Math Unit Lessons

Illustrative Math Grade 7 Unit 4 Review

by Tracey Harris

​

Warm - up​​

​Complete the first strategy section of the Unit 4 Study Guide.

​Explain how you solve measurement error and percent error questions.

​Measurement Error and Percent Error

What strategy (steps) have we been using in class to solve measurement error and percent error questions?

​Measurement Error and Percent Error

1. ​Identify Actual and Estimate

2. ​Find Error: (Difference between actual and estimate.

3. ​Form ratio: Error/Actual

4. ​Convert to Decimal

5. ​Convert to a percentage.

​Learning Targets (Unit 4 Lessons 13 and 14)

​

I can represent measurement error as a percentage of the correct measurement.​

​

I can solve problems that involve percent error.

​Measurement error

​

Measurement error is the positive difference between a measured amount and the actual amount.

​Percent error

​

Percent error is a way to describe an error, expressed as a percentage of the actual amount.

​Practice Problem 1

​A graduated cylinder actually contains 7.5 milliliters of water. When Han measures the volume of the water inside the graduated cylinder, his measurement is 7 milliliters. What is the percent error for Han’s measurement?

​Practice Problem 1

​A graduated cylinder actually contains 7.5 milliliters of water. When Han measures the volume of the water inside the graduated cylinder, his measurement is 7 milliliters. Which of these is closest to the percent error for Han’s measurement?

​

​A. 107.1%

B. 93.3%

C. 7.1%

D. 6.7%

​Practice Problem 2

​The students measured length during a science experiment, they got 12 cm. But the actual measurement was 14.25 cm. What was the percent error?

​

​

​Practice Problem 2

​The students measured length during a science experiment, they got 12 cm. But the actual measurement was 14.25 cm. What was the percent error?

​

​A. 7.1%

B. 15.79%

C. 17.1%

D. 61.7%

​Practice Problem 3

​

The attendance for the basketball game was estimated to be 5,000 people but 3,500 people attended. What was the percent error?

​

​

​Practice Problem 3

​The students measured length during a science experiment, they got 12 cm. But the actual measurement was 14.25 cm. What was the percent error?

​

The percent of error is about 42.9%.

​Practice Problem 4

​

George estimated that he scored a 75% on his math test.  To his surprise, he actually scored an 87%.  What was his percent error?

​

​

​Practice Problem 4

​George estimated that he scored a 75% on his math test.  To his surprise, he actually scored an 87%.  What was his percent error?

​

​

​

The percent of error is about 13.7%.

​Learning Targets (Unit 4 Lessons 6 and 7)

​When I know a starting amount and the percent increase or decrease, I can find the new amount.

​

I understand that if I know how much a quantity has grown, then the original amount represents 100%.

​

When I know the new amount and the percentage of increase or decrease, I can find the original amount.

​Percentage Increase

​

A percentage increase tells how much a quantity went up, expressed as a percentage of the starting amount.

​

For example, Elena had $50 in the bank on Monday. She had $56 on Tuesday. The amount went up by $6.This was a 12% increase because 6 is 12% of 50. 

Percentage Decrease

A percentage decrease tells how much a quantity went down, expressed as a percentage of the starting amount.

​

For example, a store had 64 hats in stock on Friday. They had 48 hats left on Saturday. The amount went down by 16.This was a 25% decrease because 16 is 25% of 64.

​

​

​Solving problems that involve percent increase and decrease

What strategy (steps) we have been using in class to solve measurement error and percent error questions?

​Solving problems that involve percent increase and decrease

​

1. Know the original value represents 100% of the original value.

2. ​Add/subtract the new percentage of value.

3. ​Write both in decimal.

4. ​Combine decimals.

5. ​Multiply or divide as needed.

Practice Problem 5

A practice field is 250 feet long. The game field is 40% longer than the practice field. How long is the game field?

​

​

Practice Problem 5

A practice field is 250 feet long. The game field is 40% longer than the practice field. How long is the game field?

​

​350 feet

Practice Problem 6

​A bakery used 25% less butter this month than last month. If the bakery used 240 kilograms of butter last month, how much did it use this month?

 

Practice Problem 6

​A bakery used 25% less butter this month than last month. If the bakery used 240 kilograms of butter last month, how much did it use this month?

​

 

​180 kilograms

​Learning Targets (Unit 4 Lesson 11)

​I understand and can solve problems about commission, interest, markups, and discounts.

