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
Equivalent Expressions Key:
1. no
2. yes
3. yes
4. yes
5. yes
6. yes
7. no
8-10 various answers
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

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) 8a + 14b +4-32

10)

7th Grade Mathematics Name: ______

Simplifying Expressions: Combining Like Terms

Period: ____ Date: ______

Represent the pieces in each picture in an addition expression. Then combine like terms to write the expression in a more simple way.

Picture / Addition Expression
(The Long Way) / Simplified Expression (The Short Way)
EX: / / x + 1 + 1 + x + 1 + 1 + 1 + x / 3x + 5
1. /
2. /
3. /
4. /
5. /
6. / / Hint - this answer is:
7. /
8. / You draw the pictures on 8 and 9! /
9. /
10. /

Simplify each expression by combining like terms.

11. 12.

13. 14.

15. 16.

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

27. 28.

29. 30.