Standard: 7.EE.1 Apply Properties of operations to add, subtract, factor, and expand linear expressions
with rational coefficients.
Goal: SWBAT recognize equivalent expressions that arise from distributing and combining like terms.
Task
Anticipate
Develop-- Blocks and Blocks
● Comparing patterns of
white and black blocks
-Students will create expressions (for #1 it could be 3x+4+ 3x + 4)
-lead students into seeing groupings. [for #1 it would be 2(3x+4) ]
-Students may not realize the different shape in #3 changes the expression.
- Encourage students to use variables to stand for the blocks--writing the
expressions could be a challenge. Have students recognize that they could
use a variety of variables: r and s for rectangles and squares, b and w for
black and white, x and integers, or x and y. In all of these methods it is only
possible to combine like with like
- Teachers may want to have #1-4 on one piece of paper and then work on #5
and 6 after the expressions have been written
-As an extension, students could draw their own patterns of equivalent and
non-equivalent blocks.
Solidify-- Equivalent
Expressions
● Justify (or Explain)
whether the
expressions are or are
not equivalent
- incorrectly distributing
- incorrectly combining like terms
- fractional pictures
- faulty/non precise explanation
KEY
Practice--Simplifying
Expressions: Combine Like
Terms WS
(Using Algebra Gear, you could have students model as they work through the
problems.)
- combining terms that aren’t alike
- combining constants with variable terms
Equivalent Expressions Key:
1. no
2. yes
3. yes
4. yes
5. yes
6. yes
7. no
8-10 various answers
Additional resources:
Online combining terms activity:
http://www.mathscore.com/math/practice/Simplifying%20Algebraic%20Expressions/
http://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf
Blocks and Blocks
Name__________________
Write expressions for the following sets of white and black blocks.
1)
2)
3)
4)
5) Are any of the expressions in #1-4 equivalent to each other? Justify your answer.
6) Think of other ways you could write expressions for #1-4. Justify that your expressions are
equivalent.
Name_____________________________
Equivalent Expressions
Justify whether the following pairs of expressions are equivalent or not.
1.
2.
3.
4.
5. 3
2
+
6.
7. 2
3
Create two or more equivalent expressions for the following.
8. 8x+10y-14
9) 8 a + 14b +4
10)
-32
7th Grade Mathematics
Simplifying Expressions: Combining Like Terms
Name: _________________________
Period: ____ Date: _______________
These are the
pieces in an
Algebra Lab
Gear Set:
1
x
y
x2
y2
Represent the pieces in each picture in an addition expression. Then combine like terms to
write the expression in a more simple way.
Picture
EX:
Addition Expression
(The Long Way)
Simplified Expression
(The Short Way)
x+1+1+x+1+1+1+x
3x + 5
1.
2.
3.
4.
5.
6.
Hint - this
answer is:
x 2  3x  2 y
7.
8.
You draw the pictures on 8 and 9!
9.
x2  x2  x2  x  x 1111
y2  y  y  y 111
10.
Simplify each expression by combining like terms.
11.
a 1 a  a 1
12. c  2  c  c  4
13.
3a  94 (a  3)
14. 5z  2 z
15.
7w  2w  52 w
16. 5t  3t  2t
17.
3x  2x  3
18.
19.
9.8u  6u  3  2.5
20. 4m  3  5m  4
21.
3x  6 x  7 y
22. 2( y  4)  12 ( x  9)  y  3x
23.
5a  52 a  9b
24. 2a  2a  6b  3b
25.
3
4
27.
5a  2b  3  2a  5
28. 4( x  y 2 )  13 (2 z  3)  107 (4 x  5)
29.
3( 54 x  24 y)  5  y  83
30. 8.9 x 2  3.3  x  2 x  1.2 x 2
( 13 x  2 y)  56 (7 x  2 y)
2
3
r  13 r  6
26. 4.8r  5.3s  2.5r  3s