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Remediation Math

2010

Various Units and Activities, LEAP Reference Sheet

Blackline Masters, Ninth Grade, Remediation Math Page 1

Unit 1, Activity 1, Vocabulary Self-Awareness Chart

Vocabulary Self-Awareness

As we begin this unit, rate your understanding of each word with either a “+” (understand well), a “√” (limited understanding or unsure), or a “—“(don’t know). Over the course of this unit, return to this chart and revise any √ or – marks to + marks as you learn new information. In addition, add new words as necessary. The goal is to replace all the check marks and minus signs with a plus sign. When a + mark is made for a word, provide an example and a definition in your own words. The completed chart is due when we complete the unit.

Word + or √ or - Example Definition

Rational number

Whole number

Exponent

Percent

Fraction

Decimal

Rounding

Mixed number

Integer


Unit 1, Activity 1, Fractions, Decimals, Percents

Name ________ Date_________________

Fill in the missing information in the table below.

Fraction Decimal Percent

0.75

25%

1.5

175%

0.60

40%

1


Unit 1, Activity 1, Fractions, Decimals, Percents with Answers

Name ________ Date_________________

Fill in the missing information in the table below.

Fraction Decimal Percent

0.5 50%

0.75 75%

0.25 25%

11.5 150%

0.875 87.5%

%

11.75 175%

0.60 60%

0.40 40%

1 1.625 162.5%


Unit 1, Activity 1, Comparing Rational Numbers

Name ________ Date_________________

Fill in each blank with < , > , or = to make each sentence true. Write the decimal notation beneath each fraction to check your answer.

Example: 1 1 2 > 3

0.5 > 0.333

1. 2 5 2. 3 5 3. 3 9 3 8 4 7 14 10

4. 3 7 5. 14 30 6. - 3 ___ - 12 5 8 5 13

7. 5 ___ - 25 8. 35.897 ____ 35.9 9. ____ 0.25

Write the fractions in order from least to greatest. Write the decimal notation beneath each fraction

10. 3 1 7 11. 1 1 1 12. 3 1 7 8 4 8 3 5 7 5 9 9


Unit 1, Activity 1, Comparing Rational Numbers with Answers

Name ________ Date_________________Fill in each blank with < , > , or = to make each sentence true. Write the decimal notation beneath each fraction to check your answer.

Example: 1 1 2 > 3

0.5 > 0.333

1. 2 5 2. 3 5 3. 3 9 3 > 8 4 > 7 14 < 10

4. 3 7 5. 14 30 6. - 3 > - 12 5 < 8 5 > 13

7. 5 > - 25 8. 35.897 < 35.9 9. = 0.25

Write the fractions in order from least to greatest. Write the decimal notation beneath each fraction

10. 3 1 7 11. 1 1 1 12. 3 1 7 8 4 8 3 5 7 5 9 9

, , , , , ,

0.25, 0.375, 0.875 0.14, 0.2, 0.33 0.11, 0.6, 0.78


Unit 1, Activity 2, Order Matters!

Name ________ Date_________________

Use the order of operations rules to evaluate the following expressions. Show all work on a separate sheet of paper.

1. 4 + 2 × 3

2. 7 + 9 × 2 – 3

3. (32 + 3 + 2) ÷ 7

4. 2 + 52 ÷ (15 – 20)

5. 23 × 10 - 21 – 15

6. 72 – (4 + 3) × 6 ÷ 7

7. (6 ÷ 2) + 9 - 1 + 8

8. 9 + 5 × (32 – 2) + 4

9. 12 × 24 × (10 ÷ 2 + 20) – 9

10. 49 ÷ 7 – 3 × 3


Unit 1, Activity 2, Order Matters! with Answers

Name ________ Date_________________

Use the order of operations rules to evaluate the following expressions. Show all work on a separate sheet of paper.

1. 4 + 2 × 3 = 10

2. 7 + 9 × 2 – 3 = 22

3. (32 + 3 + 2) ÷ 7 = 2

4. 2 + 52 ÷ (15 – 20) = - 3

5. 23 × 10 - 21 – 15 = 194

6. 72 – (4 + 3) × 6 ÷ 7 = 1

7. (6 ÷ 2) + 9 - 1 + 8 = 19

8. 9 + 5 × (32 – 2) + 4 = 48

9. 12 × 24 × (10 ÷ 2 + 20) – 9 = 7191

10. 49 ÷ 7 – 3 × 3 = - 2


Unit 1, Activity 3, Who’s Right and Who’s Wrong

Name ________ Date_________________

Mary, David and Larry individually worked the following problems. See their answers in the table below. Who has the correct answer? Show your work for each problem and explain what mistakes were made to generate the incorrect answers by the other two students.

ProblemMary’s answer

David’s answer

Larry’s answer

Correct answer

1. 9 × 3 + 6 ÷ 2 16.5 30 40.5Mistakes made:

2. 10 ÷ 2 × 5 – 3 + 5 3 - 7 27Mistakes made:

3. 2 + 10 ÷ 2 × 4 24 28 22Mistakes made:

4. (15 – 11)3 + 8 ÷ 2 68 36 16Mistakes made:

5. 2 + 4 × 7 – 6 ÷ 3 + 2 14 30 10Mistakes made:


Unit 1, Activity 3, Who’s Right and Who’s Wrong with Answers

Name ________ Date_________________

Mary, David and Larry individually worked the following problems. See their answers in the table below. Who has the correct answer? Show your work for each problem and explain what mistakes were made to generate the incorrect answers by the other two students.

ProblemMary’s answer

David’s answer

Larry’s answer

Correct answer

1. 9 × 3 + 6 ÷ 2 16.5 30 40.5 30Mistakes made:

Examples: addition before division; addition before multiplication and division

2. 10 ÷ 2 × 5 – 3 + 5 3 15 27 27Mistakes made:

Examples: multiplication before division; subtraction before division and multiplication

3. 2 + 10 ÷ 2 × 4 24 28 22 22Mistakes made:

Examples: addition before division; addition before multiplication

4. (15 – 11)3 + 8 ÷ 2 68 36 16 68Mistakes made:

Examples: addition before division; added four three times instead of multiplied

5. 2 + 4 × 7 – 6 ÷ 3 + 2 14 30 4 30Mistakes made:

Examples: addition before multiplication and division; subtraction before multiplication, addition before division


Unit 1, Activity 4, Scientific Notation and Rounding

Name ________ Date_________________

Convert the following numbers to scientific notation.

1. 5,300 ____________________

2. 10,543 ____________________

3. 40,000,000 ____________________

4. 2,345,000,000,000 ____________________

5. 987,000,000,000,000 ____________________

Convert the following numbers to standard notation.

1. 2.3 × 103 ____________________

2. 7.539 × 105 ____________________

3. 9.5 × 108 ____________________

4. 1.0098 × 1010 ____________________

5. 6 × 1012 ____________________

Round the numbers below to the nearest indicated place value.

3,932,639

To the nearest ten ___________To the nearest hundred ___________To the nearest thousand ___________To the nearest ten thousand ___________To the nearest hundred thousand ___________To the nearest million ___________

679.3698

To the nearest tenth ___________To the nearest hundredth ___________To the nearest thousandth ___________


Unit 1, Activity 4, Scientific Notation and Rounding with Answers

Name ________ Date_________________

Convert the following numbers to scientific notation.

1. 5,300 5.3 × 10 3

2. 10,543 1.0543 × 10 4

3. 40,000,000 4 × 10 7

4. 2,345,000,000,000 2.345 × 10 12

5. 987,000,000,000,000 9.87 × 10 14

Convert the following numbers to standard notation.

1. 2.3 × 103 2300

2. 7.539 × 105 753,900

3. 9.5 × 108 950,000,000

4. 1.0098 × 1010 10,098,000,000

5. 6 × 1012 6,000,000,000,000

Round the numbers below to the nearest indicated place value.

3,932,639

To the nearest ten 3,932,640To the nearest hundred 3,932,600To the nearest thousand 3,933,000To the nearest ten thousand 3,930,000To the nearest hundred thousand 3,900,000To the nearest million 4,000,000

679.3698

To the nearest tenth 679.4To the nearest hundredth 679.37To the nearest thousandth 679.370


Unit 1, Activity 4, Research Summary

Name ________ Date_________________

Scientific notation is used in science to represent both large and small numbers. One example of large numbers in science is the distance of the planets from the sun. Use the Internet to gather this information on each planet and complete the following table.

The Planets

PlanetDistance from sun in miles

(written in standard notation)Distance from sun in miles

(written in scientific notation)


Unit 1, Activity 4, Research Summary

Name ________ Date_________________

Louisiana Cities

Louisiana is a wonderful state with many cities. How many people live in your city? Take some time and learn more about Louisiana cities by determining how many people live in 10 of its cities. Use the Internet to gather the population information and complete the following table by rounding the numbers and writing them in scientific notation.

Louisiana City

Population in standard notation

Population rounded to the nearest ten

thousand

Population written in

scientific notation


Unit 1, Activity 5, Estimation

Name ________ Date_________________1. Determine an estimated answer for each problem without a calculator. The goal is to

estimate the answer within 15% of the exact answer. Show work and answer in part A for each problem.

2. Once part A for each problem is complete for all problems, determine the exact calculation.

3. Determine the percent difference by using the following formula:(Estimate – Exact) ÷ Exact × 100. If the percent difference is ± 15%, use a different strategy, place in part B and determine the percent difference.

Problem Estimation Strategy Exact CalculationPercent

Difference

1. 219 × 9a. _____ × _____ = ______

b. _____ × _____ = ______219 × 9 = _____

a. ______

b. ______

2. 590 ÷ 29

a. _____ ÷ _____ = ______

b. _____ ÷ _____ = ______

a. ______

b. ______

3. 7204 - 1999

a. _____ - _____ = ______

b. _____ - _____ = ______

a. ______

b. ______

4. 231 + 119

a. _____ + _____ = ______

b. _____ + _____ = ______a. ______

b. ______

5. 98 ×

a. _____ × _____ = ______

b. _____ × _____ = ______a. ______

b. ______

6. 135 ÷

a. _____ ÷_____ = ______

b. _____ ÷ _____ = ______a. ______

b. ______

7. 2 + 10 -

a. ___ + ___ - ____ = ______

b. ___ + ___ - ____ = ______a. ______

b. ______

8. 0.95 + 1.0099

a. _____ + _____ = ______

b. _____ + _____ = ______a. ______

b. ______

9. 4.05 × 2.579

a. _____ × _____ = ______

b. _____ × _____ = ______a. ______

b. ______


Unit 1, Activity 5, Estimation with Answers

Name ________ Date_________________1. Determine an estimated answer for each problem without a calculator. The goal is to

estimate the answer within 15% of the exact answer. Show work and answer in part A for each problem.

