Variables and Patterns Investigation 4 Homework Packet DUE: Thursday, May 11

Name: ____________________________________________ Hour: ___________________

Variables and Patterns Investigation 4.1 Homework-Equivalent Expressions I ANSWER KEY

RECOMMENDED DATE TO COMPLETE: Friday, April 28

1a.

1b. t=2×n+2 or t=n+n+2

2a.

2b. t=2×n+2 or t=n+n+2

2c. Lloyd’s pattern and Ahna’s pattern use the same number of toothpicks. You could imagine moving the top toothpick in Lloyd’s pattern down to the bottom and making the U shape in Ahna’s pattern.

3.

Equation: B=7× A

Variables and Patterns Investigation 4.2 Homework-Equivalent Expressions II ANSWER KEY

RECOMMENDED DATE TO COMPLETE: Monday, May 1

1. Equivalent 2. Not Equivalent 3. Not Equivalent

4. Possible answers: 5n=n+4 n or 5n=n+n+3n or 5n=n+n+n+2n or 5n=n+n+n+n+n

5. Possible answers: 2n+2=n+n+2 or 2n+2=n+n+1+1 or 2n+2=2n+1+1 or 2n+2=2(n+1)

Variables and Patterns Investigation 4.3 Homework-Equivalent Expressions III Day 1 ANSWER KEY

RECOMMENDED DATE TO COMPLETE: Tuesday, May 2

1. 4(3 + 9) = 4(3) + 4(9) 2. 5(n + 7) = 5n + 5(7) 3a. 10(13 + 7) = 10(20) = 10(13) + 10(7)

3b. (7.5 + 2.5)20 = 10(20) = 7.5(20) + 2.5(20) 3c. The expressions both have factors of 10 and 20

4a. 250n; 30n; 350; (50 + 10n) 4b. 350; 30; 350; 10

Shape Number 4 5 6 7 8 10 20

Number of Toothpicks 10 12 14 16 18 22 42

Shape Number 4 5 6 7 8 10 20

Number of Toothpicks 10 12 14 16 18 22 42

a 0 1 2 3 4 8 20 100

b 0 7 14 21 28 56 140 700

Variables and Patterns Investigation 4.3 Homework-Equivalent Expressions III Day 2 ANSWER KEY

RECOMMENDED DATE TO COMPLETE: Wednesday, May 3

1a. B=100+25n 1b. L=49n 1c. H=125n 1d. V=95

2a. C=(100+25n)+49n+125n+95 2b. C=199n+195

Variables and Patterns Investigation 4.4 Homework-Solving Equations ANSWER KEY

RECOMMENDED DATE TO COMPLETE: Thursday, May 4

1a.

1b. Superior Bus: C=2.95m Coast Transport: C=40+2n

1c. After 42 miles, it makes more sense to take Coast Transport

1d. 200 miles 1e. 230 miles

Miles 10 20 30 40 50 60 70 80 90 100

Superior Bus

29.50 59.00 88.50 118.00 147.50 177.00 206.50 236.00 265.50 295

Coast Transport

60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00 220.00 240.00

Variables and Patterns Investigation 4.5 Homework-Solving Inequalities ANSWER KEY

RECOMMENDED DATE TO COMPLETE: Friday, May 5

1. Inequality: 45 L>675; L>15 Three Specific Solutions: any number greater than 15

2. Inequality: N4

>8; N¿32 Three Specific Solutions: any number greater than 32

3. Inequality: 150−M<50; M<100 Three Specific Solutions: any number less than 100

4. Inequality: 14H>84; H>6 Three Specific Solutions: any number greater than 6

12 13 14 15 16 17 18

29 30 31 32 33 34 35

97 98 99 100 101 102 103

3 4 5 6 7 8 9

Variables and Patterns Investigation 4.1 Homework-Equivalent Expressions I

For #1-2, use the toothpick patterns created by Ahna and Lloyd to answer the questions.

1. Ahna’s Pattern

1a. What numbers go in the second row of the table comparing the shape number to the number of toothpicks?

Shape Number 4 5 6 7 8 10 20

Number of Toothpicks

1b. What euqation shows how to find the number of toothpicks t, needed for shape number n?

2. Lloyd’s Pattern

2a. What numbers go in the second row of the table comparing the shape number to the number of toothpicks?

