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Module 3 Expressions

Homework Key

Math A Honors

2015 - 2016

Created in collaboration with Utah Middle School Math Project

A University of Utah Partnership Project

San Dieguito Union High School District

SDUHSD Math A Honors Module #3 – TEACHER EDITION 2

3.1A Homework: Matching Numerical Expressions to Stories* Name: Period: Four students, Alex, Brittany, Charlie, and Darlene, wrote a numerical expression for each story problem. Look at each student’s expression and determine whether or not it is appropriate for the given story problem. Explain why the expression “works” or “doesn’t work” using complete sentences. 1. I earned $6. Then I bought 4 candy bars for $0.50 each. How much money do I have left?

Expression Evaluate

Does it work?

Why or Why Not?

a. 6 – (0.50 + 0.50 + 0.50 + 0.50) $4 Yes

This subtracts the sum of 0.50 four times.

b. 6 – (0.50 – 0.50 – 0.50 – 0.50) $7 No

We need to subtract the sum of 0.50 four times.

c. 6 – 4(0.50) $4 Yes

It is like a only multiplying instead of repeated subtraction.

2. I earned $5. Then I spent $1 a day for 2 days in a row. How much money do I have now?

Expression Evaluate

Does it work?

Why or Why Not?

a. 5 – (1 – 1) $5 No

We need to subtract the sum of the two dollars.

b. 5 – (1 + 1) $3 Yes

We are subtracting the sum of the two dollars.

Write an expression that represents the situation for each problem. Then evaluate the expression to solve the problem. Write the answer in a complete sentence. There are various accurate expressions for these problems. They should each result in the value given. 3. Josh made ten 3-pointers and a 2-pointer at his basketball game. How many points did he score?

10(3) + 1(2) 32 points

4. I bought three apples for $0.25 each and 3 pounds of cherries for $1.75 a pound. How much money did I spend? 3(0.25) + 3(1.75) $6.00


5. Jim won 30 tickets. Evan won y tickets less than Jim did. How many tickets did Evan win?

Expression

Do you think it

will work?

Evaluate y = 6

Did it work?

Why or why not?

a. 30 – y --- 24 tickets Yes This is an accurate representation of

the expression

b. y 30 --- 24 tickets No Jim won more tickets than Evan, thus we must subtract from Jim’s amount.

c. y + 30 --- 36 tickets No Evan won less tickets than Jim, thus

we need to subtract.

d. 30 ÷ y --- 5 tickets No The difference between their amounts

is absolute; we must subtract.

Write an expression for each problem. Drawing a model is optional. Answer in a complete sentence.

6. I bought m gallons of milk for $2.59 each and a carton of eggs for $1.24. How much did I spend? m(2.59) + 1.24

7. Paul bought s sodas for $1.25 each and a bag of chips for $1.75. How much did he spend? s(1.25) + 1.75

8. Bob and Fred went to the basketball game. Each bought a drink for d dollars and nachos for n dollars. How much did they spend on two drinks and two orders of nachos? 2d + 2n or 2(d+n)

Spiral Review: Simplify each expression. Show all steps. 9. 2 ∙ 3 2 1 63

10. 2 ∙ 3 2 1 3

11. 2 ∙ 3 2 1 27 12. 4 ∙ 9 8 1 3


3.1B Homework: Algebra Tile Exploration Name: Period: Use the key below to interpret or draw the algebraic expressions in your homework. Key for Tiles:

x2 = x2

= -x2

Write an expression for what you see and then write the expression in simplest form. 1. x – 1 or x + (–1)

2. -2

3.

4.

5.