2. Once part A for each problem is complete for all problems, determine the exact calculation.

3. Determine the percent difference by using the following formula:a. (Estimate – Exact) ÷ Exact × 100. If the percent difference is ± 15%, use a

different strategy, place in part B and determine the percent difference.

Problem Estimation Strategy Exact CalculationPercent

Difference

1. 219 × 9a. 220 × 10 = 2200

b. _____ × _____ = ______219 × 9 = 1971

a. 11

b. ______

2. 590 ÷ 29

a. 600 ÷ 30 = 20

b. _____ ÷ _____ = ______

590 ÷ 29 = 20.34

a. 1.4

b. ______

3. 7204 - 1999

a. 7200 - 2000 = 5200

b. _____ - _____ = ______7204 – 1999 = 5205

a. 0.1

b. ______

4. 231 + 119

a. 230 + 120 = 350

b. _____ + _____ = ______231 + 119 = 350 a. 0

b. ______

5. 98 ×

a. 100 × 0.5 = 50

b. _____ × _____ = ______ 98 × = 49 a. 2

b. ______

6. 135 ÷

a. 135 ÷1 = 135

b. _____ ÷ _____ = ______ 135 ÷ = 154.3 a. 12.5

b. ______

7. 2 + 10 -

a. 3 + 10 - 1 = 12

b. ___ + ___ - ____ = ______

2 + 10 - =

12.195a. 1.6

b. ______

8. 0.95 + 1.0099

a. 1 + 1 = 2

b. _____ + _____ = ______0.95 + 1.0099 = 1.9599

a. 2

b. ______

9. 4.05 × 2.579

a. 4 × 3 = 12

b. _____ × _____ = ______4.05 × 2.579 = 10.44

a. 14.9

b. ______


Unit 1, Activity 6, Estimation Situations

Name ________ Date_________________

In the following real-world situations, pretend that you and your friends are actually involved and use your estimation skills to determine a reasonable estimate of the answer to the questions. Since in most situations like this no calculator will be available, solve these problems without the use of a calculator.

1. Jerry went to dinner with three of his friends. Two of the dinners cost $12.95 each and the other dinners cost $14.95 each. What is a good estimate of the total cost of the dinners, not including tax or tip?

2. During spring break, Larry watched TV an average of 3.25 hours per day. Over the 5-day period, about how many hours did Larry watch TV?

3. Alyssa is a part-time cashier at Wal-Mart. She earns $128.39 per week. About how much does she earn in a year? (52 weeks = 1 year)

4. One of your New Year’s resolutions is to be more physically fit. In order to do this, you have decided to start a regular walking program. There are two walking tracks available.

The length of the long track is 1 miles long and the short track is mile long. If

during the first month you walk 5 times around the long track and 7 times around the short track, about how many miles will you have walked in the first month?

5. According to the table below, about how much money will you need to buy 10 pencils, 2 packs of paper, 1 notebook, and 5 pens?

Pencils Erasers Paper Notebooks Pens3 for 95¢ 1 pack for $1.09 $1.89 per pack $3.29 each 2 for $1.49


Unit 1, Activity 6, Estimation Situations with Answers

Name ________ Date_________________

In the following real-world situations, pretend that you and your friends are actually involved and use your estimation skills to determine a reasonable estimate of the answer to the questions. Since in most situations like this no calculator will be available, solve these problems without the use of a calculator. Write your answers in complete statements.

1. Jerry went to dinner with three of his friends. Two of the dinners cost $12.95 each and the other dinners cost $14.95 each. What is a good estimate of the total cost of the dinners, not including tax or tip?

A good estimate of the total cost of the dinners not including tax or tip is about $56.00.

2. During spring break, Larry watched TV an average of 3.25 hours per day. His friend Joshua watched TV an average of 4.8 hours per day. Over the 5-day period, about how many more hours did Joshua watch TV than Larry?

Joshua watched TV about 10 hours more than Larry.

3. Alyssa is a part-time cashier at Wal-Mart. She earns $128.39 per week. About how much does she earn in a year? (52 weeks = 1 year)

Over the year, Alyssa earns about $6,500.00.

4. One of your New Year’s resolutions is to be more physically fit. In order to do this, you have decided to start a regular walking program. There are two walking tracks available.

The length of the long track is 1 miles long and the short track is mile long. If

during the first month you walk 5 times around the long track and 7 times around the short track, about how many miles will you have walked in the first month?

In the first month, I will have walked approximately 12 miles.

5. According to the table below, about how much money will you need to buy 10 pencils, 2 packs of paper, 1 notebook, and 5 pens?

Pencils Erasers Paper Notebooks Pens3 for 95¢ 1 pack for $1.09 $1.89 per pack $3.29 each 2 for $1.49

To purchase the materials, I will need about $16.


Unit 1, Activity 7, Vocabulary Card

Name ________ Date_________________

Below is an example of a general vocabulary card and a completed vocabulary card for the word Ratio. Use these examples to show students how to construct their own vocabulary cards on index cards or in their notebook.

Vocabulary Card Example:

Definition Characteristics

Example Illustration

Example Vocabulary Card for the word Ratio

A comparison of two things. The ratio can be written as a fraction, with a colon or with the word ‘to’; the order written matters.

The ratio of boys to girls in the 3:4, 3 to 4, or

class is 3 to 4.

not


Vocabulary Word

Ratio

Unit 1, Activity 8, It’s All in the Thinking

Name ________ Date_________________

Solve the following problems dealing with rates, ratios and proportions. Show all of your work and write your answer in a complete statement. Use a calculator only when necessary.

1. A car travels 60 miles in 30 minutes. What is the rate the car is traveling? How much time, in hours, will it take the car to travel 180 miles at the same rate?

2. Store A sells 6 apples for $4.99 and Store B sells 4 apples for $2.99. Which store has the better buy on apples?

3. A 9th grade class has 9 boys and 15 girls. The whole school has 120 girls. If the ratio of boys to girls for the school is the same as the ratio of boys to girls for the class, how many boys are at the school?

4. A Toyota Camry has a mileage rating of 29 miles per gallon on the highway. Based on this rating, how many gallons of gas would be necessary for the car to travel from Shreveport to Baton Rouge. The distance from Shreveport to Baton Rouge is about 265 miles. If gas costs $2.39 per gallon, what will be the cost of gas for this trip?

5. A map has a scale of 1 inches = 20 miles. If two cities are 345 miles apart, how many

inches would be used to represent this distance on a map?


Unit 1, Activity 8, It’s All in the Thinking with Answers

Name ________ Date_________________

Solve the following problems dealing with rates, ratios and proportions. Show all of your work and write your answer in a complete statement. Use a calculator only when necessary.

1. A car travels 60 miles in 30 minutes. What is the rate the car is traveling? How much time, in hours, will it take the car to travel 180 miles at the same rate?

The car is traveling at a rate of 120 miles per hour. It will take 1.5 hours for the car to travel 180 miles at that rate.

2. Store A sells 6 apples for $4.99 and Store B sells 4 apples for $2.99. Which store has the better buy on apples?

Store A apples are about 83¢ each and Store B apples are about 75¢ each. Therefore, Store B has the better buy on apples.

3. A 9th grade class has 9 boys and 15 girls. The whole school has 120 girls. If the ratio of boys to girls for the school is the same as the ratio of boys to girls for the class, how many boys are at the school?

There are 72 boys at the school.

4. A Toyota Camry has a mileage rating of 29 miles per gallon on the highway. Based on this rating, how many gallons of gas would be necessary for the car to travel from Shreveport to Baton Rouge. The distance from Shreveport to Baton Rouge is about 265 miles. If gas costs $2.39 per gallon, what will be the cost of gas for this trip?

It will take about 9.14 gallons of gas to drive from Shreveport to Baton Rouge. At a cost of $2.39 per gallon, the cost of gas for the trip would be about $21.85.

5. A map has a scale of 1 inches = 20 miles. If two cities are 345 miles apart, how many

inches would be used to represent this distance on this map?

About 25 inches or 25.875 inches would represent 345 miles on this map.


Unit 1, Activity 9, Working with Percents

Name ________ Date_________________

Solve the following percent problems. Show all of your work and write your answer in a complete statement. Use a calculator only when necessary.

1. When Carol began working part time at the store, she earned $145 per week. As a full-time employee, her salary has increased by 150%. What is Carol’s new weekly salary?

2. Larry and three of his friends went to dinner to celebrate Larry’s birthday. The total bill came to $69.78. The group wanted to leave a 15% tip. How much money will they leave for the tip? (Remember to round your answer to the nearest cent or hundredth.)

3. Shelia earns a commission on each one of her home sales. Her last sale was for $135,000 and she earned a $9800 commission. What percent commission did she make?

4. Joe has a savings account that his parents started for him when he was 2 years old. His balance at the end of last year was $2,345. Over the course of the year his account earned 0.5% interest. How much interest did he earn this year?

Complete the table below. Show all work on a separate sheet of paper.

ItemOriginal

Price%off

Amount off

SalePrice

9%Sales Tax

Purchase Price

Pants $ 29.99 10%

Video game $ 79.99 15%

Cell phone $ 189.99 30%

Shoes $ 129.99 20%

Jacket $ 239.99 50%


Unit 1, Activity 9, Working with Percents with Answers

Name ________ Date_________________

Solve the following percent problems. Show all of your work and write your answer in a complete statement. Use a calculator only when necessary.

1. When Carol began working part time at the store, she earned $145 per week. As a full-time employee, her salary has increased by 150%. What is Carol’s new weekly salary?

Carol’s new weekly salary is $362.50

2. Larry and three of his friends went to dinner to celebrate Larry’s birthday. The total bill came to $69.78. The group wanted to leave a 15% tip. How much money will they leave for the tip? (Remember to round your answer to the nearest cent or hundredth.) The group will leave $10.47 for the tip.

3. Shelia earns a commission on each one of her home sales. Her last sale was for $135,000 and she earned a $9800 commission. What percent commission did she make?

The percent commission she made is about 7.3%.

4. Joe has a savings account that his parents started for him when he was 2 years old. His balance at the end of last year was $2,345. Over the course of the year his account earned 0.5% interest. How much interest did he earn this year? Joe earned $11.73 in interest this year.

Complete the table below. Show all work on a separate sheet of paper.

