Unit 1, Activity 1, Where Do I Belong?

Unit 1, Activity 1, Where Do I Belong?

Directions: Place an “X” in the appropriate box to indicate what set each of the numbers in the first column belong. Be ready to explain your reasoning to the rest of the class.

Number / Natural / Whole / Integer / Rational / Irrational
-2
2
3.14

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Unit 1, Activity 1, Where Do I Belong? with Answers

Directions: Place an “X” in the appropriate box to indicate what set each of the numbers in the first column belong. Be ready to explain your reasoning to the rest of the class.

Number / Natural / Whole / Integer / Rational / Irrational
X
X / X / X / X
X
-2 / X / X
X
2 / X / X / X / X
X / X / X / X
X
X
3.14 / X
X / X / X / X
X
X / X

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Unit 1, Activity 5, What Method Should I Use?

Directions: For each problem shown, decide whether it is most appropriate to solve it using ESTIMATION (not exact); MENTAL MATH (exact); Paper/Pencil (exact); or using TECHNOLOGY (exact) to obtain the solution. In the second column, write a math log (a short essay explaining your reasoning behind your choice) and be prepared to share your thoughts on each of the problems with your classmates.

Problem Math Log: Explain the method you

chose to use and why you chose it.

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Unit 1, Activity 10, Patterns in the Real World

Directions: In groups of three, read each problem carefully and answer the questions presented. Work together! Keep in mind the difficulties you have as you attempt the problems and how you overcame them to produce your solutions as you will be writing about this at the end of this activity.

1. A man is offered a $10,000 starting salary, with an annual raise of $800.

a. List his annual salaries for the first five years. Start with $10,000.

Year / 1 / 2 / 3 / 4 / 5
Salary

b. Determine his salary in year 20.

c. Write an expression showing his salary in year n.

2. A water lily has an area of 8 square inches. These lilies reproduce so fast that the area they cover will double every week.

a. If two lilies are introduced into a pond, list the total area covered at the end of each of the first five weeks.

Week / 1 / 2 / 3 / 4 / 5
Area

b. Determine the area covered by the 20th week.

c. Write an expression showing the area covered in the nth week.

3. Suppose you save the given amounts of money over a five-week period.

Week 1st 2nd 3rd 4th 5th

Money 28¢ 45¢ 62¢ 79¢ 96¢

a. Find the amount you would save in the 52nd week.

b. Write an expression showing the amount you would save in the nth week.

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Unit 1, Activity 10, Patterns in the Real World with Answers

1. A man is offered a $10,000 starting salary, with an annual raise of $800.

a. List his annual salaries for the first five years. Start with $10,000.

Year / 1 / 2 / 3 / 4 / 5
Salary / $10,000 / $10,800 / $11,600 / $12,400 / $13,200

b. Determine his salary in year 20. $25,200

c. Write an expression showing his salary in year n.

S = 800(n – 1) + 10,000 where S is salary, in dollars, and n is number of years.

2. A water lily has an area of 8 square inches. These lilies reproduce so fast that the area they cover will double every week.

a. If two lilies are introduced into a pond, list the total area covered at the end of each of the first five weeks.

Week / 1 / 2 / 3 / 4 / 5
Area / 16 sq. in. / 32 sq. in. / 64. sq. in. / 128 sq. in. / 256 sq. in.

b. Determine the area covered by the 20th week. 8,388,608 sq. in.

c. Write an expression showing the area covered in the nth week.

A = 8* 2, where A is the area, in square inches, and n is the number of weeks.

3. Suppose you save the given amounts of money over a five-week period.

Week 1st 2nd 3rd 4th 5th

Money 28¢ 45¢ 62¢ 79¢ 96¢

a. Find the amount you would save in the 52nd week. $8.95

b. Write an expression showing the amount you would save in the nth week.

A = 28 + 17 (n – 1), where A is the amount saved, in cents, and n is the number of weeks.

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Unit 1, Activity 12, Tables to Graphs

Directions: The table below shows the cost associated with renting a truck for a single day from Move-4-Less Truck Rental based upon the number of miles the truck is driven. Use this table to answer the questions that follow.

Move-4-Less Truck Rental Prices

# of Miles / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Cost to Rent / $45.50 / $46.00 / $47.00 / $48.50

1. Fill in the table of values based upon the pattern you see in the data.

2. Based upon the pattern in the table, how much would it cost to rent the truck for a single day even if you didn’t have any mileage associated with the rental?

3. Explain in words what the pattern is in the table and what the cost associated with renting a truck from Move-4-Less entails.

4. Based upon your explanation in question 3, write an equation relating the cost, C, in dollars of renting a truck for a single day if you were to drive m miles.

5. Look at the numberless graphs shown below. Based upon the data in the table, which graph do you think best matches the situation presented here? Explain in words why you think the graph you have chosen best matches, and explain why each of the others are not a match to the data shown.

