Teaching Algebra with Manipulatives

Chapter
8
Conic Sections
Teaching Notes and Overview
Algebra Activity
Recording Sheet
Midpoints and Distance Formulas in
Three Dimensions
(p. 263 of this booklet)
Use With Lesson 8-1 as a follow-up activity.
This corresponds to the activity on pages
417–418 in the Student Edition.
Objective Find the distance between two
points and the midpoint of a segment in
three-dimensional space.
Materials
none
This is a follow up activity from formulas for
finding the midpoint of a segment and the
distance between two points in two-dimensional
space to three-dimensional space. As you go
over the three-dimensional formulas used in
Examples 1 and 2, you may want to display the
two-dimensional formulas too. Ask students to
compare and contrast the formulas.
Form groups of two or three students to
complete Exercises 1–9. When the groups have
finished these exercises, discuss their answers.
Before assigning the remaining exercises, have
students state the plan they will use to solve
each exercise. Discuss their plans. As soon as
the groups have completed Exercises 10–17,
have them explain their solutions. Allow for a
few minutes to ask the groups what they
learned from working these exercises.
Answers
See Teacher Wraparound Edition pp. 417–418.
Materials
waxed paper
This small group activity requires students to
follow a step-by-step process that uses three
pieces of waxed paper to make three differentshaped
parabolas. Then students compare the
shapes. Students are asked to decide how the
distance between the focus and the directrix
affect the shape of the parabola.
Answers
See Teacher Wraparound Edition p. 421.
Mini-Project
Conics
(p. 265 of this booklet)
Use With Lesson 8-2.
Objective Model and analyze parabolas.
Materials
clear acetate
grid paper
Divide students into groups to complete this
Mini-Activity. Groups will need acetate paper
and grid paper. At the conclusion of the project,
discuss Exercise 5. Then ask each group to
display their answers to Exercises 8 –10.
Require students to explain their work. Discuss
Exercise 11. Show the graph of the equation.
Answers
1. See students’ work.
2. parabola
3. See students’ work.
Algebra Activity
Recording Sheet
Parabolas
(p. 264 of this booklet)
Use With the activity on page 421 in Lesson
8-2 of the Student Edition.
Objective Model and analyze the shapes of
three parabolas.
4. See students’ work.
5. The parabola becomes narrower.
6–10. See students’ work.
1
11. y x 1 6
2
Algebra 2—Chapter x 8
© Glencoe/McGraw-Hill 259 Teaching Algebra with Manipulatives