ItemOriginal

Price%off

Amount off

SalePrice

9%Sales Tax

Purchase Price

Pants $ 29.99 10% $ 3.00 $ 26.99 $ 2.43 $ 9.42

Video game $ 79.99 15% $ 12.00 $ 67.99 $ 6.12 $ 74.11

Cell phone $ 189.99 30% $ 57 $ 132.99 $ 11.97 $ 144.96

Shoes $ 129.99 20% $ 26 $ 103.99 $ 9.36 $ 113.35

Jacket $ 239.99 50% $ 120 $ 119.99 $ 10.80 $ 130.79


Unit 1, Activity 10, 4-Step Problem Solving

Name _____________ Date_________________

Use the 4-step problem solving process to solve the problems below. Include information for each of the 4 steps for each problem. Show all work on a separate sheet of paper. Some problems may require additional information to solve. For these problems, complete the ‘Understand’ portion of the 4-step problem solving process and identify the information needed.

1. A cylindrical water storage tank has a height of 50 feet and a diameter of 15 feet. What is the volume of the tank?

2. Jessica needs a box that is at least 225 in3 for a math class project. Her shoe box at home is 6 inches tall, 3 inches long and 14 inches deep. Is this box big enough to use for the class project? If the box is not big enough, how much more space will she need? If the box is big enough, how much, if any, space does she have left over?

3. Larry is going shopping at Game Stop to buy some new games. The only money he has is the money he earned from his part-time job last week. He earns $7.75 per hour. Does Larry have enough money to buy a game for $67.89 at a tax rate of 9%?

4. Mr. Smith is considering switching his savings account from Bank A to Bank B. Bank B promises to give Mr. Smith an interest rate 0.05% higher than Bank A if he will switch his account. If Bank A’s interest rate is 5%, what interest rate will Bank B give Ms. Smith on his account?

5. Mr. Wu begins work at 7:30 a.m. and leaves at 3:15 p.m. He works Monday through Friday and takes an unpaid lunch break of ½ hour each day. He is paid for holidays and sick days. His hourly wage is $15.20. How much does Mr. Wu earn in a year?

6. A hardware company adds a late fee to bills that are not paid within a 30-day period. A carpenter is unable to pay a bill of $85.99 until the 31st day. What is the fee charged on the $85.99?

7. Mary’s mother is planning to place new carpet in Mary’s room. Mary’s room has a length of 13 feet and a width of 14 feet. If the carpet costs $6.99 per square foot, how much will the carpet cost for Mary’s room?


Unit 1, Activity 10, 4-Step Problem Solving with Answers

Name _____________ Date_________________

Use the 4-step problem solving process to solve the problems below. Include information for each of the 4 steps for each problem. Show all work on a separate sheet of paper. Some problems may require additional information to solve. For these problems, complete the ‘Understand’ portion of the 4-step problem solving process and identify the information needed.

1. A cylindrical water storage tank has a height of 50 feet and a diameter of 15 feet. What is the volume of the tank? The volume of the tank is 8831.25 ft3

2. Jessica needs a box that is at least 225 in3 for a math class project. Her shoe box at home is 6 inches tall, 3 inches long and 14 inches deep. Is this box big enough to use for the class project? If the box is not big enough, how much more space will she need? If the box is big enough, how much, if any, space does she have left over?

The volume of the box is 252 in3. It is big enough with 27 in3 left over.

3. Larry is going shopping at Game Stop to buy some new games. The only money he has is the money he earned from his part-time job last week. He earns $7.75 per hour. Does Larry have enough money to buy a game for $67.89 at a tax rate of 9%?

Not enough information.

4. Mr. Smith is considering switching his savings account from Bank A to Bank B. Bank B promises to give Mr. Smith an interest rate 0.05% higher than Bank A if he will switch his account. If Bank A’s interest rate is 5%, what interest rate will Bank B give Mr. Smith on his account?

Bank B will give Mr. Smith an interest rate of 5.0025%.

5. Mr. Wu begins work at 7:30 a.m. and leaves at 3:15 p.m. He works Monday through Friday and takes an unpaid lunch break of ½ hour each day. He is paid for holidays and sick days. His hourly wage is $15.20. How much does Mr. Wu earn in a year?

Mr. Wu earns $28,652 per year.

6. A hardware company adds a late fee to bills that are not paid within a 30-day period. A carpenter is unable to pay a bill of $85.99 until the 31st day. What is the fee charged on the $85.99?

Not enough information

7. Mary’s mother is planning to place new carpet in Mary’s room. Mary’s room has a length of 13 feet and a width of 14 feet. If the carpet costs $6.99 per square foot, how much will the carpet cost for Mary’s room?

The carpet will cost $1272.18.



Name _____________________________________ Date ____________

As we begin this unit, rate your understanding of each word with either a “+” (understand well), a “√” (limited understanding or unsure), or a “—“(don’t know). Over the course of this unit, return to this chart and revise any √ or – marks to + marks as you learn new information. In addition, add new words as necessary. The goal is to replace all the check marks and minus signs with a plus sign. When a + mark is made for a word, provide an example and a definition in your own words. The completed chart is due when we complete the unit.


Bar graph

Box-and-whisker plot

Circle graph

Extreme

Histogram

Line graph

Mean

Measure of central tendency

Median

Mode

Quartile

Range

Scatter plot

Stem-and-leaf plot


Unit 2, Activity 1, Understanding Graphs

Name _______________________________ Date _____________

Use the information below as a starting point for giving an overview of graphs. Show a picture of each of the graphs as it is being discussed, and ask students questions that allow them to compare the attributes and uses of each type of graph.

Bar GraphA bar graph displays numerical comparisons of similar categories. It is one of the most common ways to display categorical data.

HistogramA histogram displays the frequency at which things occur. The data are organized in equal intervals; the data values are marked on the horizontal axis. Bars of equal width are drawn for each interval without any space between them.

Stem-and-Leaf PlotA stem-and-leaf plot is a plot where each data value is split into a stem (usually the tens digit) and a leaf (the ones digit). The leaves on each stem are ordered from least to greatest.

Line graphA line graph is used for continuous data and shows change of a numeric quantity over time.

Circle graphA circle graph, or pie chart, is a circle divided into parts or sectors. The graph shows a part-whole relationship represented by each of the parts or sectors.

Scatter plotA scatter plot shows a relationship between two variables and shows how the two variables are related. Unlike on a line graph, the points on a scatter plot are not connected.

In addition to the information above, remind students that all graphs must have a title, labels, and scale.


Unit 2, Activity 1, Comparing and Contrasting Graphs Word Grid

Name ___________________________________ Date _____________

Has x- and y-axis

Categorical data

Numerical data only

Individual data points

Circle graph

Bar graph

Histogram

Line graph

Scatterplot


Unit 2, Activity 2, Data, Data, Data

Name ________________________________ Date ______________

Part I. Each group works with only one set of data.

Data Set 1:The height of a plant as measured over a period of 8 weeks: Week one: 2 cmWeek two: 3.1 cmWeek three: 4.3 cmWeek four: 5.0 cmWeek five: 7.2 cmWeek six: 9.0 cmWeek seven: 9.2 cmWeek eight: 9.3 cm

Data Set 2: Kinds of pets in a neighborhood:7 dogs, 10 cats, 2 birds, 5 fish, 1 turtle

Data Set 3

Scores on a test:0 - 20 3 students21 - 40 12 students41 - 60 20 students61 - 80 31 students81 - 100 22 students

Data Set 4Comparison of shoe size and age for 10 females:

Size 4, 9 yearsSize 8, 27 yearsSize 5, 13 yearsSize 7, 50 years Size 9, 20 yearsSize 3, 8 yearsSize 10, 23 yearsSize 8, 42 yearsSize 1, 7 yearsSize 6, 14 years

Data Set 5Favorite colors Blue 10%Red 25%Green 15%Yellow 20%


Unit 2, Activity 2, Data, Data, Data

Name ___________________________________ Date ___________

Part II.

Name of group performing analyses: __________________Name of group providing graph

Indicate ways in which the graph chosen was appropriate and provide reasons.

1.

2.

3.


Unit 2, Activity 3, Data Everywhere!

Name ________________________________________ Date _______________

Make a scatter plot for the data in Tables 1. For Table 2, working in groups of three, measure the arm span and height of each student in the class. Enter this data in the table. Plot the data and sketch a trend line.

Table 1. Math Test Data Table 2. Arm Span (cm) vs. Height (cm)

Student Number

Hours Slept

Test Score

1 8 832 7 863 7 744 8 885 6 766 5 637 7 908 4 609 9 8910 7 81

Based on the plots developed above, write an explanation of what the scatterplots tell you about relationships between the values in each table.

Table 1

Table 2


Person # Arm Span Height1234567891011121314151617181920

Unit 2, Activity 4, Circle Up

Name _________________________________ Date __________

Directions: Students will create circle graphs based on the directions below.

1. Team Honda had a really good sales week. The breakdown of their sales was as follows: Civic – 35, Accord – 27, CR-V - 23, Prelude – 15

Complete the table by calculating the percent of each model sold. Show all of your calculations. Then use the information to construct a circle graph.

Model # sold % soldCivic 35

Accord 15CR-V 27

Prelude 23

On a separate sheet of paper, construct a circle graph to show the sales distribution. Calculate the angles needed for each of the sectors and use a protractor to draw the sectors.

2. Brainstorm what it would cost to take your dream vacation. Where would you go? Complete the table below. Show all of your calculations.

Description of Expense Costs

% of total cost

Use this information to create a circle graph showing the distribution of expenses. Use a protractor to draw the sectors.


Unit 2, Activity 5, A Picture is Worth a Thousand Words

Name ________________________________ Date _____________

Directions: Part I: For each graph below, label the y-axis with a category. Then write a short story explaining what the graph could represent. There is no need to put numbers on the graph. Just discuss what the graph could be representing and what might be causing it.

a. b.

Time Sales

c. d.

Time Days

Part II. Sketch a graph to represent each situation below.

a. You move at a steady speed away from your starting point.

b. You move at a constant speed for 3 minutes, then increase your speed.

c. You are walking along a path at a constant speed. You begin to walk up an incline and your speed decreases. You immediately begin to walk down hill and your speed increases until you come to a complete stop.


Unit 2, Activity 6, Center Stage

Name _________________________________________ Date ____________

Directions: Find the mean, median and mode for each data set.