​

​

​There are many everyday situations where a percentage is added to or subtracted from that amount, for a number of reasons including payment of income or purchasing an item of clothing.

​Vocabulary (Unit 4 Lesson 11)

Solve problems involving commission, interest, markups, and discounts.

1. ​Make sense of the problem.

2. Know the original value represents 100% of the original value.

3. ​When the original price is unknown use a variable like x.

4. ​Add/subtract the new percentage from the original percentage.

5. ​Write percentages as a decimal.

6. ​Multiply or divide as needed.

7. ​Is my answer reasonable?

Practice Problem 7

​Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

​

Noah paid $28 for the jeans after using the coupon. What is the regular price of the jeans?

​

 

​

Practice Problem 7

​Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

​

Noah paid $28 for the jeans after using the coupon. What is the regular price of the jeans?

​

​The regular price of the jeans is $40?

​

 

Practice Problem 8

​Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

​

The regular price of a hoodie is $27. What did Noah pay for the hoodie?

​

 

​

Practice Problem 8

​Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

​

The regular price of a hoodie is $27. What did Noah pay for the hoodie?

​

​With the 30% coupon, Noah paid $18.90 for the hoodie. 

​

Practice Problem 9

​Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

​

If the regular price of an item is x dollars, what is the discount price in dollars? (Hint: Your final answer will include a variable.)

​

 

​

Practice Problem 9

​Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodie and a pair of jeans.

​

​If the regular price of an item is x dollars, what is the discount price in dollars? (Hint: Your final answer will include a variable.)

​

​ (0.70)(x)

​

​

 

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

Practice Problem 10

​Jada’s sister works in a furniture store.

​

Jada’s sister earns $15 per hour. The store offers her a raise—a 9% increase per hour. After the raise, how much will Jada’s sister make per hour?

​

​

 

​

Practice Problem 11

​Jada’s sister works in a furniture store.

​

​The store purchased a table for $200 and sold it for $350. What percentage was the markup?

​

​

 

​

Practice Problem 12

​Jada’s sister works in a furniture store.

​

Jada’s sister earns a commission. She makes 3.5% of the amount she sells. Last week, she sold $7,000 worth of furniture. How much was her commission?

​

 

​

​Learning Targets (Unit 4 Lesson 10)

I understand and can solve problems about sales tax and tips.

​Solving problems that involve tax and tips

1. ​Know the original value represents 100% of the original value.

2. ​Add/subtract the new percentage of value.

3. ​Write both in decimal.

4. ​Combine decimals.

5. ​Find the amount of taxes or tips (if not given).

6. Use correct operations as needed.

Practice Problem 13

​Kiran’s mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20% as a tip. What is the total after the discount and tip? Explain or show your reasoning.

Practice Problem 13

​Kiran’s mother gets a restaurant bill for $25. She has a coupon for 15% off. After the discount is applied, she adds 20% as a tip. What is the total after the discount and tip? Explain or show your reasoning.

​

​$25.50. The coupon takes away 15% of $25, which is $3.75. The cost after the coupon is $21.25. The added tip is $4.25, 20% of $21.25. The total is $25.50, the sum of $21.25 and $4.25.

​Learning Targets (Unit 4 Lesson 2)

I can solve problems about ratios of fractions and decimals.

​

Ratio: a quantitative comparison between two amounts

​

Dependent variable: a variable (often denoted by y ) whose value depends on that of another.

​

Independent Variable: a variable (often denoted by x ) whose variation does not depend on that of another.

​Learning Targets (Unit 4 Lesson 10)

I understand and can solve problems about sales tax and tip.

​Solving problems about ratios of fractions and decimals.

1. Use division to find the rate in miles per hour (k = y/x)

2. ​Understand relationship between variables.

3. ​hours (x) independent variable

4. ​miles (y) dependent variable

5. ​Show work.

Practice Problem 14

It takes Deigo 1/24 of an hour to complete a lap on a circular bike track. The track is 1/3 mile long. What is Diego's speed? (Hint: How fast is Deigo going in miles per hour?)

​

​Show work:

Practice Problem 15

A cyclist rode 3 3/4 miles in 3/10 hours. How fast was the cyclist going in miles per hour?

​

​Show work:

Practice Problem 16

Cool Down Practice Problems 3 and 4

The attendance for the basketball game was estimated to be 5,000 people but 3,000 people attended. What was the percent of error?

