Name ____________________________________ Date ________________________Mrs. Labuski / Mrs. Portsmore Period ________ Module 4 Lessons 18-29 Qz Review

Module 4 Lesson 18 Writing and Evaluating Expressions – Addition and SubtractionRead the story problem. Identify the unknown quantity and write an addition or subtraction expression that is described. Then evaluate your expression given the further information.

Story ProblemDescription with Units

ExpressionEvaluate the

Expression if:Show your Work

and Evaluate

Robby has two more basketballs than his brother Michael.

Let e=¿ the number of balls

Michael hase+2

Michael has 7 basketballs.

e+27+2

9Robby has 9 basketballs.

Ella baked 8 more cupcakes than Anna in the sixth grade.

Anna baked 10 cupcakes in the

sixth grade.

Lisa has been surfing for 3 more years than Danika.

Danika has been surfing for 9 years.

Mrs. Labuski went running yesterday. Now she has run 5 more miles than Bob. Write an expression to represent the number of miles Bob ran. Let m = the number of miles Mrs. Labuski ran.

Write an expression to represent the number of miles Mrs. Labuski ran. Let b = the number of miles Bob ran.

If Mrs. Labuski ran 8 miles, how many miles did Bob run?

Module 4 Lesson 19 Substituting to Evaluate Addition and Subtraction Expressions

Sara and Tiffany are in 6th grade and both take drum lessons at School of Rock Music Store. This is Sara’s first year, while this is Tiffany’s fifth year. Both girls plan to continue taking lessons throughout high school.a. Complete the table showing the number of years the girls will have been drumming at the music store.

GradeSara’s Years of Experience

With DrumsTiffany’s Years of Experience

With Drums

Sixth

Seventh

Eighth

Ninth

Tenth

Eleventh

Twelfth

b. If Sara has been taking drum lessons for y years, what expression could represent how many years has Tiffany been taking lessons?

c. If Tiffany has been taking drum lessons for x years, what expression could represent the number of years Sara has been taking lessons?

3. The elementary school Writer’s Club has 15 poets this year. The Writing Club instructor insists that there are to be 5 more essay writers than poets at all times.a. How many essay writers are in the Writer’s Club this year?

b. Write two expressions that describes the relationship of the number of poets ( p) and the number of essay writers (e).

c. If there are only 12 essay writers interested in joining the Writer’s Club next year, how many poets will the Writing Club instructor want in the club?

Module 4 Lesson 20 Writing and Evaluating Expressions – Multiplication and Division

Joe earns $75.00 per day. Create a table of values that shows the relationship between the number of days that Joe worked , d, and the amount of money that he earned, e.

a. If we let d represent the number of days that Joe worked, what is the expression that shows how much money Joe earned.

b. Use your expression to determine how much Joe earned if he worked 12 days.

c. If let e represent how much money Joe earned, what is the expression that shows how many days he worked.

d. Use your expression to determine how many days Joe worked if he earned $600.00.

Module 4 Lesson 21 Writing and Evaluating Expressions – Multiplication and Addition

The PTA is planning a weekend field trip for its graduating seniors. The cost of the bus is $350.00 for the weekend. In addition, each student will have to pay $5 for the price of the trip. Complete the table below to calculate the amount of money the PTA will collect if ten seniors go on the trip.

a. Write an expression that shows the amount of money the PTA collects if s number of students attend the trip.

b. Use your expression to determine the amount of money the PTA would collect if 60 students attend the trip.

Module 4 Lesson 22 Writing and Evaluating Expressions – ExponentsJudah had two children. When those children grew up, each one also had two children, who later each had two children as well. If this pattern continues, how many children are there in the 5th generation?

Generation Number of ChildrenNumber of Children written

as a power of 2

a. Write an expression for how many children would be born after g generations.

b. Use your expression to determine how many children would be born after 10 generations.

Module 4 Lesson 23 True or False Number Sentences

Substitute the value for the variable and state in a complete sentence whether the resulting number sentence is true or false. If true, find a value that would result in a false number sentence. If false, find a value that would result in a true number sentence.