6.

x

1

1

1

1

1

x

x

x

x

x

x

x

x

x

x

1 1

1 1

1 1

x

x

x

x

1 1 1

1 1

x

x

x

111

x

x

1 1

1

x

x

x

x 1

xx

1 11 1

x

x

x

x

x

x

x – 2 or x + (–2)

3x – 3 or 3x + (-3)

x2 + x

–2x + 3

-x2


Draw a model for each of the expressions using the tile key. Simplify the expression if you can. 7. 2x + 4 8. 2x – 3 + 5

2x+2

9. 2x + 1 + 3 – 5 2x - 1

10. -3x + 2 + 2x - x + 2

1. –2x + 3 + 5x – 2 3x + 1

12. 5x – 3 – 4 + x 6x - 7

13. x + 4 + (–3x) – 7 -2x - 3

14. –x – 3 + 2x – 2 x – 5

15. 4x – 3 – 7x + 4 -3x + 1


Simplify each expression without using models. 16. 9 16 27 13 8 5

22 24 22

17. 2 3 6 9 5 7

7 8 13

Matching: Write the letter of the equivalent simplified expression on the line. 18. _e___ 3x – 5x

19. _a___ 4a – 12a

20. _ j___ 3x + 5x

21. _i___ 16a + a

22. _f___ 2x – 2y + y

23. _b___ 2x – 2 – 4

24. _h___ x – y + 2x

25. _c___ –y + 2y – x

26. _g___ 5x + 4y – 3x – x + 3y – 6y

27. _d___ 4x + 3y + 5x – 7y

a) –8a

b) 2x – 6

c) –x + y

d) 9x – 4y

e) –2x

f) 2x – y

g) x + y

h) 3x – y

i) 17a

j) 8x

Simplify each expression by combining like terms. 28. 13 9 22b 29. 45 12 33y

30. 11 14 13 –2u + 11 31. 6 4 2 10a – 2b

32. 1 3 5 33.

34. 3.4 21.4 3.4 2.2 –21.4x – 3.4y + 5.6

35.

36. 2 0.5 3 4.75 9.8 2.5x + 1.75y + 9.8

37. 14 9 15 16 –2w + 24

38. 2 39. 4 6 2 5 19 6m − 18

40. 6 16 9 18 2 -z + 2 or 2 - z 41. 88.5 22.4 4.04 26.3 92.54z - 22.4y + 26.3

42. 2 2 3 8 10x + 1 43. 65 4.2 65 2.2 5.4 3 5.4


44. Identify the terms, constants, coefficients, and like terms in each algebraic expression.

Expression Terms Constants Coefficients Like Terms

a. 7 3 2 1

7x, –3x, 2y, –1 –1 7, -3, 2 7x, –3x

b. 7 2 3 5 -7z, -2z, -3z, –5 –5 -7, -2, -3 -7z, -2z, -3z

c. 8 9 7 6

8, -9b, 7a, 6b 8 -9, 7, 6 -9b, 6b

d.

w, -x, -y, -z None 1, –1, –1, –1 None

45. Find the value for a for which the expressions 2a and 2 + a have the same value. Show work to

support your answer. 2


Section 3.1 Review Name: Period: For #1-3, simplify each expression.

1. 12 3 7 2 13 2 2.

3. ∙

∙

2169 3 -1 For #4-6, evaluate each expression if c = 6, d = 3, e = 4, and f = 5. Show all work. 4. 4de + 3f 5. 4(de + 3f) 6. 4c3 – 2e 63 108 856 For #7-12, simplify each expression. 7. 11 7 8 9 2

9 10 8. 8 3 5 7 3

3 10 3

9. 1 5

4

10. 5 7 9 8 14

11. 8 3 12 5 4 7 16 1

12. 4 3 7 2 10

For #13-14, write an expression. Simplify, if possible. State your answer in a complete sentence. 13. Chloe bought 14 puzzles. Chloe’s brother

Oliver bought y less puzzles than Chloe. How many puzzles did Oliver buy? 14 Oliver bought 14 puzzles

14. Hazel and her friends went to a Los Angeles Kings game. They bought x hamburgers for $8.75 each and x nachos for $5 each. How much did they spend? 8.75 5 Hazel and her friends spent $13.75


15. Sally bought 4 cupcakes for $3 each and 2 slices of pie for $1 each. Circle all of the expressions that accurately represent this situation.

a) 4 + 4 + 4 + 2

b) 4(3) + 2(1)

c) 3 + 3 + 3 + 3 + 1 + 1 d) (4 + 3)(2 + 1)

For #16-18, identify the terms, constants, coefficients, and like terms in each algebraic expression.