1) 4, 1, 0, 2, 3, 5, 2

2) 18, 14, 15, 16, 20, 17

3) 3.6, 2.5, 4.2, 3.3, 5.4

4) 145, 95, 90, 120, 105, 85, 95

5) Each of Larry’s last seven tests in Mr. Smith’s class were worth 100 points and his scores are as follows: 90, 50, 80, 100, 80, 85, 89. If Larry has the option of choosing which measure Mr. Smith uses for his overall class grade, which of the following should Larry choose? Explain your answer.

a. mean b. median c. mode d. drop the lowest grade and take the average

Would you use mean, median, or mode for each situation? Explain.

6) The average score on the last Pre-Algebra test was 77.

7) The most common height on the basketball team is 6 ft 1 in.

8) The most common price of a certain type of car is $25,000.

9) Jack noticed that half of the cereal brands in the store cost more than $2.00.

10) One-half of the cars at a dealership cost less than $23,000.


Unit 2, Activity 6, Center Stage with Answers

Name _________________________________________ Date ____________

Directions: Find the mean, median and mode for each data set.

1) 4, 1, 0, 2, 3, 5, 2 mean: 2.4 median: 2 mode: 2

2) 18, 14, 15, 16, 20, 17 mean: 16.7 median: 16.5 mode: none

3) 3.6, 2.5, 4.2, 3.3, 5.4 mean: 3.8 median: 3.6 mode: none

4) 145, 95, 90, 120, 105, 85, 95 mean: 105 median: 95 mode: 95

5) Each of Larry’s last seven tests in Mr. Smith’s class were worth 100 points and his scores are as follows: 90, 50, 80, 100, 80, 85, 89. If Larry has the option of choosing which measure Mr. Smith uses for his overall class grade, which of the following should Larry choose? Explain your answer.

a. mean b. median c. mode d. drop the lowest grade and take the average

Larry should choose ‘d’ because it will give him the highest grade.

Would you use mean, median, or mode for each situation? Explain.

6) The average score on the last Pre-Algebra test was 77. mean

7) The most common height on the basketball team is 6 ft 1 in. mode

8) The most common price of a certain type of car is $25,000. mode

9) Jack noticed that half of the cereal brands in the store cost more than $2.00. median

10) One-half of the cars at a dealership cost less than $23,000. median


Unit 2, Activity 7, Box-and-Whisker Plots

Name _______________________________ Date _____________

Directions: Create a box and whisker plot for the following sets of data.

1. 5, 1, 5, 7, 2, 4, 1, 3, 5

2. 5, 6, 8, 2, 5, 16, 23, 13, 23

3. 35, 45, 33, 45, 12, 11. 10. 4. 7

4. 20, 15, 45, 33, 19, 30, 31, 32, 31, 30, 27, 34, 50, 22, 29, 30

5. Listed below is the per game point summary scored by Lebron James in the last 18 games. Use the data to create a box and whisker plot. Analyze the chart and write a summary of Lebron James’ performance.

15, 18, 21, 7, 29, 20, 9, 23, 25, 45, 29, 14, 18, 26, 28, 27, 19, 26


Unit 3, Activity 1, Vocabulary Self-Awareness

Name _______________________________ Date ________________

As we begin this unit, rate your understanding of each word with either a “+” (understand well), a “√” (limited understanding or unsure), or a “—“(don’t know). Over the course of this unit, return to this chart and revise any √ or – marks to + marks as you learn new information. In addition, add new words as necessary. The goal is to replace all the check marks and minus signs with a plus sign. When a + mark is made for a word, provide an example and a definition in your own words. For the words volume and surface area, also include common units for measuring. The completed chart is due when we complete the unit.

Word

+ or √ or

- Definition

Common Units

used to measure

Real – life examples

Surface Area

Volume


Unit 3, Activity 1, Surface Area

Names of Group Members:

________________________ ________________________ _________________________

Materials needed: rectangular prism (box), ruler, Post-it® notes, calculator, markers

1. Describe your rectangular prism type, color, etc.)

2. Carefully open all sides of your box to create a net that lies flat on a desk or table. As you

look at your box, describe the shapes you see.

3. On the inside of your box, label or identify the length, width and height.

4. Use your knowledge of finding the area of a rectangle to determine the surface area of the box. In the space below, describe your process for determining the surface area and draw a picture of the net labeling each part with its respective area, including the proper units (the box may be measured in centimeters, millimeters or inches).

5. Based on your work, derive a formula for finding the surface area of a rectangular box. Write the formula algebraically. Refer to your LEAP Reference Sheet.

Extension Activity: Repeat the activity above using a cylinder. Record your information on a separate sheet of paper.


Unit 3, Activity 2, Understanding Surface Area and Volume

Work with a partner to complete the surface area and volume problems below. (Work must be turned in for each student.) Show all work. Be sure to include the appropriate units in all of your answers. Round all answers to the nearest whole number. Be prepared to discuss with the class.

Name __________________________________ Date _________________

1. The dimensions of a packing crate are 10 inches by 12 inches by 18 inches. How many square inches of wrapping paper are needed to cover the entire crate?

2. Find the volume of a cylinder with a diameter of 7 inches and a height of 9 inches.

3. The dimensions of a box are 3 feet by 5 feet by 6 inches. The box has no lid. What is its total surface area? (Report answer in cubic feet.)

4. Mrs. Gibson has a bedroom that measures 14 feet by 10 feet. She loves fish and decides to place a beautiful fish border around the room. She will also cover the floor with new carpet. How many square yards of carpet will it take to cover the floor?

5. The cost for painting a cylindrical tank is $2.24 per square foot. How much will it cost to paint the tank if it has a diameter of 15 feet and a height of 60 feet?

6. A manufacturing company charges $0.13 per square inch to wrap containers. Which of the following containers has the highest wrapping cost? Container 1: Rectangular box with dimensions of 5 inches x 4 inches x 7 inches. Container 2: Cylindrical box with a diameter of 6 inches and a height of 7 inches.


Unit 3, Activity 2, Understanding Surface Area and Volume with Answers

Work with a partner to complete the surface area and volume problems below. (Work must be turned in for each student.) Show all work. Be sure to include the appropriate units in all of your answers. Round all answers to the nearest whole number. Be prepared to discuss with the class.

Name __________________________________ Date _________________

1. The dimensions of a packing crate are 10 inches by 12 inches by 18 inches. How many square inches of wrapping paper are needed to cover the entire crate?

1032 in2

2. Find the volume of a cylinder with a diameter of 7 inches and a height of 9 inches.

346 in3

3. The dimensions of a box are 3 feet by 5 feet by 6 inches high. The box has no lid. What is its total surface area in cubic feet? (Report answer in cubic feet.)

23 ft3

4. Mrs. Gibson has a bedroom that measures 14 feet by 10 feet. She loves fish and decides to place a beautiful fish border around the room. She will also cover the floor with new carpet. How much carpet will it take to cover the floor?

140 ft2

5. The cost for painting a cylindrical tank is $2.24 per square foot. How much will it cost to paint the tank if it has a diameter of 15 feet and a height of 60 feet?

$7121

6. A manufacturing company charges $0.13 per square inch to wrap containers. Which of the following containers has the highest wrapping cost? Container 1: Rectangular box with dimensions of 5 inches x 4 inches x 7 inches. Container 2: Cylindrical box with a diameter of 6 inches and a height of 7 inches.

Container 1 cost: $21.58 Container 2 cost: $24.49 Therefore, container 2 has the highest wrapping cost.


Unit 3, Activity 4, Conversions and Comparisons

Name __________________________________ Date ____________________

Complete the following conversions. Show your work on a separate sheet of paper.

1. 8 pints = ___ quarts 6. 3 L = ___ mL

2. 2 quarts = ___ cups 7. 250 mL = ___ L

3. 6 quarts = ___ gallons 8. 0.05 L = ___ mL

4. 2 pints = ___ ounces 9. 4 quarts = ___ pints = ___ cups

5. 0.5 gallon = ___ pints 10. 24 cups = ___ pints = ___ gallons

11. A gallon of milk is half empty. How many cups of milk are left in the container? Show your work and explain your answer.

12. The caterer has 5 liters of punch to place in the punch bowl. He can choose from the following punch bowls: 2 quarts, 4 quarts, 6 quarts, or 8 quarts. Which punch bowl should he choose if he wants to use the smallest bowl possible to hold all the punch? Show your work and explain your answer.

13. The caterer is making punch using a new recipe that calls for 6 cups of Sprite. Will one 1-liter bottle of Sprite be enough to make the punch? Show your work and explain your answer.

14. Jerry went to the store to buy two gallons of milk. The store was out of gallons of milk, but did have some quarts and pints. Give two different combinations of quarts and pints that will make two gallons. Show your work and explain your answer.

15. Lisa needs to fill a 3 liter container with tap water. If the only measuring container she has measures one pint, about how many of the small containers of water will she need to fill the three liter container?


Unit 3, Activity 4, Conversions and Comparisons with Answers

Name __________________________________ Date ____________________

Complete the following conversions. Show your work on a separate sheet of paper.

1. 8 pints = 4 quarts 6. 3 L = 3000 mL

2. 2 quarts = 8 cups 7. 250 mL = 0.25 L

3. 6 quarts = 1.5 gallons 8. 0.05 L = 50 mL

4. 2 pints = 32 ounces 9. 4 quarts = 8 pints = 16 cups

5. 0.5 gallon = 4 pints 10. 24 cups = 12 pints = 1.5 gallons

11. A gallon of milk is half empty. How many cups of milk are left in the container? Show your work and explain your answer.

8 cups. Explanations may vary. One possible answer is that there are 4 quarts in a gallon. Half a gallon would be 2 quarts. There are 4 cups in each quart, so there are 8 cups in 2 quarts.

12. The caterer has 5 liters of punch to place in the punch bowl. He can choose from the following punch bowls: 2 quarts, 4 quarts, 6 quarts, or 8 quarts. Which punch bowl should he choose if he wants to use the smallest bowl possible to hold all the punch? Show your work and explain your answer.

Since a liter is a little larger than a quart, the 6 quart punch bowl should be the smallest one he can use.

13. The caterer is making punch using a new recipe that calls for 6 cups of Sprite. Will one 1-liter bottle of Sprite be enough to make the punch? Show your work and explain your answer.

A liter is a little bigger than a quart. One quart equals 4 cups. Therefore, he will not have enough Sprite because he only has a little more than 4 cups.

14. Jerry went to the store to buy two gallons of milk. The store was out of gallons of milk, but did have some quarts and pints. Give two different combinations of quarts and pints that will make two gallons. Show your work and explain your answer.

Examples: 4 quarts and 8 pints, 6 quarts and 4 pints, 2 quarts and 12 pints.

