Teaching Algebra with Manipulatives

Chapter
4
Graphing Relations and Functions
Teaching Notes and Overview
Using Overhead
Manipulatives
Relations
(p. 85 of this booklet)
Use With Lesson 4-3.
Objective Model a relation and its inverse
Materials
overhead geoboard*
geobands*
* available in Overhead Manipulative Resources
This demonstration uses geoboards with
geobands to construct triangles. Students are
asked to name the points in the interior of the
triangles. They are told that this set of points is
a relation. Students state the domain and range
of the relation. Next, students write the inverse
of this relation by switching the coordinates of
each ordered pair of the relation. Then students
construct the triangle containing these interior
points.
In the Extension, students are asked to repeat the
same activity for a rectangle with given vertices.
Then students compare the size, the shape and
the position of the two rectangles. Next, students
are given the vertices of a triangle and asked to
repeat the activity again. The comparison shows
that the triangles have the same shape and size,
and are in the same position. Thus, the relation
and its inverse are equivalent. Students are asked
to experiment with other figures on the geoboard
and try to predict the figure corresponding to the
inverse of the relation.
Answers
Answers appear on the teacher demonstration
instructions on page 85.
Algebra Activity
Recording Sheet
Relations and Inverses
(p. 86 of this booklet)
Use With the activity on page 207 in Lesson
4-3 of the Student Edition.
Objective Graphing a relation and its inverse.
Materials
colored pencils
You may want to use student pairs to do this
activity or do it as a classroom demonstration
with student participation. If you decide to do a
classroom demonstration, prior to class, prepare
an easel pad with a one-inch by one-inch
coordinate grid. In addition, give a sheet of
coordinate grid paper to each student. Have a
student graph the relation on the easel grid
paper with a colored marker. Then another
student can graph the inverse of the relation
with a different colored marker. In the
meantime, students can be doing the activity at
their seats. Ask for assistance to fold the grid
paper. You may choose to answer Exercises 1–4
with the entire class or have pairs of students
work on the exercises.
Answers
See Teacher Wraparound Edition p. 207.
Using Overhead
Manipulatives
Graphing Linear Relations
(p. 87 of this booklet)
Use With Lesson 4-5.
Objective Graphing linear equations on a
coordinate plane.
Materials
coordinate grid transparency*
transparency pen*
transparency prepared as described on the
activity
three blank transparencies
* available in Overhead Manipulative Resources
This demonstration requires you to prepare a
transparency like the table in the activity. Do
not copy the numbers shown in the parentheses
or the heading of the second column. Have
students work in groups of two or three. On the
transparency, write x 1 in the heading of the
second column. Complete the first row with the
class. Then have them complete the table and
© Glencoe/McGraw-Hill 82 Teaching Algebra with Manipulatives