18b ≥ 54. Substitute 3 for b.

28 + c = 35. Substitute 8 for c.

18 ≥ 33 – t. Substitute 15 for t.

Module 4 Lesson 24 True of False Number Sentences.State whether the sentence is true or false.

56 – 14 < 48

33 ≥ 13 + 23

State when the following equations and inequalities will be true and when they will be false.

6r > 36

15 = 6 + d

32 – t < 18

Module 4 Lesson 26 One Step Equations – Addition & Subtraction

Find the solution of the equations using a tape diagram. Check your answer.p + 5 = 11 f – 8 = 10

Find the solution of the equations below algebraically. Check your answer.

k – 29 = 54 46 + m = 100

46 = t – 4 n + 5 = 17

Module 4 Lesson 27 One Step Equations – Multiplication & Division Find the solution of the equations using a tape diagram. Check your answer.

4x = 20m3 = 9

Find the solution of the equation below algebraically. Check your answer.

7x = 35 12y = 60

h5 = 6

k7 = 2

Module 4 Lesson 28 Two-Step Problems – All OperationsFind the solution of the equation below algebraically. Check your answer.

x + 15 − 6 = 18 y + 9 +12 = 40

x + x =12 n + 2n = 9

Barry had 50 doubles last season which is 10 more than his best season. Willy had 8 more doubles than Derek last season. Willy had the same number of as Barry’s best season. Let b represent the number of doubles Barry had during his best season, d represent the number of Derek’s doubles last season, and w represent the number of Willy’s doubles last season. How many doubles did Derek have last season?

Lesson 29 Multi-Step Problems – All Operations

Solve the problem using tables and equations, and then check your answer with the word problem. Try to find the answer only using two rows of numbers on your table.

1. The PE teachers are organizing supplies for this year’s field day. In order to have enough materials for all of the students, they need twice as many hula hoops as Frisbees. The number of flags required is ten times more than the number of hula hoops. The number of cones that is needed is half as many flags. If they have a total of 315 supplies, how many cones do they have?ANSWER:

Flags Cones Frisbees Hula hoops total

Name ____________________________________ Date ________________________Mrs. Labuski / Mrs. Portsmore Period ________ Module 4 Lessons 18-29 Qz Review

Module 4 Lesson 18 Writing and Evaluating Expressions – Addition and SubtractionRead the story problem. Identify the unknown quantity and write an addition or subtraction expression that is described. Then evaluate your expression given the further information.

Story ProblemDescription with Units

ExpressionEvaluate the

Expression if:Show your Work

and Evaluate

Robby has two more basketballs than his brother Michael.

Let e=¿ the number of balls

Michael hase+2

Michael has 7 basketballs.

e+27+2

9Robby has 9 basketballs.

Ella baked 8 more cupcakes than Anna in the sixth grade.

Let c = the number of

cupcakes Anna has

a + 8

Anna baked 10 cupcakes in

the sixth grade.

a + 810 + 8

18Ella bakes 18

cupcakes

Lisa has been surfing for 3 more years than Danika.

Let d = number of years Danika

has been surfing

d + 3Danika has been surfing for 9 years.

d + 39 + 3

11Lisa has been surfing for 11

years.

Mrs. Labuski went running yesterday. Now she has run 5 more miles than Bob. Write an expression to represent the number of miles Bob ran. Let m = the number of miles Mrs. Labuski ran.

m - 5

Write an expression to represent the number of miles Mrs. Labuski ran. Let b = the number of miles Bob ran.

b + 5

If Mrs. Labuski ran 8 miles, how many miles did Bob run?m – 58-53

Bob ran 3 miles

Module 4 Lesson 19 Substituting to Evaluate Addition and Subtraction ExpressionsSara and Tiffany are in 6th grade and both take drum lessons at School of Rock Music Store.

This is Sara’s first year, while this is Tiffany’s fifth year. Both girls plan to continue taking lessons throughout high school.d. Complete the table showing the number of years the girls will have been drumming at the music store.