Expression Terms Constants Coefficients Like Terms

16. 5x + 3y + 2x – y + 4

5x, 3y, 2x, -y, 4

4

5, 3, 2, -1

5x, 2x, 3y, -y

17. 8p + 12 - 3p – 6p + 7

8p, 12, -3p, -6p,

7

12, 7

8, -3, -6

8p, -3p, -6p

12, 7 18. x + y – z + 9

x, y, -z, 9

9

1, 1, -1

None

For #19-20, write a simplified expression for each model. Key for Tiles:

= 1

= –1

19. -2x + 2

20. x - 2

– X

– X

– X

X

-1

-1

1

1

1

1

1

X

– X -1 -1

-1

1 1

-1

X -1

1

-1


For #21-24, write an expression for what you see and then write the expression in simplest form. 21. 2 1 7 Model:

Simplified expression: 5 1

22. 3 3 4 Model:


23. 4 3 2 5 2


24. 2 5 2


-1

-1

-1

-1

-1

-1

-1

-1

-1 -1 -1

-1 -1

– X

– X

-1 -1 -1 -1 -1

1 1


3.2A Homework: Iterating Groups* Name: Period: Draw a model that represents each problem. Simplify each expression. 1. 3(x + 1) 3x + 3

2. 2(3x + 2) 6x + 4 3. 4(x + 3) 4x + 12

4. 2(3x – 1) 6x – 2 or 6x + (–2)

5. 3(2x – 3) 6x - 9 6. 5(x – 1) 5x - 5

1 X

1 X

1 X

1

X

1 X

X

1

X

1 X

X

1 X 1 1

1 X 1 1

1 X 1 1

1 X 1 1

-1 X

X

X

-1 X

X

X

-1

X

X -1 -1

-1

X

X -1 -1

-1

X

X -1 -1

-1X

-1X

-1X

-1X

-1X


Simplify each expression. 7. 12(x – y) 12x – 12y 8. r(c – d) rc - rd

9. 8(6 – k) -8k + 48 10. 10(3p + 5) 30p + 50

11. 6(0.3c + 1.2d) 1.8c + 7.2d 12. r(r – 7) 7

13. 0.2(2 + 3e) 0.6e + 0.4 14. 12 4 -x + 3

Spiral Review: In the number squares below, each row, column, and diagonal must have the same sum. Complete each number square and state the common sum. 15.

5 -9

-1

-3 -7

16.

-5 6

4 3

2 0 5

-3 -6

Sum: Answers given in class

Sum: Answers given in class


3.2B Warm Up: Iterating Groups with Rectangles

3.2B Homework: More Simplifying* Name: Period: Simplify the following expressions. Models are optional. Show your work.

1. (51x + 34)

6x + 4

2. – 3(2x + 1) 6x – 3

3. – 3(2x – 1) 6x + 3

4. – (x + 4) x – 4

5. – (x – 4) x + 4

6. – (4 – x) 4 + x or x – 4

7. – 2(4x – 3) 8x + 6

8. – 5.1(3x + 2) 15.3x – 10.2

9. – (4x – 5)

14x +

10. 5x + 1 (x + 3)

6 x +

11. 5x + 2(x – 3) 7x – 6

12. 5x – 2(x + 3) 3x – 6

13. 5x – 2(x – 3) 3x + 6

14. 3x + 2 – 4x + 2(3x + 1) 5x + 4

15. –7x + 3 + 2x – 3(x +2) 8x – 3


16. 10x – 4 – 7x – 4(2x 3) 5x + 8

17. 4x – 5(2x 5) – 3x + 4 9x + 29

18. x – 7 – 2(5x – 3) + 4x 5x – 1


For #19-20, read and answer each question carefully. 19. The price for each notebook is p dollars. The number of notebooks bought by Lucy, Joe, and Kate is

represented by a, b, and c. Which expression represents the total price?

a. b. 3 c. 3 d.