​

​George estimated that he scored 75% on his math test. To his surprise, he actually scored 87%. What was his percent error?

Multiple Choice

The attendance for the basketball game was estimated to be 15,000 people but 12,500 people attended. What was the percent error?

• 16.67%

• 20%

• 2500%

• 80%

Multiple Choice

The deer population is estimated to be 17,600 in northern Illinois, but an actual count was 21,300. What is the percent error?

• 21%

• 17.37%

• 17.4%

• 21.02%

Multiple Choice

Jessie estimates the weight of her cat to be 8 pounds.  The actual weight of the cat was 10 pounds.  Find the percent error.  

• 15%
• 20%
• 25%
• 30%

Multiple Choice

Find the total cost of a spa treatment that costs $42. The sales tax is 6% and you want to leave a 20% tip.

• 52.92

• 67.20

• 44.42

• 89.04

Multiple Choice

A manicure costs $30. The sales tax is $1.50. What is the sales tax rate (percent)?

• 4%

• 7%

• 5%

• 6%

Multiple Choice

A customer wants to tip 15% on a restaurant bill that is $35. What will the total bill be?

• 40.25

• 5.25

• 30.75

• 5.75

Multiple Choice

A chair costs $279 and is marked up 24%. What is the selling price?

• $345.96

• $66.96

• $212.31

• $303

Multiple Choice

Walmart buys a yoga mat for $8.50. The markup is 75%. What does Walmart sell the yoga mat for?

• $6.37

• $2.13

• $12.50

• $14.87

Multiple Choice

What is 23% of 65?

• 14.95
• 15.95
• 16
• 13.75

Multiple Select

Tyler ate x fruit snacks, and Han ate 3/ 4 less than that. Select all of the expression for the number of fruit snacks Han ate.

• 1/4x

• Han ate 3/4 x less than the Tyler

• 1- 3/4x = 1/4x

• None of the above

Multiple Choice

Sally went to the clearance rack at a department store and found a shirt she wanted to buy.  The shirt was $36.00 and is on sale for $24.00.  What is the percent of the decrease?

• 33%
• 67%
• 50%
• 34%

Multiple Choice

Henry mowed 15 out of a total of 60 lawns. What percent of the lawns did he mow?

• 15

• 25

• 19

• 4

Multiple Choice

What is 10% of 15?

• 1.5

• 1.56

• 2.5

Multiple Choice

Did you meet the Learning Goal below?

I can solve problems about ratios of fractions and decimals.

• Yes

• No

• Not sure

Multiple Choice

In math, what does the word "of" mean

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Whitney's bill at dinner came to $26.00. She left $5.20 as a tip. What percent of a tip did she leave?

• 10%

• 15%

• 5%

• 20%

Multiple Choice

The iphone 11 costs $990. It is on sale for 15% off. What would the cost of the iphone be?

• $148.50

• $841.50

• $1138.50

• $905.50

Multiple Choice

It costs $89.50 to go to Adventure Land. I have a coupon for 12% off. What would I pay to get into Adventure Land if I use the coupon?

• $88.42

• $100.24

• $10.74

• $78.76

Multiple Choice

Sam bought a pair of chairs from Brown's Shoes for $86.25. The guy that sold them to me gets an 8% commission for every pair of shoes they sell. How much commission does the guy make?

• $6.90

• $93.15

• $79.35

• $8.90

Multiple Choice

There are 75 students in the school band.  45 students play woodwind instruments.  What percent of students play woodwinds?

• 35%
• 60%
• 55%
• 70%

Multiple Choice

The movie theater has 250 seats. 225 seats were sold for the current showing. What percent of seats are empty?

• 10%
• 20%
• 80%
• 90%

Multiple Select

Mai skated x miles, and Clare skated 3/5 farther than that. Select all the expressions for the distance Clare skated.

• 8/5x

• x + 3/5x = 8/5x

• 1 3/5x

• none of the above

Multiple Choice

What is 50% of 250?

• 100

• 125

• 50

• 150

Multiple Choice

In 1999, the price of unleaded fuel was $1.09.  In 2015, the price of unleaded fuel is $1.89.  What is the percent change?

• 173% increase
• 73% increase
• 73% decrease
• 27% increase

Multiple Choice

You guessed that there were 256 gumballs in the jar. There were actually 510. Find your percent error. Round to the nearest tenth if necessary.