15. Lisa needs to fill a 3 liter container with tap water. If the only measuring container she has measures one pint, about how many of the small containers of water will she need to fill the three liter container?

She will need six to seven small containers to fill the three liter bottle.


Unit 3, Activity 5, Area and Volume Conversions

Name ______________________________ Date _______________

Write the conversion ratio for each problem and use the ratio to solve each problem using proportions. Show all work in setting up and solving the proportions on separate paper. Round US conversion answers to the nearest hundredth.

ConversionRatio

ConversionRatio

1. 3 yd2 = ___ ft2 6. 3 m2 = ___ cm2

2. 12 ft2 = ___ yd2 7. 8 ft3 = ____ yd3

3. 2 ft2 = ___ in2 8. 1.5 yd3 = ___ ft3

4. 200 in2 = ___ ft2 9. 2 yd3 = ___ in3

5. 3 cm2 = ___ m2 10. 2 m3 = ___ cm3

11. The area of a lot is 125 feet X 250 feet. What is the area of the lot in square yards?

12. A contractor wants to order concrete for a wall that is 20 ft long, 8 ft high, and 8 inches thick. How many cubic yards should she order?

13. A landscape architect needs to purchase 10 cubic yards of soil. If the soil is sold in 50 cubic feet bags, how many bags will he need to buy?

14. The area of a counter top is 5 m2. Approximately how many 25 x 25 cm tiles are needed to cover the floor?


Unit 3, Activity 5, Area and Volume Conversions with Answers

Name ______________________________ Date _______________

Write the conversion ratio for each problem and use the ratio to solve each problem using proportions. Show all work in setting up and solving the proportions on separate paper. Round US conversion answers to the nearest hundredth.

ConversionRatio

ConversionRatio

1. 3 yd2 = 27 ft2 9 ft 2 1 yd2

6. 3 m2 = 35000 cm210000 cm 2

1 m2

2. 12 ft2 = 1.33 yd2 1yd 2 9 ft2

7. 8 ft3 = 0.30 yd3 1 yd 3 27 ft3

3. 2 ft2 = 288 in2 144 in 2 1 ft2

8. 1.5 yd3 = 40.5 ft3 27 ft 3 1 yd3

4. 200 in2 = 1.39 ft2 1 ft 2 144 in2

9. 2 yd3 = 3456 in3 1728 in 3 1 yd3

5. 3 cm2 = 0.0003 m2 1 m 2 10,000 cm2

10. 2 m3 = 2000000 cm3 1,000,000 cm 3 1 m3

11. The area of a lot is 125 feet X 250 feet. What is the area of the lot in square yards?

2083.3 yd2

12. A contractor wants to order concrete for a wall that is 20 ft long, 8 ft high, and 8 inches thick. How many cubic yards should she order?

3.97 yd3 which requires the purchase of 4 yd3

13. A landscape architect needs to purchase 10 cubic yards of soil. If the soil is sold in 50 cubic feet bags, how many bags will he need to buy?

270 bags

14. The area of a counter top is 5 m2. Approximately how many 25 x 25 cm tiles are needed to cover the floor?

Approximately 80 tiles are needed.


Unit 3, Activity 6, Understanding and Using Rates

Name ____________________________________ Date ___________

Solve the following rate problems. Be sure to show all of your work.

1. Sandra traveled from Lafayette, Louisiana, to New Orleans, Louisiana, to see the New Orleans Hornets play the Charlotte Bobcats. If the total distance traveled was approximately 125 miles and it took her two and one half hours, with no stops along the way, what was her average speed driven?

2. Mr. Clark needs to be at work for 8:00 a.m. The distance from his house to his job is 25 miles. If he is able to travel at the posted speed of 50 miles per hour, what time does he need to leave home to make it to work by 8:00 a.m.?

3. The jeweler has a piece of silver with a mass of 160 grams and a volume of 5 cubic centimeters. What is the density of the silver?

4. Larry is traveling to Mexico. If he buys a hat for 65 pesos, how much did he spend in U.S. dollars if the exchange rate is 12.52 pesos per dollar?

5. What is the mass of a substance with a volume of 25 cubic centimeters and a density of 12.6 grams per cubic centimeter?


Unit 3, Activity 6, Understanding and Using Rates with Answers

Name ____________________________________ Date ___________

Solve the following rate problems. Be sure to show all of your work.

1. Sandra traveled from Lafayette, Louisiana, to New Orleans, Louisiana, to see the New Orleans Hornets play the Charlotte Bobcats. If the total distance traveled was approximately 125 miles and it took her two and one half hours, with no stops along the way, what was her average speed driven?

Average speed is 50 miles per hour.

2. Mr. Clark needs to be at work for 8:00 a.m. The distance from his house to his job is 25 miles. If he is able to travel at the posted speed of 50 miles per hour, what time does he need to leave home to make it to work by 8:00 a.m.?

Mr. Clark needs to leave home at about 7:30 a.m.

3. The jeweler has a piece of silver with a mass of 160 grams and a volume of 5 cubic centimeters. What is the density of the silver?

Density = 32 grams per cubic centimeter

4. Larry is traveling to Mexico. If he buys a hat for 65 pesos, how much did he spend in U.S. dollars if the exchange rate is 12.52 pesos per dollar?

Larry spent about $5.19.

5. What is the mass of a substance with a volume of 25 cubic centimeters and a density of 12.6 grams per cubic centimeter?

Mass = 315 grams



Name _____________________________________ Date ____________

As we begin this unit, rate your understanding of each word with either a “+” (understand well), a “√” (limited understanding or unsure), or a “—“(don’t know). Over the course of this unit, return to this chart and revise any √ or – marks to + marks as you learn new information. In addition, add new words as necessary. The goal is to replace all the check marks and minus signs with a plus sign. When a + mark is made for a word, provide an example and a definition in your own words. The completed chart is due when we complete the unit and should be placed in the math learning log.


symmetry

similar / similarity

congruent

bisect

translation

reflection

rotation

dilation

complementary angles

supplementary angles

alternate interior angles

alternate exterior angles

corresponding angles

adjacent angles


Unit 4, Activity 1, Vocabulary Card

Name ________ Date_________________

Below is an example of a general vocabulary card and a completed vocabulary card for the word Ratio. Use these examples to show students how to construct their own vocabulary cards on index cards or in their notebook.

Vocabulary Card Example:

Definition Characteristics

Example Illustration

Example Vocabulary Card for the word Ratio

A comparison of two things. The ratio can be written as a fraction, with a colon or with the word ‘to’; the order written matters.

The ratio of boys to girls in the 3:4, 3 to 4, or

class is 3 to 4.

not


Vocabulary Word

Ratio

Unit 4, Activity 2, Similar Triangles

1. The two triangles below are similar. Find the length of side AB.

2. Larry is 5.5 feet tall, and his shadow measured 9 feet long at noon. At the same time, a nearby flagpole cast a 45 ft. shadow. The triangles created are similar. What is the height of the flagpole?

3. Draw and label two similar triangles. Explain your reasoning for declaring the triangles similar.


Unit 4, Activities 3 and 7, Coordinate Grid


Unit 4, Activity 7, Transformation

Name ____________________________________ Date ________________

1. Give the coordinates of the vertices of the figure in its original position, and then give the coordinates of the new vertices based on stated transformation. The rotation is 90°clockwise about the origin. The reflection is across the y-axis. Draw and label the transformations on the grid below.

Shape Original Position

Translate Rotate Reflect across y-axis

Rectangle A( 2 , 3 )B( 2 , 6 )C( , )D( , )

A( , )B( 2 ,-4)C( , )D( , )

A( , )B( , )C( , )D( , )

A( , )B ( , )C( , )D( , )


Unit 4, Activity 7, Transformation

Name ____________________________________ Date ________________




Right Triangle H( 0 , 3 )R( 0 , 0 )J( , )

H( 2 ,-1 )R(2 , -4)J( -1 , -4 )

H( , ) R( , ) J( , )

H( , ) R( , ) J( , )


Unit 4, Activity 7, Transformation with Answers




Rectangle A( 2 , 3 )B( 2 , 6 )C( 7, 6 )D( 7 , 3 )

A( 2, -7)B( 2 ,-4)C( 7 ,-4)D( 7, 7)

A( 3 ,-2)B( 6, 2 )C( 6 , -7)D( 3 , -7)

A( -2, 3)B ( -2 , 6)C( -7 , 6 )D( -7 , 3)

Right Triangle H( 0 , 3 )R( 0 , 0 )

J(-3 , 0 )*

H( 2 , -1)R(2 , -4)J( -1 , -4)

H( 3 , 0)R( 0 , 0)

J ( 0 , 3 )

H( 0 , 3 )R( 0 , 0)J( 3, 0 )

* Answers may vary depending on the coordinates chosen.


Unit 4, Activity 8, Quadrant I Grid

Name _________________________________ Date ______________ Hour ____________


x

y

Unit 4, Activity 10, Centimeter Grid

Name _____________________________________ Date ______________


Unit 4, Activity 10, Pythagorean Theorem

Work with your partner to complete these problems. Draw and label the sides of the right triangle that is being used to solve the problem.

1. Find the length of a rectangle with a diagonal of 25 feet and a width of 15 feet.

2. Firefighters need to reach a window that is 20 feet above the ground. The ladder they are working with is 20 feet long. For safety reasons, the base extends out 5 feet from the building. Will the firefighters be able to place the ladder on the ledge of the window?

3. What is the diagonal of a square whose area is 81 square feet?

Listed below are the side lengths of three triangles. Are the triangles right triangles? Explain your reasoning.

4. 3, 4, 7

5. 5, 12, 13

6. 20, 21, 27


Unit 4, Activity 10, Pythagorean Theorem with Answers

Work with your partner to complete these problems. Draw and label the sides of the right triangle that is being used to solve the problem.

1. Find the length of a rectangle with a diagonal of 25 feet and a width of 15 feet.

Length of the rectangle is 20 feet.

2. Firefighters need to reach a window that is 20 feet above the ground. The ladder they are working with is 20 feet long. For safety reasons, the base extends out 5 feet from the building. Will the firefighters be able to place the ladder on the ledge of the window?

The ladder would only extend 19.5 feet; therefore, the firefighter would not be able to place the ladder on the ledge of the window. It would be 6 inches too short.

3. What is the diagonal of a square whose area is 81 square feet?

The diagonal of the square is 12.73 feet.

Listed below are the side lengths of three triangles. Are the triangles right triangles? Explain your reasoning.