GradeSara’s Years of Experience

With DrumsTiffany’s Years of Experience

With Drums

Sixth 1 5Seventh 2 6Eighth 3 7Ninth 4 8Tenth 5 9

Eleventh 6 10Twelfth 7 11

e. If Sara has been taking drum lessons for y years, what expression could represent how many years has Tiffany been taking lessons?

y + 5

f. If Tiffany has been taking drum lessons for x years, what expression could represent the number of years Sara has been taking lessons?

x - 5

3. The elementary school Writer’s Club has 15 poets this year. The Writing Club instructor insists that there are to be 5 more essay writers than poets at all times.a. How many essay writers are in the Writer’s Club this year?

15 = 5 = 20b. Write two expressions that describes the relationship of the number of poets ( p) and the number of essay writers (e).

e + 5 = p p – 5 = e

c. If there are only 12 essay writers interested in joining the Writer’s Club next year, how many poets will the Writing Club instructor want in the club?

e + 5 = p12 + 5 = p

17 = pThe instructor will want 17 poets.

Module 4 Lesson 20 Writing and Evaluating Expressions – Multiplication and Division

Joe earns $75.00 per day. Create a table of values that shows the relationship between the number of days that Joe worked , d, and the amount of money that he earned, e.

Number of Days Joe Worked, d Amount Earned, e, in Dollars

1 75

2 150

3 225

4 300

a. If we let d represent the number of days that Joe worked, what is the expression that shows how much money Joe earned.

75d

b. Use your expression to determine how much Joe earned if he worked 12 days.75d

75 12900

Joe will earn $900 if he works 12 days.

c. If let e represent how much money Joe earned, what is the expression that shows how many days he worked.

e ÷ 75

d. Use your expression to determine how many days Joe worked if he earned $600.00.

e ÷ 75600 ÷ 75

8Joe worked 8 days.

Module 4 Lesson 21 Writing and Evaluating Expressions – Multiplication and Addition

The PTA is planning a weekend field trip for its graduating seniors. The cost of the bus is $350.00 for the weekend. In addition, each student will have to pay $5 for the price of the trip. Complete the table below to calculate the amount of money the PTA will collect if ten seniors go on the trip.

Number of Students on the Trip (s)

Total Cost in Dollars (d)

1 3552 3603 3654 3705 3756 3807 3858 3909 39510 400

a. Write an expression that shows the amount of money the PTA collects if s number of students attend the trip.

350 + 5s

b. Use your expression to determine the amount of money the PTA would collect if 60 students attend the trip.

350 + 5s

Module 4 Lesson 22 Writing and Evaluating Expressions – Exponents

Judah had two children. When those children grew up, each one also had two children, who later each had two children as well. If this pattern continues, how many children are there in the 5th generation?

Generation Number of ChildrenNumber of Children

written as a power of 21 2 21

2 4 22

3 8 23

4 16 24

5 32 25

a. Write an expression for how many children would be born after g generations.

2g

b. Use your expression to determine how many children would be born after 10 generations.

2g

210

1024

Module 4 Lesson 23 True or False Number SentencesSubstitute the value for the variable and state in a complete sentence whether the resulting number sentence is true or false. If true, find a value that would result in a false number sentence. If false, find a value that would result in a true number sentence.

18b ≥ 54. Substitute 3 for b. True. Any value less than 3 will result in a false statement

28 + c = 35. Substitute 8 for c.False. The number 7 is the only value that will result in a true number sentence.

18 ≥ 33 – t. Substitute 15 for t.True. Any value 18 or greater will result in a true sentence.

Module 4 Lesson 24 True of False Number Sentences.State whether the sentence is true or false. 56 – 14 < 48

True

33 ≥ 13 + 23 False

State when the following equations and inequalities will be true and when they will be false.

6r > 36This inequality is true for any value that is greater than 6 and false then the value is less than or equal to 6.15 = 6 + dThis equation is true when the value of d is 9 and false when the value is any other number.32 – t < 18 This inequality is true for any value that is less than 14 and false then the value is greather than or equal to 14.