(a) (b) (c)

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Unit 1, Activity 12, Tables to Graphs with Answers

Move-4-Less Truck Rental Prices

# of Miles / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Cost to Rent / $45.00 / $45.50 / $46.00 / $46.50 / $47.00 / $47.50 / $48.00 / $48.50 / $49.00

1. Fill in the table of values based upon the pattern you see in the data.

2. Based upon the pattern in the table, how much would it cost to rent the truck for a single day even if you didn’t have any mileage associated with the rental?

It would cost $45.00.

3. Explain in words what the pattern is in the table and what the cost associated with renting a truck from Move-4-Less entails.

The initial cost of renting the truck is $45.00 and with each mile you travel it adds $0.50 more to the cost of the truck rental. The pattern in the table reflects this amount added as each mile is traveled.

4. Based upon your explanation in question 3, write an equation relating the cost, C, in dollars of renting a truck for a single day if you were to drive m miles.

C = 45 + .5m

(a) (b) (c)

The correct graph is (b) since it reflects an initial cost not equal to $0 and an increase in cost as the miles increase.

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Unit 2, Activity 3, How Many Significant Digits Are There?

Directions: In this activity, work with a partner and discuss the answers to the following questions presented. Write your answers in the space provided. Be ready to justify your answers in a whole-class discussion.

Examples of Significant Digits

Example / Number of Significant Digits / Justification for Answer
1278.50 m
8.002 g
43.050 m
5.420 x 10
6271.91
543, 091
453 kg
5057 L
5.00 kg
0.007 L

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Unit 2, Activity 3, How Many Significant Digits Are There? with Answers

Examples of Significant Digits

Example / Number of Significant Digits / Justification for Answer
1278.50 m / 6 / Additional zeros to the right of decimal and a sig. dig. are significant.
8.002 g / 4 / Zeros between 2 sig. dig. are significant.
43.050 m / 5 / Additional zeros to the right of decimal and a sig. dig. are significant.
Zeros between 2 sig. dig. are significant.
5.420 x 10 / 4 / Additional zeros to the right of decimal and a sig. dig. are significant.
6271.91 / 6 / All non-zero digits are always significant.
543, 091 / 6 / Zeros between 2 sig. dig. are significant.
453 kg / 3 / All non-zero digits are always significant.
5057 L / 4 / Zeros between 2 sig. dig. are significant.
5.00 kg / 3 / Additional zeros to the right of decimal and a sig. dig. are significant.
0.007 L / 1 / Placeholders are not sig.

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Unit 2, Activity 6, Multiplication and Division Using Significant Digits

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Unit 2, Activity 6, Multiplication and Division Using Significant Digits

Directions: Part I—Read the following informational text to help you answer the questions that follow regarding multiplying and dividing numbers utilizing significant digits.

Informational Text: Suppose you used a calculator and determined that “25 feet divided by 6.0 equals 4.166666667 feet,” which is what your calculator will tell you. Since the measurement of 25 feet is measured to the nearest foot, you should wonder, “Can you get an answer that is accurate to a billionth of a foot?” The answer, of course, is no. Therefore, when dealing with measurement problems that involve multiplication and division operations, it is important to understand some “rules” for expressing answers to problems with the correct number of significant digits.

The rule for multiplying and dividing is this:

RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided quantity having the least number of significant digits.

Example 1: When dividing 25 by 6.0 in a measurement problem, since each number has two significant digits, the answer will have two significant digits. So even though the answer using a calculator would result in 25÷6.0=4.166666667, the proper way to express this answer would be to round off to two significant digits. Therefore the answer will be 25÷6.0=4.2.

Example 2: Suppose the length of a walkway was 81.7 meters and its width was measured to be 2.405 meters, what would its area be if you are using the correct number of significant digits in your calculation? In order to find the area, you would need to multiply 81.7m ×2.405 m. Your calculator says 196.4885. But since the number 81.7 has three significant digits and the number 2.405 has four significant digits, the rule says that the final answer should have the smaller of the number of significant digits, which in this case is 3 significant digits. Therefore, the answer must be rounded to 196 square meters (in order to have three significant digits).

Additional examples are shown below:

Multiplication / The answer must be rounded off to 2 significant figures, since 1.6 only has 2 significant figures.
Division / The answer must be rounded off to 3 significant figures, since 45.2 has only 3 significant figures.
Important: Any rounding takes place at the end of the calculation process.

Directions: Part II—After reading the informational text, work with a partner on the questions below and be ready to discuss your answers with the rest of the class. You must use the informational text to justify your answers.

1. In your own words, explain the rule for multiplying and dividing two quantities when using significant digits.

2. A wall is 9.42 meters long and 2.3 meters tall. Calculate the area of the wall with the correct number of significant digits.

3. Janice rode 8 miles in 50 minutes. What is her average speed in miles per minute, taking into account significant digits?

4. Using your calculator, find 34.78×11.7÷0.17, then express the result with the correct number of significant digits.

5. What is the product of 45 x 3.00 if you use significant digits in our answer?

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Unit 2, Activity 6, Multiplication and Division Using Significant Digits with Answers

1. In your own words, explain the rule for multiplying and dividing two quantities when using significant digits.