4. 3, 4, 7 Are not the side lengths of a right triangle.

5. 5, 12, 13 Can be the side lengths of a right triangle.

6. 20, 21, 27 Are not the side lengths of a right triangle.


Unit 4, Activity 11, Angle Relationships

Work with your partner to determine the measures of the missing angles in the following diagram. Provide the reasoning behind your answer.

AngleAngle

measure Reasoning or justification for measurement

1

2 40° Given

3

4

5

6

7

8


Unit 4, Activity 11, Angle Relationships with Answers

Work with your partner to determine the measures of the missing angles in the following diagram. Provide the reasoning behind your answer.

AngleAngle

measure Reasoning or justification for measurement

1 140° Reasons will vary.

2 40° Given

3 40°

Reasons will vary.







Unit 4, Activity 12, Scale Drawings

Work in groups of three to complete the scale drawing activities below.

Name ____________________________________ Date __________

1. Draw a diagram of a rectangular room with dimensions of 25 feet by 20 feet. Use a scale of 0.5 inch = 5 feet.

2. A map uses a scale of ¼ inch = 50 miles. If on the map two cities are 3 ¼ inches apart, how far in miles are the cities apart?

3. An interior designer uses a scale drawing to help design a kitchen. The length of the kitchen is 20 feet and the length of the drawing is 8 inches. Find the drawing’s scale.

4. Give the students the dimensions of the classroom. (length, width, distance of door from walls, door width, width of windows, etc.) Have the students develop a scale drawing of the classroom. Each group will present their drawing to the class. Consider providing posters for this activity.


Unit 4, Activity 12, Scale Drawings with Answers

Work in groups of three to complete the scale drawing activities below.

Name ____________________________________ Date __________

1. Draw a diagram of a rectangular room with dimensions of 25 feet by 20 feet. Use a scale of 0.5 inch = 5 feet.

Students should draw a rectangular figure with dimensions of 2.5 inches by 2 inches.

2. A map uses a scale of ¼ inch = 50 miles. If on the map two cities are 3 ¼ inches apart, how far in miles are the cities apart?

The cities are 650 miles apart.

3. An interior designer uses a scale drawing to help design a kitchen. The length of the kitchen is 20 feet and the length of the drawing is 8 inches. Find the drawing’s scale.

1 inch = 2.5 feet

4. Give the students the dimensions of the classroom (length, width, distance of door from walls, door width, width of windows, etc.). Have the students develop a scale drawing of the classroom. Each group will present its drawing to the class. Consider providing posters for this activity.

Answers will vary.


Unit 5, Activity 1, Permutations

Name ____________________________________________ Date ____________

Evaluate the following situations and determine the number of permutations possible for each.

1. Three friends, Larry, Randy and Shawn, are standing in line for a concert. How many different ways can they stand in line? Show your result in a list and a tree diagram.

2. Make a list of all the possible four-letter permutations of the letters in the word STAR.

3. Seven teams participate in a basketball tournament. If trophies are given for first, second, and third place, how many different ways can the trophies be given?

4. Find the number of permutations of the letters in each of the following words:

a. games b. section


Unit 5, Activity 1, Permutations with Answers

Name ____________________________________________ Date ____________

Evaluate the following situations and determine the number of permutations possible for each.

1. Three friends, Larry, Randy and Shawn are standing in line for a concert. How many different ways can they stand in line? Show your result in a list and a tree diagram.

List: LRS, LSR, RLS, RSL, SRL, SLR

2. Make a list of all the possible four-letter permutations of the letters in the word STAR.

STAR TSAR ASTR RSTASTRA TSRA ASRT RSATSATR TASR ATSR RTSASART TARS ATRS RTASSRTA TRSA ARST RASTSRAT TRAS ARTS RATS

3. Seven teams participate in a basketball tournament. If trophies are given for first, second, and third place, how many different ways can the trophies be given?

There are 210 different ways.

4. Find the number of permutations of the letters in each of the following words:

b. games b. section

120 5040


Unit 5, Activity 2, How Many are There?

Name ____________________________________________ Date ____________

Evaluate the following situations and determine the number of combinations possible for each. Show your work for each situation.

1. Make a list of the three letter combinations of the word STAR.

2. On a restaurant menu, a choice of two vegetables comes with a dinner. If there are five vegetables to choose from, how many different combinations of two vegetables can the restaurant offer?

3. Randy is planning to paint his room. He will blend two colors of paint to make the color for his room. He will choose from six colors. How many combinations of 2 colors can he choose?

4. Jessie is a junior at a local university. He is planning his schedule for the spring semester and needs to choose two math classes. He can choose from the following math classes: trigonometry, Calculus I, differential equations and business math. How many different combinations of two math classes can he choose from?

5. How many combinations of three books can be chosen from a collection of six books?

Determine whether each of the following situations is a permutation or a combination. Explain your choice.

6. Choosing 5 friends to invite to the movies. ____________________

7. Choosing the arrangement of 12 books on a shelf. _____________________

8. Choosing which three videos to select from a choice of 12. ____________________

9. Choosing the order a group of 7 students will line up in. ____________________

10. Choosing how many different arrangements of the word STEP can be made. ________


Unit 5, Activity 2, How Many are There? with Answers

Name ____________________________________________ Date ____________

Evaluate the following situations and determine the number of combinations possible for each. Show your work for each situation.

1. Make a list of the three letter combinations of the word STAR.

STA, STR, ATR, SAR

2. On a restaurant menu, a choice of two vegetables comes with a dinner. If there are five vegetables to choose from, how many different combinations of two vegetables can the restaurant offer?

10

3. Randy is planning to paint his room. He will blend two colors of paint to make the color for his room. He will choose from six colors. How many combinations of 2 colors can he choose?

15

4. Jessie is a junior at a local university. He is planning his schedule for the spring semester and needs to choose two math classes. He can choose from the following math classes: trigonometry, Calculus I, differential equations and business math. How many different combinations of two math classes can he choose from?

65. How many combinations of three books can be chosen from a collection of six books?

20

Determine whether each of the following situations is a permutation or a combination. Explain your choice.

6. Choosing 5 friends to invite to the movies. combination

7. Choosing the arrangement of 12 books on a shelf. permutation

8. Choosing which three videos to select from a choice of 12. combination

9. Choosing the order a group of 7 students will line up in. permutation

10. Choosing how many different arrangements of the word STEP can be made. permutation


Unit 5, Activity 3, Experiments in Probability

Work in groups of three to complete the following probability experiments.

Group members’ names: _________________ _________________ __________________

Experiment #1: Flip a coin

Directions: Flip a coin 25 times and record the number of heads and tails that result. Write the result as a fraction and percent.

Number of heads(Place tally marks here.)

Number of tails(Place tally marks here.)

Total Heads: Total Tails:

Fraction of heads: % of heads Fraction of tails: % of tails:

Experiment #2: Flip two coins

Directions: Flip two coins 25 times and record the number of two heads, two tails or one head, one tail results. Write the result as a fraction and percent.

Number of two heads(Place tally marks here.)

Number of two tails(Place tally marks here.)

Number of one head, one tail(Place tally marks here.)

Total Two Heads: Total Two Tails: Total One Head, One Tail:

Fraction of two heads:

% of two heads

Fraction of tails:

% of two tails:

Fraction of tails:

% of one head, one tail:

Be prepared to discuss your results with the whole class.


Unit 5, Activity 4, Crossing the River

Crossing the RiverGame Rules:

1. Game requires two players.2. Each player starts with 12 boats (Any small object can serve as a boat.). Each player’s

boats should be of the same color but a different color than the other player’s boats.3. Each player decides on which number he/she wants to place his/her boats on his/her side

of the river. Some numbers may have more than one boat; some numbers may have no boats.

4. Each player takes turn rolling two number cubes and finding the sum of the cubes.5. If the player has a boat on the same number as the sum, the player moves one of his boats

to the other side of the river.6. If a player cannot move a boat, based on the sum rolled, he/she loses a turn.7. The winner is the player that moves all of his/ her boats to the other side of the river first.

1THE

RIVER

1

2 2

3 3

4 4

5 5

6 6

7 7

8 8

9 9

10 10

11 11

12 12


Unit 5, Activity 6, Rubric to Evaluate Presentations

Math - Problem Solving : Professor-Know-It-All

Teacher Name: __________________

Student Name: ________________________________________

CATEGORY 4 3 2 1Mathematical Concepts

Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).

Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s).

Explanation shows some understanding of the mathematical concepts needed to solve the problem(s).

Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.

Explanation Explanation is detailed and clear.

Explanation is clear.

Explanation is a little difficult to understand, but includes critical components.

Explanation is difficult to understand and is missing several components OR was not included.

Working with Others

Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson.

Student was an engaged partner but had trouble listening to others and/or working cooperatively.

Student cooperated with others, but needed prompting to stay on-task.

Student did not work effectively with others.

Mathematical Reasoning

Uses complex and refined mathematical reasoning.

Uses effective mathematical reasoning

Some evidence of mathematical reasoning.

Little evidence of mathematical reasoning.


Unit 5, Activity 6, Special Probabilities

Name ________________________________________________ Date _____________

Analyze each situation below and determine the probability.

1. When rolling two number cubes, what is the probability of rolling

a. a sum of 8?

b. a sum of 11?

c. a sum that is odd?

d. a sum of 6 and then a sum of 9?

2. A brown paper bag contains 8 red balls, 5 green balls, 4 blue balls, 2 orange balls, and 1 purple ball. If one ball is randomly removed from the bag,

a. What is the probability that the ball is green?

b. What is the probability that the ball is white?

c. Which color ball has the best chance of being pulled?

d. What is the probability that the ball will be either orange or green?

3. Sarah has 4 pairs of jeans: 3 blue, 2 black and 1 white. She also has 6 new shirts: 2 blue and white, 2 white, 1 red, and 1 yellow. If she reaches into her closet and selects a shirt and pair of jeans without looking, what is the probability that she will select a pair of blue jeans and a blue and white shirt?

4. A spinner is divided into 16 equal sections labeled with the number 1 through 16. If the spinner is spun, what is the probability of the spinner landing on a number that is a multiple of 3?


Unit 5, Activity 6, Special Probabilities with Answers

Name ________________________________________________ Date _____________

Analyze each situation below and determine the probability.

1. When rolling two number cubes, what is the probability of rolling

e. a sum of 8?

f. a sum of 11?

g. a sum that is odd?

h. a sum of 7 and then a sum of 9?