Module 4 Lesson 26 One Step Equations – Addition & Subtraction Find the solution of the equations using a tape diagram. Check your answer.p + 5 = 11 f – 8 = 10

p = 6

p + 5 = 11 f – 8 = 106 + 5 = 11 18 – 8 = 1011 + 11 10 = 10

Find the solution of the equations below algebraically. Check your answer.

f = 18

k – 29 = 54 46 + m = 100k – 29 + 29 = 54 + 29 46 + m – 46 = 100 – 46 k = 83 m = 54check checkk – 29 = 54 46 + m = 10083 – 29 = 54 46 + 54 = 10054 = 54 100 = 100

46 = t – 4 n + 5 = 1746 + 4 = t – 4 + 4 n + 5 – 5 = 17 – 5 50 = t n = 12check check46 = t – 4 n + 5 = 1746 = 50 – 4 12 + 5 = 1746 = 46 17 = 17

Module 4 Lesson 27 One Step Equations – Multiplication & Division Find the solution of the equations using a tape diagram. Check your answer.

4x = 20m3 = 9

x = 5

check check

4x = 20m3 = 9

4(5) = 20 27 ÷ 3 = 920 = 20 9 = 9

Find the solution of the equation below algebraically. Check your answer.7x = 35 12y = 607x ÷ 7 = 35÷ 7 12y ÷ 12 = 60 ÷ 12x = 5 y = 5

check check7x = 35 12y = 607(5) = 35 12(5) = 6035 = 35 60 = 60

h5 = 6

k7 = 2

h ÷55 = 65 k÷ 77 = 27h = 30 k = 14check checkh ÷5 = 6 k÷ 7 = 230 ÷5 = 6 14÷ 7 = 26 = 6 2 = 2

Module 4 Lesson 28 Two-Step Problems – All OperationsFind the solution of the equation below algebraically. Check your answer.

x + 15 − 6 = 18 y + 9 +12 = 40x + 9 = 18 y + 21 = 40x + 9 - 9= 18 - 9 y + 21 – 21 = 40 - 21x = 9 y = 19check checkx + 15 − 6 = 18 y + 9 +12 = 409 + 15 − 6 = 18 19 + 9 +12 = 4018 = 18 40 = 40

x + x =12 n + 2n = 92x = 12 3n = 92x ÷ 2 = 12÷ 2 3n ÷ 3 = 9 ÷ 3x = 6 n = 3check checkx + x =12 n + 2n = 96 + 6 =12 3 + 2(3) = 912 = 12 3 + 6 = 9

9 = 9

Barry had 50 doubles last season which is 10 more than his best season. Willy had 8 more doubles than Derek last season. Willy had the same number of as Barry’s best season. Let b represent the number of doubles Barry had during his best season, d represent the number of Derek’s doubles last season, and w represent the number of Willy’s doubles last season . How many doubles did Derek have last season?Solution:Barry

50

b 10

Willy b

d 8

Derekd

Let’s Start with Barryb + 10 = 50 b + 10 – 10 = 50 – 10b = 40

Now we can solve Willy’s tape diagramb = d + 840 = d + 840 – 8 = d + 8 – 832 = d

Derek had 32 doubles

Lesson 29 Multi-Step Problems – All OperationsSolve the problem using tables and equations, and then check your answer with the word problem. Try to find the answer only using two rows of numbers on your table.

1. The PE teachers are organizing supplies for this year’s field day. In order to have enough materials for all of the students, they need twice as many hula hoops as Frisbees. The number of flags required is ten times more than the number of hula hoops. The number of cones that is needed is half as many flags. If they have a total of 315 supplies, how many cones do they have?ANSWER:

Flags Cones Frisbees Hula hoops total

20 10 1 2 33240 120 12 24 396

They will have a total of 120 cones.

Let f represent the number of Frisbees. Therefore, 2f represents the number of hula hoops, and 20frepresents the number of flags and 10f represents the number of cones.

f + 2f + 10f + 20 f = 39633f = 396

33f ÷ 33 = 396 ÷ 33f = 12

Therefore, the PE teachers have 120 cones because 10(12)=120