20. There are 3 groups of students that are planting trees. Each student plants 2 trees. The number of

students in each of the 3 groups is represented by i, j, and k. Which expression represents the total number of trees planted?

a. 2 b. 2 3 c. 2 d. 6

Spiral Review: Find the area and perimeter. Use a formula, show the substitution step and remember the units on the final answer. 21. 32 m 45 m 22. 12 in

18 in

23. 7.4 cm 8.2 cm 13.1 cm

Area: 1440 m2 Perimeter: 154 m

Area: 108 in2 Perimeter: 54 in

Area: 96.94 cm2 Perimeter: 42.6 cm


3.2B Extra Practice: Simplified Expressions * Name: Period: Matching: Write the letter of the equivalent expression on the line: 1. B 3 6

2. I 3 6

3. J 3 1

4. A 3 1

5. G 6 3

6. H 6 18

7. E 6 18

8. F 6 1

9. C 3 2

10. D 3 2

A. 3 3

B. 3 18

C. 2 6

D. 2 6

E. 6 1

F. 6

G. 6 18

H. 6 1

I. 3 18

J. 3 3

Practice: Simplify each expression. 11. 7 3

7 21 12. 8 8

8 64 13. 6 6

6 6

14. 3 4 3 12

15. 9.8 5.2 9.8 50.96

16. 4 6 6 24 24

17. 7 7 7

18. 2 6

3

19. 9 4 7 63 36

20.

21. 1 4 4

22. 5

553

23. 2 3 2 6 4

24. – 3 6 3 6

25. 4 1 4 4

26. 1.6 2 2 3.2 3.2

27. 3 5 2 15 6

28. 7 3 2 21 14

29. 3 1 3

30. 14 12 14 168

31. 6 4 4 24


Simplify. 32. 5 10 2 4 3

4 14 33. 5 10 2 4 3

10 6

34. 2 5 2 4 2 2

35. 7 3 5 8 6 10 5 3 11

36. 4 2 5 8 20

37. 6 4 2 12 24

38. 8 6 2 12 16

39. 3 5 3 15 9

40. 6 8

3 4

41. 1 2 2

42. 3 6 3 6

43. 3 5 3 5

44. 7 2 7 2

45. 7 5 7 35

46. 3 4 2 5 8 17

47. 12 6 4 2 12 12

48. 5 8 6 6 3

49. 4 3 5 5 7

50. 2 6 8 10 12 6

51. 5 1 2 6 7 6


3.2C Homework: Properties and Proofs* Name: Period: Complete the table below:

1. Identity Property of Addition: Rule: 0

Show the Identity Property of Addition with 2.17 2.17 + 0 = 2.17 3 0 3

Show the Identity Property of Addition with 3

2. Identity Property of Multiplication: Rule: ∙ 1

23 ∙ 1 23

Show the Identity Property of Multiplication with 23

Show the Identity Property of Multiplication with 3b 3 ∙ 1 = 3

3. Multiplicative Property of Zero:

Rule: ∙ 0 0

43.581 ∙ 0 0

Show Multiplicative Property of Zero with 43.581

4 ∙ 0 0

Show the Multiplicative Property of Zero with 4xy

4. Commutative Property of Addition:

4.38 + 2.01 is the same as: 2.01 + 4.38 x + z is the same as:

5. Commutative Property of Multiplication: ab = ba

∙ is the same as: ∙

6k is the same as: ∙ 6

6. Associative Property of Addition: (a + b) + c = a + (b + c)

(1.8 + 3.2) + 9.5 is the same as: 1.8 + (3.2 + 9.5 ) (x + 1) + 9 is the same as: x + (1 + 9)

7. Associative Property of Multiplication:

(2.6 · 5.4) · 3.7 is the same as: 2.6· (5.4· 3.7)

is the same as:

Use the listed property to fill in the blanks.

