Teaching Algebra with Manipulatives
Teaching Algebra with Manipulatives
Teaching Algebra with Manipulatives
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Chapter 3 <strong>Teaching</strong> Notes and Overview<br />
groups of two or three students to work the<br />
remaining exercises.<br />
Answers<br />
See Teacher Wraparound Edition pp. 136–137.<br />
<strong>Algebra</strong> Activity<br />
Equations of Planes<br />
(pp. 226–227 of this booklet)<br />
Use With Lesson 3-5.<br />
Objectives Determine the octant in which a<br />
point in space is located and graph it.<br />
Graph linear equations in space, and determine<br />
the intercepts and traces.<br />
Answers<br />
1. 1; 5; none<br />
2. See students’ graphs.<br />
3a. See students’ graphs; (3, 0, 0), (0, 3, 0),<br />
(0, 0, 3);x y 3, x z 3, y z 3<br />
3b. See students’ graphs; (3, 0, 0), (0, 6, 0),<br />
(0, 0, 2); 2x y 6, 2x 3z 6,<br />
y 3z 6<br />
3c. See students’ graph; (5, 0, 0), (0, 3, 0),<br />
(0, 0, 15); 3x 5y 15, 3x z 15,<br />
5y z 15<br />
3d. See students’ graphs; (4, 0, 0), (0, 3, 0),<br />
none; 3x 12, 4y 12, 3x 4y 12<br />
Materials<br />
classroom set of <strong>Algebra</strong> Activity worksheets<br />
transparency master of <strong>Algebra</strong> Activity<br />
Tinkertoys® or similar construction toys (6<br />
sticks, 1 circle per group)<br />
string (about 2 feet per group)<br />
Prior to the activity, assemble a set of<br />
Tinkertoys® to simulate x-, y-, and z-axes.<br />
Calibrate the sticks using 1- or 2-cm intervals.<br />
Cut the transparency on the dashed line. Pass<br />
out the <strong>Algebra</strong> Activity worksheet.<br />
Form student groups. Ask the groups to<br />
assemble their Tinkertoys® to simulate x-, y-,<br />
and z-axes. Show the students your model. Have<br />
the students use their Tinkertoy® model to help<br />
them answer Exercise 1 on the worksheet.<br />
Next, display the transparency and graph<br />
(3, 2, 6) (Figure 1). Then graph (2, 5, 4)<br />
(Figure 2). Then complete Exercise 2 on the<br />
worksheet.<br />
Discuss finding the x-, y-, and z-intercepts of the<br />
equation x 2y z 4. Wrap the string around<br />
the sticks on the model, where x 4, y 2, and<br />
z 4, connecting the trace in each coordinate<br />
plane. Repeat the procedure for 5x 15y <br />
6z 30.<br />
Now display the transparency and show the<br />
diagram for the above equations, using Figures<br />
3 and 4. Complete the worksheet as a whole<br />
group or individual activity.<br />
<strong>Algebra</strong> 2—Chapter 3<br />
© Glencoe/McGraw-Hill 221 <strong>Teaching</strong> <strong>Algebra</strong> <strong>with</strong> <strong>Manipulatives</strong>
Change language