Teaching Algebra with Manipulatives

Chapter
1
Mini-Project
Evaluating Expressions
(p. 30 of this booklet)
Use With Lesson 1-2.
Objective To use manipulatives to represent
expressions and evaluate them.
Materials
none
This activity requires students to work in
groups of two or three to find ways to represent
algebraic expressions in a pictorial manner.
They then use their representations to evaluate
expressions for certain real-number values.
Sample Answers
The Language of Algebra
Teaching Notes and Overview
1. Answer provided on worksheet.
2. Let ◆ represent x.
3x 3 ◆ or ◆◆◆
4x 4 ◆ or ◆◆◆◆
2x 2 ◆ or ◆◆
3. 3x ◆◆◆ 4 4 4 or 12
7c. 3x 2 4y 2 3(5 2 ) 4(3 2 )
3(25) 4(9)
75 36
111
7d. 3(2x y) 3(2 5 3)
3(10 3)
3(13)
39
Using Overhead
Manipulatives
Distributive Property
(pp. 31–32 of this booklet)
Use With Lesson 1-5.
Objective Use a geometric model of the
Distributive Property to simplify expressions.
Materials
centimeter grid paper transparency*
overhead area/algebra tiles*
transparency pen*
blank transparencies
* available in Overhead Manipulative Resources
Algebra 1—Chapter x 1
4. Let ♠ represent y.
3x 2y ◆◆◆ ♠♠
5 5 5 4 4 or 23
5. Let ◆ represent x.
2x 5x ◆◆ ◆◆◆◆◆
2(3) 5(3)
6 15 or 21
6. Replace each variable by the number given.
Simplify expressions inside grouping
symbols.
Find the values of the powers.
Multiply and divide from left to right.
Add and subtract from left to right.
7a. 8x 3y 8(5) 3(3)
40 9
49
This demonstration contains three activities.
• Demonstration 1 shows the Distributive
Property in terms of the area of a rectangle
using real numbers. Use this before the
Algebra Activity on page 6 (Student Edition
page 28).
• Demonstration 2 shows an application of the
Distributive Property to validate sums of like
terms.
• Extension questions ask students to apply
what they have learned to expressions
involving subtraction.
Answers
Answers appear on the teacher demonstration
instructions on pages 31–32.
7b. 5x 2 2y 5(5 2 ) 2(3)
5(25) 2(3)
125 6
131
© Glencoe/McGraw-Hill 27 Teaching Algebra with Manipulatives