1. Unit 3. Day 2.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Distributive Property & Adding/Subtracting expressions
Use properties of operations to generate equivalent expressions

3. Today’s Lesson (1) 7th Grade distributing
(2) Adding & Subtracting expressions

4. 𝑥+ = So far all the previous examples were from 6th grade. 7th Grade:
CCSS.MATH.CONTENT.6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x
7th Grade:
CCSS.MATH.CONTENT.7.EE.B.4.A Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.
 p(x + q) = r
2 3
  𝑥+ =
3 4
− 4 5

5. Example A: Simplify
2 3 𝑥−
+ 5
− 2 6 +5
2 3 𝑥 −
2 6 −
− 1 3
+ 5 1
2 3 𝑥 − 1 15

6. Example B*: Simplify
𝑦− 1 3 − 2𝑦+4 1
− 1 12
3 20 −4 −2
3 20 𝑦
3 20 𝑦
− 1 12
1 12 −
−2𝑦
−2𝑦 −4 −4
− 1 12
3 20
− 4 1
− 2 1
− 𝑦 −
− 12 − 12
20 − 20 1 3 48 40

7. Today’s Lesson (1) 7th Grade distributing
(2) Adding & Subtracting expressions

8. Today’s Lesson (1) 7th Grade distributing
(2) Adding & Subtracting and Multiplying (a little) expressions

9. Q: What is an equation?
A: A math sentence WITH an equal sign
4=7−3
2𝑥+4=7
5𝑥−6𝑦=8
3 𝑥 2 −7𝑥+13=0
Q: What is an expression?
A: A math sentence WITHOUT an equal sign
4+7−3
2𝑥+5
5𝑥−6𝑦−8
3 𝑥 2 −7𝑥+13

10. 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

11. Expressions Linear Non-Linear 4𝑥+6 4𝑥+ 6 2 2𝑦+3 𝑥 2 −4 2𝑦+3𝑥−4 4𝑚
4 𝑚 2
−7 5 −7

12. 1 + 1 −3𝑎 + 2 + 5𝑎 −3 2𝑎 −1 Example C: Find the sum of −3𝑎+2 and 5𝑎−3

13. Example D*:
Find the sum of 2x−10+𝑦 and 8−3y−11x
Example E*: Find the sum of 𝑏 and − 1 2 𝑏− 1 4

14. 1 + 1 + − 9𝑥 −9𝑥 − 2 − 2 − 2𝑦 − 2𝑦 Example D*:
Find the sum of 2x−10+𝑦 and 8−3y−11x
2𝑥−10+𝑦
8−3y−11x 1
2𝑥−10+𝑦
2𝑥−10+𝑦 + 1
8−3y−11x
8−3𝑦−11𝑥 2𝑥
−10
+ 𝑦 +
− 9𝑥
−9𝑥
− 2
− 2
− 2𝑦
− 2𝑦

15. 3 4 𝑏+ 5 8
− 1 2 𝑏− 1 4
Example E*: Find the sum of 𝑏 and − 1 2 𝑏− 1 4
3 4 𝑏
3 4
5 8
− 1 2
− 1 2 𝑏 − 1 4
− 1 4 1 + 1
1 4 𝑏
3 8 +
4 − 4 3 2
1 4
8 − 8 5 2
3 8 = = = =

16. 4𝑥+11 3𝑥+5𝑦−4 1 3𝑥+5𝑦−4 − 1 3𝑥 + 5𝑦 − 4 −4𝑥 −11 − 𝑥 1 + 5𝑦 − 15
Example F: “Find the difference when 4𝑥+11 is subtracted from 3𝑥+5𝑦−4 “
4𝑥+11
3𝑥+5𝑦−4 1
3𝑥+5𝑦−4 − 1 3𝑥
+ 5𝑦
− 4
−4𝑥
−11
− 𝑥 1
+ 5𝑦
− 15

17. 𝑡+3𝑚 − −20𝑚+17+12𝑡 Example G*: −𝑎+ 1 3 𝑏+2 − 5 6 𝑏− 7 8 𝑎+ 2 3
𝑡+3𝑚 − −20𝑚+17+12𝑡
−𝑎+ 1 3 𝑏+2 − 𝑏− 7 8 𝑎+ 2 3
Example H*:

18. 1 𝑡+3𝑚 − −20𝑚+17+12𝑡 𝑡+3𝑚 1 1𝑡 + 3𝑚 +20𝑚 −17 −12𝑡 −11𝑡 + 23𝑚 − 17
Example G*: 1
𝑡+3𝑚 − −20𝑚+17+12𝑡
𝑡+3𝑚 1 1𝑡
+ 3𝑚
+20𝑚
−17
−12𝑡
−11𝑡
+ 23𝑚
− 17

19. −𝑎+ 1 3 𝑏+2 − 5 6 𝑏− 7 8 𝑎+ 2 3 −𝑎+ 1 3 𝑏+2 1 1 − 5 6 𝑏 + 7 8 𝑎 − 2 3
Example H*:
−𝑎+ 1 3 𝑏+2 − 𝑏− 7 8 𝑎+ 2 3
−𝑎+ 1 3 𝑏+2 1 1
1 3
2 1
− 5 6 𝑏
+ 7 8 𝑎
− 2 3
− 5 6
+ 7 8
− 2 3 −1
− 1 8 𝑎
− 1 2 𝑏
4 3 +
− 1 1
6 − 6 − 2 8 7 6 5
− 3 6
− 1 8
3 − 3 2
4 3 = = = = = =

20. What mistake did we make?
Example I: Find the product of 4 and 2𝑥−6𝑦 4
2𝑥−6𝑦 ∙
2𝑥−6𝑦 8𝑥 8𝑥
−24𝑦
−6𝑦
What mistake did we make?

21. −𝑥− 1 3 𝑦+ 5 8
Example J: Find the product of −2 and −𝑥− 1 3 𝑦+ 5 8 −2
−𝑥− 1 3 𝑦+ 5 8 ∙ 𝑦
− 5 4 2𝑥
−2 ∙− 1 3 1
2 3
− 2 1 ∙ 5 8
− 10 8
− 5 4 = = =