• 49.8%
• 49.9%
• 50.2%
• 50.3%

Multiple Choice

18 is 30% of what number?

• 25

• 40

• 55

• 60

Multiple Choice

Solve mentally $$5\div\frac{1}{3}$$  

• 15

• $$\frac{5}{3}$$  

• $$\frac{15}{3}$$  

Multiple Choice

 A T-shirt launcher can launch 5 shirts in 20 minutes. What is the rate in shirts per hour?

• 4
• 100
• .40
• 55

Multiple Choice

Five lemons cost $1.80.What is the cost per lemon?

• .78
• .34
• .56
• .36

Multiple Choice

A TV that normally cost $800 is on sale for 33% off.  There is a 6% sales tax on the purchase.  What is the final cost of the TV?

• $536.00
• $568.16
• $279.84
• $321.60

Multiple Choice

You plan to purchase a plane ticket for $299.00 and you are going to use a discount code to receive 15% off.  How much will the ticket cost?

• $149.50
• $254.15
• $343.85
• $44.85

Multiple Choice

You are planning a vacation to Hawaii that will cost $5875, but if you schedule it today you can save 20%.  How much will you save by scheduling it today?

• $7050.00
• $4700.00
• $1175.00
• $117.50

Multiple Choice

Mrs. Frost is a real estate agent.  She earns 6% commission on her sales plus $2,000 each month.  Last month her sales totaled $523,250.00.  How much did she earn last month?

• $31,395.00
• $33,395.00
• $313,950.00
• $333,950.00

Multiple Choice

Henry earns $7.75 per hour.  He just received a 3% raise.  How much does he now earn if he works for 40 hours?

• $7.98
• $403.20
• $319.20
• $2.33

Multiple Choice

The number of students in the school went from 1028 down to 755.  What is the percent decrease?

• 26%
• 27%
• 36%
• 136%

Poll

Did you meet the  Learning Goal?

-When there is a constant rate, I can identify the two quantities that are in a proportional relationship.

• Yes

• No

• Kinda/Maybe

Multiple Choice

It costs $3.45 to buy $$\frac{3}{4}$$  lb of chopped walnuts. How much would it cost to purchase 7.5 lbs of walnuts?

• 46.00

• $34.50

• 13.80

• 56.25

Poll

What was your strategy for finding the cost of the Walnuts?

• I noticed that 7.5 is ten times $$\frac{3}{4}$$ , because 10 the decimal form of 3/4 is 0.75. So simply multiplied 3/4 by 10.

• I made drawings the represented 3/4 of walnuts. I kept making drawings of 3/4 walnuts until I had 7.5 walnuts. When I noticed that I made 10 drawings of 3/4 walnuts I multiplied 3.45 by 10 to get the answer 34.50.

• I used the following operation: $$3.45\div\frac{3}{4}=4.6$$ Then $$4.6\cdot7.5=34.50$$

• I used a different operation. Be prepared to share your strategy with the class.

Multiple Choice

It takes an ant farm 3 days to consume ½ of an apple. 

At that rate, in how many days will the ant farm consume 3 apples?

• 9

• 27

• 18

• 3

Multiple Choice

Kiran read for x minutes, and Andre read for 5/8 more than that. Which equation relates the number of minutes Kiran read with y , the number of minutes that Andre read.

• y=0.625x

• y=1.5x

• y=1.25x

• y=1.625x

Multiple Choice

Tony bought a $48 sweatshirt and used a coupon for a 10% discount. Keith bought an identical sweatshirt at a different store for $42.95. Which statement is true?

• Tony paid $0.25 less than Keith paid.

• Tony paid $4.95 less than Keith paid.

• Keith paid $0.25 less than Tony paid.

• Keith paid $4.95 less than Tony paid.

Multiple Choice

Erica saw a skateboard on sale for $59.95. The original price of the skateboard was $79.95. What is the approximate percent discount on the skateboard?

• 20%

• 25%

• 75%

• 80%

Multiple Choice

The number of fish in a lake decreased by 25% between last year and this year. Last year there were 60 fish in the lake. What is the population this year? If you get stuck, consider drawing a diagram.

• 45

• 35

• 15

• 3

Multiple Choice

A company claims that their new bottle holds 25% more laundry soap. If their original container held 53 fluid ounces of soap, how much does the new container hold?

• 62.5 fluid ounces

• 66.25 fluid ounces

• 67.85 fluid ounces

• 54.33 fluid ounces