8. Multiplicative Inverse Property: 1 5 = 1 ¼ ( 4 ) = 1

9. Additive Inverse Property: a + (–a) = 0

+ = 0 x + –x = 0

10. Substitution Property: 2 + 3 = 5 (3 + 4)y = 7y


Name the property/definition demonstrated in each statement. Use the complete name.

11. 9 ∙ 7 7 ∙ 9 Commutative Property of Multiplication

12. 2 3 2 3 Definition of Subtraction

13. 25 + (–25) = 0 Additive Inverse Property

14. 515

1 Multiplicative Inverse Property

15. (x + 3) + y = x + (3 + y) Associative Property of Addition

16. 1 mp = mp Identity Property of Multiplication

17. (-20 + 7)y = -13y Substitution Property

18. 0 + 6b = 6b Identity Property of Addition

19. 7x 0 = 0 Multiplicative Property of Zero

20. 4(3z)=(43)z Associative Property of Multiplication

21. x + 4 = 4 + x Commutative Property of Addition

22. 3(x + 2) = 3x + 6 Distributive Property

23. Define the operation @ in this way: If A and B are any integers, then A@B = A – B + 1. For

example:9@3 = 9 – 3 + 1 = 7

a. Find 2@4 Answers given in class

b. Find 3@(2@4).

c. Find (3@2)@4.

d. Based on the two questions above, does it appear that the associative property works for the operation @? Explain.

e. Find a number E so that E@(5@E) = 1. Explain how you found your answer.


Using the properties, complete the following algebraic proofs stating the property that is used to move to the next step. 24. -5x + 8 + x = -5x + 8 + 1x _____________________________________________

= -5x + 1x + 8 _____________________________________________

= (-5 + 1)x + 8 _____________________________________________

= -4x + 8 _____________________________________________

25. 7z – 5(3 + z) = 7z – 15 - 5z _____________________________________________ = 7z + (-15) + (-5z) _____________________________________________ = 7z + (-5z) + (-15) _____________________________________________ = [7 + (-5)]z + (-15) _____________________________________________ = 2z + (-15) _____________________________________________ = 2z – 15 _____________________________________________ Spiral Review: Fill in the table:

Simplified Fraction Decimal Percent

26. 45

0.8 80%

27. 8899

0. 88 888899

%

28. 2150

0.42 42%

29. 13

0. 3 3313%

30. 6310

6.3 630%

Identity Property of Multiplication

Commutative Property of Addition

Distributive Property



Substitution Property

Substitution Property

Definition of Subtraction

Commutative Property of Addition

Definition of Subtraction


3.2D Homework: Modeling Backwards Distribution* Name: Period: Write each in reverse (factored) distributed form. Use a model to justify your answer. Label all part of the model.

1. 2x + 4 2(x + 2)

2. 3x + 12 3(x + 4)

3. 2x + 10 2(x + 5)

4. 3x + 18 3(x + 6)

5. x2 + 2x x(x + 2)

6. x2 + 5x x(x + 5)

Simplify each expression. Draw and label a model to justify your answer. 7. 2x + 3x 5x

8. (2x)(3x) 6x2

X

X

X

X

X

SDUHSD Math A Honors Module #3 - TEACHER EDITION 25

1. Looking at #7 and #8, explain how these expressions are the same and how are they different. You may want to reference your models in your explanation.

Simplify the following expressions without a model: 2. 4(x + 7)

4x + 28 3. 7(x – 3)

7x - 21 4. -2(x + 4)

-2x - 8

5. 3x2(x + 2y) 3x3 + 6x2y

6. 3p(p + 3q) 3p2 + 9pq

7. a(a – 12) a2 – 12a

8. 3m(m + 2) 3m2 + 6m

9. x(x + 9) x2 + 9x

10. 12(4k + 13) 48k + 156

Factor (reverse distribute) the following expressions completely. 11. 5x + 35

5(x + 7) 12. a2 + 4a

a(a + 4) 13. 9x – 81

9(x – 9)

14. 4x + 18 2(2x + 9)

15. 42y + 18 6(7y + 3)

16. 6y2 - 9y 3y(2y – 3)

17. 10x + 30 10(x + 3)

18. 12f2 + 18f 6f(2f + 3)

19. 14g3 – 8g 2g(7g2 – 4)

Spiral Review: 20. Which statement(s) is/are false? If false, give a counterexample (an example that proves it doesn’t

work) and explain your example.

a. The opposite of a non-zero whole number is negative.

b. The sum of a number and its additive inverse is one.

c. The product of a number and its multiplicative inverse is one.

d. The sum of a number and zero is the original number.