2. A brown paper bag contains 8 red balls, 5 green balls, 4 blue balls, 2 orange balls, and 1 purple ball. If one ball is randomly removed from the bag,

e. What is the probability that the ball is green?

f. What is the probability that the ball is white?

g. Which color ball has the best chance of being pulled? Red

h. What is the probability that the ball will be either orange or green?

3. Sarah has 4 pairs of jeans: 3 blue, 2 black and 1 white. She also has 6 new shirts: 2 blue and white, 2 white, 1 red, and 1 yellow. If she reaches into her closet and selects a shirt and pair of jeans without looking, what is the probability that she will select a pair of blue jeans and a blue and white shirt?

4. A spinner is divided into 16 equal sections labeled with the number 1 through 16. If the spinner is spun, what is the probability of the spinner landing on a number that is a multiple of 3?


Unit 5, Activity 7, Opinionnaire

Directions: Determine whether the statements or situations below represent a method of gathering data from a survey, or sampling, which is random or biased. Explain the reason for your opinion..

1. A school wants to determine if it is providing a good education to its students. Therefore, the principal surveys the students in the honors classes. Random or biased?

Why?

2. A restaurant requests surveys from all of its customers for one month in order to determine customer satisfaction. Random or biased?

Why?

3. To determine the most popular song played by the school band, the band surveys all of the members of the band. Random or biased?

Why?

4. All of the 9th grade students are surveyed to determine the most popular location for a 9th grade field trip. Random or biased?

Why?

5. In evaluating the possibility of changing the school uniform, the principal surveys all of the parents at one of the monthly parent forums. Random or biased?

Why?

6. A company surveys the current members of a health club to determine if it should add child care services for its members. Random or biased?

Why?

7. To determine the favorite music artist for teenagers, a store surveys a local middle school. Random or biased?

Why?


Unit 5, Activity 7, Opinionnaire with Answers

Directions: Determine whether the statements or situations below represent a method of gathering data from a survey, or sampling, which is random or biased. Explain the reason for your opinion.

1. A school wants to determine if it is providing a good education to its students. Therefore, the principal surveys the students in the honors classes. Random or biased ?

Why?

2. A restaurant requests surveys from all of its customers for one month in order to determine customer satisfaction. Random or biased?

Why?

3. To determine the most popular song played by the school band, the band surveys all of the members of the band. Random or biased?

Why?

4. All of the 9th grade students are surveyed to determine the most popular location for a 9th grade field trip. Random or biased?

Why?

5. In evaluating the possibility of changing the school uniform, the principal surveys all of the parents at one of the monthly parent forums. Random or biased?

Why?

6. A company surveys the current members of a health club to determine if it should add child care services for its members. Random or biased?

Why?

7. To determine the favorite music artist for teenagers, a store surveys a local middle school. Random or biased?

Why?


Unit 6, Activity 1, Operations with Integers

Name __________________________________________ Date ____________________

Solve the following problems.

1. -7 + 15 = _______ 8. (6)(-3) = _______

2. 5 – 24 = _______ 9. 20 – (-22) = _______

3. (-7)(-4) = _______ 10. 19 + (-7) = _______

4. 16 ÷ (-8) = _______ 11. -20 ÷ (-5) = _______

5. -20 + (-5) = _______ 12. (-3)(-4)(-2) = _______

6. -3 – 15 = _______ 13. 6 + 4 – (-2) = _______

7. (-5)(12) = _______ 14. (-2)(3)(-5)(2) = _______

15. The Saints lost 4 yards on one play. On the next play, they moved forward 7 yards. What is the result of the two plays combined?

16. Over a 5 hour period, the temperature fell from 6°F to -3 °F. What was the overall change in temperature?

17. A group of hikers descends 35 meters in 5 hours. What is the average change in their position in meters per hour?

18. A diver’s depth changed -8 feet per second for 7 seconds. How many feet did the diver’s depth change?

19. Jerry has -45 points. He wins 125 points, and then loses 30 points. How many points does he have now?

20. Michelle answers 6 questions correctly and 4 questions incorrectly. Each correct answer is worth 5 points and each incorrect answer is worth -2 points. How many points does Michelle have?


Unit 6, Activity 1, Operations with Integers with Answers

Name __________________________________________ Date ____________________

Solve the following problems.

1. -7 + 15 = 8 8. (6)(-3) = -18

2. 5 – 24 = -19 9. 20 – (-22) = 42

3. (-7)(-4) = 28 10. 19 + (-7) = 12

4. 16 ÷ (-8) = -2 11. -20 ÷ (-5) = 4

5. -20 + (-5) = -25 12. (-3)(-4)(-2) = - 24

6. -3 – 15 = -18 13. 6 + 4 – (-2) = 12

7. (-5)(12) = - 60 14. (-2)(3)(-5)(2) = 60

15. The Saints lost 4 yards on one play. On the next play, they moved forward 7 yards. What is the result of the two plays combined?

+ 3 yards

16. Over a 5 hour period, the temperature fell from 6°F to -3 °F. What was the overall change in temperature?

9°F

17. A group of hikers descends 35 meters in 5 hours. What is the average change in their position in meters per hour?

7 meters per hour

18. A diver’s depth changed -8 feet per second for 7 seconds. How many feet did the diver’s depth change?

- 56 feet

19. Jerry has -45 points. He wins 125 points, and then loses 30 points. How many points does he have now?

110 points

20. Michelle answers 6 questions correctly and 4 questions incorrectly. Each correct answer is worth 5 points and each incorrect answer is worth -2 points. How many points does Michelle have?

22 points


Unit 6, Activity 3, Coordinate Graphing


Unit 6, Activity 5, Words to Equations to Tables to Graphs

Directions: Complete the tables below. Show all work on a separate sheet of paper. After completing the tables, create graphs of each line on a coordinate plane using graph paper.

1. Equation: y = x + 2 2. Equation: 2x + y = -4

x - coordinate

y – coordinate

Ordered pair

-2-1012

3. Equation: y = 2x + 5 4. Equation: y = 2x – 8

x-coordinate

y - coordinate

Ordered pair

-2-1012

5. Write the verbal descriptions of the equations in problems 1 and 4.

6. Using the equation, y = - x + 5, create a table and a graph.

7. From the verbal description, y is the same as three times x increased by 2, write an equation, develop a table and create a graph.


x - coordinate

y - coordinate

Ordered pair

-2-1012

x - coordinate

y - coordinate

Ordered pair

-2-1012

Unit 6, Activity 5, Words to Equations to Tables to Graphs with Answers

Name _______________________________ Date ______________

Directions: Complete the tables below. Show all work on a separate sheet of paper. After completing the tables, create graphs of each line on a coordinate plane using graph paper.

1. Equation: y = x + 2 2. Equation: 2x + y = -4

x - coordinate

y – coordinate

Ordered pair

-2 0 (-2,0)-1 1 (-1,1)0 2 (0,2)1 3 (1,3)2 4 (2,4)

3. Equation: y = 2x + 5 4. Equation: y = 2x – 8

x-coordinate

y - coordinate

Ordered pair

-2 1 (-2, 1)-1 3 (-1,3)0 5 (0,5)1 7 (1,7)2 9 (2,9)

5. Write the verbal descriptions of the equations in problems 1 and 4.

1. y is the same as a number increased by 2.2. Twice a number increased by a number is -4.3. y is twice a number increased by 5.4. y is twice a number decreased by 8.

6. Using the equation, y = - x + 5, create a table and a graph.

7. From the verbal description, y is the same as three times x increased by 2, write an equation, develop a table and create a graph.

y = 3x + 2


x - coordinate

y - coordinate

Ordered pair

-2 0 (-2,0)-1 -2 (-1,-2)0 -4 (0,-4)1 -6 (1, -6)2 -8 (2, -8)

x - coordinate

y - coordinate

Ordered pair

-2 -12 (-2, -12)-1 -11 (-1, -11)0 -8 (0, -8)1 -6 (1, -6)2 -4 (2,-4)

Unit 6, Activity 6, Solving Equations

Name ________________________________ Date _____________

Directions: Solve the following equations and check to verify that each answer is correct. Use a separate sheet of paper if necessary.

1. 5 + m = - 12 2. 5x – 12 = 38 3. + 7 = 10

4. 4x – 3.8 = 12.2 5. – 3x – 7 = 14 6. k + 4.7 = 35

Set up and solve an equation for each situation.

7. Jamal’s friend gave him 27 baseball cards. Jamal now has 146 baseball cards. How many baseball cards did Jamal have before his friend gave him cards?

8. Melissa earns $7.50 per hour working at the mall. If she earned $108.75 this week, how many hours did she work?

9. A group of Peace Corps volunteers received a care package and split it evenly among the group of 7. If each person received 5 bottles of water, how many bottles of water were in the package?

10. To raise money for a competition, the cheerleaders sold pom poms for $1.50 each. Their parent booster club donated $50. If their fundraising goal was $500, how many pom poms do they need to sell to reach their goal?


Unit 6, Activity 6, Solving Equations with Answers

1. 5 + m = - 12 2. 5x – 12 = 38 3. + 7 = 10

m = -17 x = 10 d = 9

4. 4x – 3.8 = 12.2 5. – 3x – 7 = 14 6. k + 4.7 = 35

x = 4 x = -7 k = 30.3

Set up and solve an equation for each situation.

11. Jamal’s friend gave him 27 baseball cards. Jamal now has 146 baseball cards. How many baseball cards did Jamal have before his friend gave him cards?

x + 27 = 146; x = 119

12. Melissa earns $7.50 per hour working at the mall. If she earned $108.75 this week, how many hours did she work?

7.50x = 108.75; x = 14.5

13. A group of Peace Corps volunteers received a care package and split it evenly among the group of 7. If each person received 5 bottles of water, how many bottles of water were in the package?

= 5; x =35

14. To raise money for a competition, the cheerleaders sold pom poms for $1.50 each. Their parent booster club donated $50. If their fundraising goal was $500, how many pom poms do they need to sell to reach their goal?

1.5x + 50 = 500; x =300


Unit 6, Activity 8, Fall Sports Banquet

Name: _____________________________________

Directions: Use the information below to plan for proper seating at your school’s fall sports banquet where your top athletes will be honored. Show all work. Use additional paper if necessary.

Arrangement #1: Tables are separate, no sides touching. 2 tablesUse the square tiles or drawings to help you complete the table. Record the number of people that can sit at a given number of tables. Each square tile represents one table and only one person can sit on each side of the square.

Number of Tables

Number of People

1 42345

1. Describe any patterns you notice.

2. Without using the tiles or drawing a picture, can you determine the number of people who could sit at 6 tables? _____ 7 tables? _______

Describe how you came up with these values. Is there another way you could have thought about it?

