Name: _____________________________
Date: _____________________
Class Period:___________
Learning Target:
Expressions – Pretty as a Picture
Directions: Get a set of algebra tiles and organize your pieces into piles on your desk according to shape
and size putting identical pieces together in a pile. How many piles do you have?
1. Here are the dimensions of the unit tile (the small square tile), you find the area.
-1 unit
-1 unit
R
Red
Area:________
1 unit
1 unit Cream
Area: _______
2. Use your unit tiles to make some deductions about the other two tiles in your bag (rectangular tile
and large square tile). What do you know about the dimensions of the other tiles? Write your
observations below using complete sentences.
3. Label the diagrams below with the correct dimensions and then find the area of each tile.
Green
Red
Area: _____ Area: _______
Green
Area:__________
Red
Area:_________
4. Let’s Begin to use the algebra tiles to represent algebraic expressions as pictures. For example, look
at the group of tiles below. Underneath each tile, write the number or variable each tile represents (the
tile’s area).
Cream
Red
Green
Green
Cream
Cream
Red
R
Red
R
Red
All of the variables and numbers represented above are terms within the same algebraic expression,
each tile represents one term. Below, you are about to write the algebraic version of the expression.
A. Using complete sentences, explain any math rules you must keep in mind when translating the
picture expression into an algebraic expression.
B. Write the algebraic expression and compare your expression with that of the teams around you.
5. Look at the next example below, create this same example on your desk using your algebra tiles:
Cream
Red
Red
Green
Red
Cream
R
Red
R
Red
Green
Red
R
Red
A. Write the above pictorial expression as an algebraic expression, use the tiles on your desk to
help you. Using complete sentences, explain any strategies you used to write the expression.
B. Look at your expression, is there any way to simplify your expression? Compare your answer to
the answers of other groups around you.
6. There is phrase we use in math called “like terms.” Each algebra tile represents one term in your
expression. Which of the terms below do you think represent “like terms?” Take coloring
pencils and color the “like terms” the same color in order to match them.
Cream
R
Red
Green
Red
Red
Red
7. Explain how you knew which tiles represented “like terms,” use complete sentences.
8. Look at the following algebraic expression and use your tiles to represent this pictorially.
2x + x2 – 1 + 2x2 – x + 3
A. Simplify the number of terms (reduce the number of terms written) in this expression by
combining the “like terms”. Compare your answer to your partner’s answer.
B. How can we recognize the “like terms” when they are written algebraically?
9. Practice combining more like terms to simplify the number of terms in each of the following
expressions. Use your algebra tiles to help you see the expression pictorially and sketch that
picture below each expression. You may use coloring pencils or right the word for the color of
the tiles you use.
A. -3x + 2 – 3x2 + 2x – 4 + x2
C. 5x – 2x2 + 3 – 2x + 2x2 - 4
Picture:
Picture:
Simplified Expression:__________________
Simplified Expression:_______________
B. 5 + x2 – 4x + 3x2 – 2x + 3
Picture:
Simplified Expression:_____________________
D. 4 – 3x2 + 5 – 4x + x2 + 3x
Picture:
Simplified Expression:______________________
10. Represent the following expression using your algebra tiles. Sketch your pictorial
representation below.
2(3x + 4)
A. What does the 2 in front of the parentheses mean?
B. Simplify your expression by combining like terms and write your new algebraic expression below
11. Represent the following expression using your algebra tiles. Sketch your pictorial
representation below.
3(x2 – 3x)
A. What does the 3 in front of the parentheses mean?
B. Simplify your expression by combining like terms and write your new algebraic expression below
12. In the two examples above (questions 10 and 11) you demonstrated the Distributive Property.
This property is very powerful in algebra. Why do you think it is called the Distributive Property,
use complete sentences?
13. Using the Distributive Property, combining like terms, and your tiles, simplify the following
expressions by first sketching the pictorial version of the expression and then writing the
simplified algebraic version of the expression.
A. 4(3x + 5)
C. 3(-2x2 – 4)
Picture:
Picture:
Simplified Expression:__________________
Simplified Expression:_____________________
B. 2(3x2 – 2x)
D. -5(2x – 3)
Picture:
Picture:
Simplified Expression:__________________
Simplified Expression:_____________________
C. 3(-2x2 + 2) – 2x2
G. -3(2x2 – 3) + x2 + 6
Picture:
Picture:
Simplified Expression:__________________
Simplified Expression:_____________________
D. -2 + x(x + 3) + 4
Simplified Expression:__________________
H. 4 – x(2x + 5)
Simplified Expression:_____________________