Section 3.2 Review Name: Period:

1. The neighbors have a triangular yard with a perimeter of 4 3 2. Which of the following could be side lengths of the yard? Circle all that apply.

a. 4y – 2x + 1, 4x – 4, and 2x + 1 b. -4 + 2x – y, 5y + 3x, and –2x + 2 c. 6 – 2x, –y + 7x, and 5y – 2x – 8 d. 3(x + y–1), -(2x–2), and x – y – 1 e. –2(2y – 3x + 1), –3(–2y + x + 2), and 2y + 6

2. Name the property to justify each step. (Yes, spelling counts!) Statement/Steps Algebra Property to justify change from one step to the next:

a. 2x(1)+ 20 + 4x

Multiplicative Identity 2x + 20 + 4x

b. 2x + 20 + 4x

Commutative Property of Addition 2x + 4x + 20

c. 2x + 4x + 20

Associative Property of Addition (2x + 4x)+20

d. (2x + 4x) + 20

Distributive Property 2x(1 + 2) + 20

e. 2x(1 + 2) + 20

Substitution Property 2x(3) + 20

f. 2x(3) + 20

Commutative Property of Multiplication (3)2x + 20

3. Write each expression in reverse distributed (factored) form. Draw a model using tiles to justify your

answer.

a. 5 15 b. 4 c. 20 30 d. 14 28 5 3 4 10 2 3 14 2

4. Which expression(s) below is (are) equivalent to 5 10 :

a. 10 5

b. 2 c. – 2 d. 2 1

e. 10 5

f. 5 10


5. Jason tells you the expression 4 7 can be expanded to 28 4 using the Distributive Property. Is he correct? Explain.

Jason is incorrect. Distributive Property is multiplication over addition or subtraction. The correct Simplification of the expression is -28yz 6. Model each expression and simplify: a. 4 3 3 Model: Simplified expression: 3 7

b. 2 4 2 1 Model: Simplified expression: 2 2 1

c. 3 2 1 Model: Simplified expression: 6 3

7. Write each expression in reverse distributed (factored) form. Draw a model to justify your answer. a. 5 15 Reverse distributed form: 5 3 Model:

b. 4 Reverse distributed form: 4 Model:

For #8-10, write a simplified expression. Verify that your expression is equivalent to the one given by evaluating both expressions using x = 5. 8. 3x + (2 – 4x)

-x + 2 Evaluation: -3 9. -3x + (2 + 4x)

x + 2 Evaluation: 7 10. 3x – (-2 + 4x)

-x + 2 Evaluation: -3 For each proof, identify the property used in each line. Write the complete name. 11.

1 1∙

1 ∙

Associative Property of Multiplication Multiplicative Inverse Property Identity Property of Multiplication

12. 1 ∙ 1 1

1 1

∙ 0

0

Identity Property of Multiplication Distributive Property _____ Additive Inverse Property Multiplicative Property of Zero


Simplify the following expressions. 13. 5 3 6 6

2 14. 5 3 5 8

8 13

15. 4 7 2 5 3 2 5

16. 7 7 5 35 14

17. 3 2 4 4 6 4 7 2 10

18. 17 2 12 12 15 14 14

19. 3 6 5 2 4 3 2 5

20. 10 10 3 20 3

21. 31 5 4 12 13 23 8 8 8

22. 3 2 5 5 10 3 8

23. 3 6

2 4

24. 6 1 2 12 6

25. 0.25 7 0.25 1.75

26. 3 3 3 9

27. 4 1 6 24 4

28. 0.8 0.5 0.7 0.56 0.4

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