3. How many people can sit at 20 tables? Explain in words how you determined this.

4. How many people would be able to sit if there were 100 tables?

5. Describe in words how you would figure how many people can sit at any number of tables.

6. Translate your words in question 5 into numbers and symbols to write a number sentence that describes how to determine the number of people can be seated given any number of tables.

7. If the Function Coordinator lets 137 people into the banquet hall, how many tables would be needed? Show or explain how you know.


Unit 6, Activity 8, Fall Sports Banquet with Answers


Arrangement #1: Tables are separate, no sides touching. 2 tablesUse the square tiles or drawings to help you complete the table. Record the number of people that can sit at a given number of tables. Each square tile represents one table and only one person can sit on each side of the square.

Number of Tables

Number of People

1 42 83 124 165 20

1. Describe any patterns you notice.Answers will vary.

2. Without using the tiles or drawing a picture, can you determine the number of people who could sit at 6 tables? 24 7 tables? 28


3. How many people can sit at 20 tables? Explain in words how you determined this.80

4. How many people would be able to sit if there were 100 tables?400

5. Describe in words how you would figure how many people can sit at any number of tables.multiply the number of tables by 4

6. Translate your words in question 5 into numbers and symbols to write a number sentence that describes how to determine the number of people given any number of tables.

p = number of people t = number of tablesp = 4tDifferent variables may be used, but they should be defined.


The coordinator will need at least 35 tables.


Unit 6, Activity 8, Fall Sports Banquet


Arrangement #2: Tables touch at one side. 2 tablesUse the square tiles or drawings to help you complete the table. Record the number of people that can sit at a given number of tables. Each square tile represents one table and only one person can sit on each side of the square.

Number of Tables

Number of People

2 6345


2. Without using the tiles or drawing a picture, can you determine the number of people who could sit at 6 tables? _____ 7 tables? _______


3. How many people can sit at 20 tables? Explain in words how you determined this.

4. How many people would be able to sit if there were 100 tables? (Assume the room will accommodate 100 tables in a straight line.)

5. Describe in words how you would figure how many people can sit at any number of tables.

6. Write a number sentence for your answer in question 5 that describes how to determine the number of people for a given number of tables.





Arrangement #2: Tables touch at one side. 2 tablesUse the square tiles or drawings to help you complete the table. Record the number of people that can sit at a given number of tables. Each square tile represents one table and only one person can sit on each side of the square.

Number of Tables

Number of People

2 63 84 105 12


Answers will vary.

2. Without using the tiles or drawing a picture, can you determine the number of people who could sit at 6 tables? 14 7 tables? 16


3. How many people can sit at 20 tables? Explain in words how you determined this.42

4. How many people would be able to sit if there were 100 tables? (Assume the room will accommodate 100 tables in a straight line.)

202

5. Describe in words how you would figure how many people can sit at any number of tables.Multiply the number of tables by 2 and add 2 OR add 1 to the number of tables and then

multiply that number by 2.

6. Write a number sentence for your answer in question 5 that describes how to determine the number of people for a given number of tables.

p = number of people n = number of tablesp = 2n + 2 or p = 2(n+1)different variables may be used, but they need to be defined




The coordinator will need at least 68 tables.


Unit 6, Activity 9, Quadrant I Grid

Name _________________________________ Date ______________ Hour ____________


x

y

Unit 6, Activity 10, Not Necessarily Equal

Name ____________________________ Date ________________

Directions: Solve the following inequalities and graph the solution on a number line.

1. x + 5 > 15 6. -4d + 7 < 19

2. x – 3 < 14 7. – x – 8 ≥ 10

3. 2x + 2 ≤ 10 8. 2x + 3 < - 15

4. -3t > 12 9. - 7 ≤ - 3

5. ≥ 4 10. y + 6.8 > 8.2

Directions: For the following problems, write an inequality to represent each problem, solve the inequality, and graph the solution on a number line.

11. Jasmine has $62.00 and plans to purchase tickets for a concert. If the concert tickets cost $18.00 each, how many tickets can Jasmine buy without exceeding her $62.00?

12. To avoid fees, Jacob has to have at least $300.00 in his savings account at the end of each month. Because of an unexpected expense, on the 8th of the month, his balance is $75.00. If he earns $25.00 for each lawn he mows, how many lawns must he mow before the end of the month in order to have a balance of at least $300.00 in his savings account?

13. The cab driver charges a flat fee of $8.00 plus $0.45 per mile. If James has only $26.00 in his pocket, how many miles can he afford to pay for?


Unit 6, Activity 10, Not Necessarily Equal with Answers

Name ____________________________ Date ________________

Directions: Solve the following inequalities and graph the solution on a number line.

1. x + 5 > 15 6. -4d + 7 < 19

x > 10 d < 3

2. x – 3 < 14 7. – x – 8 ≥ 10

x < 17 x≤ 18

3. 2x + 2 ≤ 10 8. 2x + 3 < - 15

x ≤ 4 x < -9

4. -3t > 12 9. - 7 ≤ - 3

t < -4 x 16

5. ≥ 4 10. y + 6.8 > 8.2

x ≤ -8 y > 1.4

Directions: For the following problems, write an inequality to represent each problem, solve the inequality, and graph the solution on a number line.

11. Jasmine has $62.00 and plans to purchase tickets for a concert. If the concert tickets cost $18.00 each, how many tickets can Jasmine buy without exceeding her $62.00?

18x ≤ 62; x ≤ 3 Jasmine can buy 3 tickets.

12. To avoid fees, Jacob has to have at least $300.00 in his savings account at the end of each month. Because of an unexpected expense, on the 8th of the month, his balance is $75.00. If he earns $25.00 for each lawn he mows, how many lawns must he mow before the end of the month in order to have a balance of at least $300.00 in his savings account?

25x + 75 ≥ 300; x ≥ 9 Jacob must mow at least 9 lawns.

13. The cab driver charges a flat fee of $8.00 plus $0.45 per mile. If James has only $26.00 in his pocket, how many miles can he afford to pay for?

0.45x + 8 ≤ 26; x ≤ 40 James can travel up to 40 miles.


Unit 7, Activity 3, Real-Life Algebra

Name ___________________________________ Date ___________________

Write real world situations for each of the expressions or equations below.

1. n + 8

2.

3. 4x = y

4. = y

5. 3k + 2 = z

6. For # 5 above, create a table of x- and y- values and draw a graph to represent the situation.


Unit 7, Activity 4, Real-Life Algebra, Too

Write an equation or inequality to represent each of the real-life situations below. Then solve the equations or inequalities to find the answer to the problem. Show all work.

1. On one day of their vacation, the Brown family drove 195 miles at a speed of 65 miles per hour before stopping for lunch. How many hours did they drive during this period?

2. Jacob pays thirty dollars per month plus five cents per minute to use his cell phone. If his cell phone bill this month was one hundred and thirty five dollars, how many minutes did he talk?

3. Sherry is five years older than seven times Lisa’s age. If Sherry is thirty-three years old, how old is Lisa?

4. Mr. Smith needs at least sixty points to win the prize. He has twelve points and earns three points for each correct answer. How many more correct answers does he need to get to have at least sixty points?

5. Laura’s mother gave her some money to go to the store. She spent $6.38 at the store and has $17.12 left in her purse. How much money did her mother give her?

6. Jordan has $35 to spend at the book store. He finds his favorite book for $23.75. He decides to spend the remaining money on pencils that cost $0.50 each. How many pencils can he buy without exceeding the $35? (Assume tax has already been included in the prices.)


Unit 7, Activity 4, Real-Life Algebra, Too with Answers

Write an equation or inequality to represent each of the real-life situations below. Then solve the equations or inequalities to find the answer to the problem. Show all work.

1. On one day of their vacation, the Brown family drove 195 miles at a speed of 65 miles per hour before stopping for lunch. How many hours did they drive during this period?

h represents the number of hours drive65h = 195. They drove 3 hours.

2. Jacob pays thirty dollars per month plus five cents per minute to use his cell phone. If his cell phone bill this month was one hundred and thirty five dollars, how many minutes did he talk?

m represents the number of minutes talked 135 = 0.05m + 30. Jacob talked 2100 minutes.

3. Sherry is five years older than seven times Lisa’s age. If Sherry is thirty-three years old, how old is Lisa?

s is Sherry’s age in yearsl is Lisa’s age in yearss = 7l + 5. Lisa is 4 years old.

4. Mr. Smith needs at least sixty points to win the prize. He has twelve points and earns three points for each correct answer. How many more correct answers does he need to get to have at least sixty points?

c is the number of correct answer Mr. Smith needs 3c + 12 ≥ 60. Mr. Smith needs at least 16 more correct answers.

5. Laura’s mother gave her some money to go to the store. She spent $6.38 at the store and has $17.12 left in her purse. How much money did her mother give her?

t is the amount of money Laura’s mother gave her t – 6.38 = 17.12. Laura’s mother gave her $23.50.

7. Jordan has $35 to spend at the book store. He finds his favorite book for $23.75. He decides to spend the remaining money on pencils that cost $0.50 each. How many pencils can he buy without exceeding the $35? (Assume tax has already been included in the prices.)

p is the number of pencils Jordan can buy 0.5p – 23.75 ≤ 35. Jordan can buy 22 pencils.


Unit 7, Activity 6, Going Fishing

Group Members: ___________________, ____________________,____________________

Follow the directions below to complete the activity.

Collect the data1. Use the cup to collect a sample of beans from the bag and pour the beans onto the paper

plate.2. Mark an “x” on both sides of the beans with the marker and count the beans. These are

your tagged “fish.” Total number of tagged fish ________.3. Return the tagged fish to the bag.

Recapture process4. Gently shake the bag.5. Remove the first sample from the pond using the cup and place them on the paper plate.

Count the total number of fish and the number of tagged fish in the sample and record in the table as sample 1.

6. Return all of the fish to the bag and gently shake to mix them up.7. Repeat steps 4 -7 until you have collected and recorded data for 10 samples.

1. Find the average number of tagged fish and total fish from all 10 samples.

2. Use the proportion below to estimate the total number of fish in your pond:

Average number of tagged in sample = Total number tagged in pond Average number in sample Total number of fish in pond

3. Based on your calculations what is the estimated population in the pond? _______4. Count all the fish in the bag. What is the actual population in the pond? _______5. How close was your population estimate to the actual population? __________


Sample Number

Number of tagged fish in

sample

Total number of fish in sample

12345678910

Average

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