Shape Number 4 5 6 7 8 10 20

Number of Toothpicks

2b. What euqation shows how to find the number of toothpicks t, needed for shape number n?

2c. How is the relationship between Lloyd and Ahna’s Patterns similar or different?

3. Use the pattern in the table to find the missing enteries. Then write an equation relating the two variables.

A 0 1 2 3 8 20 100

B 0 7 14 21 28

Equation: ______________________

Variables and Patterns Investigation 4.2 Homework-Equivalent Expressions II

SHOW ALL WORK!!!

1. Determine if the expressions below are equivalent by testing them for when n = 1, 2, 3, 10.

4 n+12 4 (n+3)

These two expressions are (circle one) Equivalent Not Equivalent

2. Determine if the expressions below are equivalent by testing them for when m = 1, 2, 3, 10.

m+m+3m (3m+2)

These two expressions are (circle one) Equivalent Not Equivalent

3. Determine if the expressions below are equivalent by testing them for when p = 1, 2, 3, 10.

p+ p p+7

These two expressions are (circle one) Equivalent Not Equivalent

4. Use what you know about equivalent expressions to write TWO equivalent expressions to 5n

5. Use what you know about equivalent expressions to write TWO equivalent expressions to 2n+2

Variables and Patterns Investigation 4.3 Homework-Equivalent Expressions III Day 1

For #1-2, the diagrams show rectangles divided into two smaller rectangles. Use the DISTRIBUTIVE PROPERTY to write two equivalent expressions for the area of the larger rectangle.

1.

2.

3. Use the DISTRIBUTIVE PROPERTY to write two equivalent expressions for the area of each figure below.

4. You are given the expression 250n−30n+350n−(50+10n)

a. What are the terms in the expression?

b. What numbers are coefficients in the expression?

Variables and Patterns Investigation 4.3 Homework-Equivalent Expressions III Day 2

The Ocean Bike Tours partners decided to offer a two day trip from Philadelphia to Atlantic City and back. They did some research and found these costs for the trip.

1. Write equations that show how these variables depend on the number n of customers that go on the tour.

a. bike rental B b. lunch and snacks L

Equation: _________________________ Equation: ___________________________

c. hotel rooms H d. rental of the tour support van V

Equation: _________________________ Equation: ___________________________

2a. Write a rule that shows how the total operating cost C (remember, total operating cost is the cost of everything together) depends on the number of riders n. The rule should show how each cost variable adds to the total.

2b. Write another rule for the total operating cost C (remember, total operating cost is the cost of everything together). This rule should be as simple as possible for calculating the total cost.

2c. Explain how your two expressions are equivalent.

Variables and Patterns Investigation 4.4 Homework-Solving Equations

1. A baseball team wants to rent a small bus for travel to their tournaments for the summer. They have two bus options available to them.

• Superior Bus charges $2.95 per mile driven

• Coast Transport charges $40 plus $2 per mile

a. Complete the chart below showing the cost for each company for the given number of miles.

Miles 10 20 30 40 50 60 70 80 90 100

Superior Bus

Coast Transport

b. Write an equation relating the cost c depends on the number of miles driven m.

Superior Bus:

Coast Transport:

c. After how many miles will it make sense for the team to go with Coast Transport than Superior Bus?

d. The team decided to go with Superior Bus to get to their Spring Tournament. Their bill was $590. How many miles did the team travel? Show all work!!!

e. The team decided to go with Coast Transport for a different tournament. Their bill was $500. How many miles did the team travel? Show all work!!!

Variables and Patterns Investigation 4.5 Homework-Solving Inequalities

For #1-4 below complete the following:

Write an inequality that helps answer the question. Give at least 3 specific number solutions to the inequality Graph the solution on a number line

1. A lawn service charges $45 to mow a lawn. How many lawns are will they need to mow L to make more than $675 in a day?

Inequality: ____________________ Three specific solutions: _______________________________

2. Victor has 4 bowls. How many oranges N does he need to have more than 8 oranges in each bowl?

Inequality: ____________________ Three specific solutions: _______________________________

3. Theresa has $150. How much money M will she need to spend to have more than $50 left?

Inequality: ____________________ Three specific solutions: _______________________________

4. Angie charges $14 per hour to babysit. How many hours H will she need to babysit to make more than $84?

Inequality: ____________________ Three specific solutions: _______________________________