.
Objective Write linear equations in pointslope
and standard forms.
This demonstration contains two activities.
• Demonstration 1 shows the graph of a line
with a point S. Using the graph, students
are asked to find the slope of the line. The
coordinates of a known point and the slope of
the line are used to write the equation of the
line in point-slope form. Rewriting the pointslope
form into standard form is covered. The
process is repeated for another point on the
graph.
• Demonstration 2 shows a graph of a line that
passes through the origin. Students are asked
to write an equation of the line in point-slope
form and standard form.
Answers
Answers appear on the teacher demonstration
instructions on pages 100–101.
Algebra Activity
Slopes of Parallel and
Perpendicular Lines
(pp. 102–103 of this booklet)
Use With Lesson 5-6 as a preview activity.
Objective Discover the relationship between
slopes of parallel lines and slopes of
perpendicular lines.
Materials
centimeter grid paper transparency*
parallel and perpendicular lines transparency*
(p. 103)
tracing paper
graph paper
* available in Overhead Manipulative Resources
Students find the slopes and y-intercepts of
the lines a and b shown on a transparency.
The centimeter grid paper and parallel/
perpendicular lines transparencies follow this
teacher demonstration for Lesson 5-6. The
Algebra Activity worksheet follows the latter.
They work in groups to complete Exercises 1
and 2 on the Algebra Activity worksheet. Have
students complete Exercises 3 and 4. Discuss
the relationship of slopes of parallel lines. Next,
students find the slopes of lines c and d shown
on the overhead. Again they work in groups to
complete Exercises 5 through 8 on the Algebra
Activity worksheet. Discuss the relationship of
slopes of perpendicular lines.
Answers
1. Students trace and cut out Figure 1.
2. Answers will vary.
3. The slopes are the same and the y-intercepts
are different.
4. Answers will depend on Exercise 1.
5. Students trace and cut out Figure 2.
6. Answers will vary.
7. The product of their slopes is 1 or one
slope is the negative reciprocal of the other.
The y-intercepts are different.
8. Answers will depend on Exercise 5.
Algebra Activity
Recording Sheet
Perpendicular Lines
(p. 104 of this booklet)
Use With the activity on page 293 in Lesson
5-6 of the Student Edition.
Objective Discover the relationship between
slopes of perpendicular lines.
Carefully review the directions for Steps 1
and 2. Next, ask students to read exercises
1 through 9. Some students may need
clarification as to the meaning of rotation.
You may want to form groups of two or three
students to do this activity. Have each group
follow the directions for Steps 1 and 2. Allow
© Glencoe/McGraw-Hill 94 Teaching Algebra with Manipulatives