1

Critical Terms Supplemental terms
Percent increase Tax
Percent decrease Gratuity
Percent error Area
Markdowns Simple interest
Markups Equivalent
Scale Ratio
Commission Proportion
Fee Primeter
Dimension Volume
Scale factor Similar figures
Scale Drawing
2

 Rates, ratios, percentages and proportional relationships can be applied to problem solving situations such as interest, tax, discount, etc.
 Rates, ratios, percentages and proportional relationships can be applied to solve multi-step ratio and percent problems.
 Scale drawings can be applied to problem solving situations involving geometric figures.
 Geometrical figures can be used to reproduce a drawing at a different scale.
Essential Questions:
 How can I use proportional relationships to solve ratio and percent problems?
 How can I use proportional relationships to solve percent of increase, decrease and error problems?
 How can I use proportional relationships to solve multi-step ratio and proportion problems?
 How can I use scale drawings to compute actual lengths and area?
 How can I use geometric figures to reproduce a drawing at a different scale?
3

Key Vocabulary Terms Visual Representations
Real-Life Examples
4

7.RP.3 - Analyze proportional relationships and use them to solve realworld and mathematical problems.
Use proportional relationships to solve multi-step ration and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
7.G.1 – Draw, construct, and describe geometrical figures and describe the relationships between them.
Solve problems involving scale drawing of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a sale drawing in a different scale.
5

Mathematical Practices:
(Practices to be explicitly emphasized are indicated with an *.)
*1. Make sense of problems and persevere in solving them. Students exhibit this standard when they represent and interpret proportional relationships to solve ratio and percent problems using visual models, proportions and other equations. They also make sense of proportional situations that involve the scale drawings using diagrams and equations.
*2. Reason abstractly and quantitatively. Students will reason about the value of the rational numbers in real-world contexts when representing and solving problems. They will apply proportional reasoning to scale drawing and determine if calculations are appropriate to the contexts.
3. Construct viable arguments and critique the reasoning of others. Students will be expected to articulate their problem solving processes and explain the connection between the various representations (visual, tabular, algebraic, real-life) used to solve problems involving scale drawing and other proportional relationships.
*4. Model with mathematics. Students will use double number lines, tape diagrams and ratio charts to represent real-world situations involving proportional relationships.
5. Use appropriate tools strategically. Students are expected to select appropriate measurement and construction tools when reproducing scale drawings.
6. Attend to precision. Students will attend to the units of measurement when solving and representing problems with scale drawings. They will also attend to precise mathematical language when interpreting and communicating about problem solving with ratio and percent situations.
7. Look for and make use of structure. Students look for patterns when solving proportional relationships and interpreting scale drawings.
8. Look for and express regularity in repeated reasoning. Students use repeated reasoning when they replicate drawing at different scales.
6

Lesson 1 of 4
I Can…
 Solve problems involving simple interest and tax
 Solve problems involving markups and markdowns, gratuities and commissions, and fees.
Purpose: Students will be able to solve problems involving simple interest and tax. Students will be able to solve problems involving markups and markdowns, gratuities and commissions, and fees.
7

Lesson 1, Segment 1: Visual Models
WARM-UP
PRE-Assessment: visual Models
Use a tape diagram, table, or number lines to solve the following problems.
1.
If 75% of the budget is $1200, what is the full budget?
2.
There are 400 7 th graders at school. 80% say pizza is their favorite food. How many students do not like pizza?
3.
A pair of shoes sells for $95. If you have a 10% off coupon, how much will you save?
4.
There are 110 boys in 7 th grade. 15 make the basketball team. What percent of boys make the team?
5.
After a 15% discount, the price of a couch is $750. What was the original price of the couch?
8

Whole Group Discussion (after pre-assessment) with focus on: o Multiple ways to solve each problem o Connections between problems o Proportional relationships within problems
Use space below to take notes (use the back of this page, if needed):
Homework:
Find an example using percent, such as an advertisement, coupon, news article, etc. to share with the class.
9

Lesson 1, Segment 2 of 8: Double Number Line Review
Warm-Up
1) What is a double number line? Explain in words, then draw an example.
2) When would you use a double number line? Give a specific example.
3) What does each part of a double number line represent?
Skill Review 1:
Video: http://www.youtube.com/watch?v=2NYSq_i1i3Q
Use the space below for notes and practice problems:
10

Skill Review Name______________________
11

Lesson 1, Segment 3: Sample Percent Questions
Warm-Up
Look at your Sample Percent that you brought to class, and answer the following questions.
1.
What is PERCENT?
2.
What does the PERCENT in your example represent?
3.
Give at least one other example of a percent that is different than the one you brought.
12

13

14

15

(Class Discussion Questions for Percent problems brought to class may differ.)
1. Sale ads:
- Take a look at the different sale ads. What does it mean for a clothing item to be, say, 15% off?
- How does the percent off affect how much is actually paid?
- How might a sale impact the amount of tax paid on an item?
2. Polls
- What does it mean to say 75% of students like pizza?
3. Sports
- If a player makes 65% of shots, how do you determine how many shots were made or missed?
4. Probability
- Does a 20% change of snow mean it will snow 20% of the time? Explain.
5. Total
- 12% of the daily recommended calories allows you how many calories?
16

Lesson 1, Segment 3 continued: On Sale Activity
The ‘Video Game Wars’ have begun! The stores
are competing for your business and are having
sales. Review the sale prices for a game that
costs $55 and answer the following questions.
1.
Which store offers the best deal?
_______________________________________________________________________
Justify your answer.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
2.
Which store offers the worst deal?
________________________________________________________________________
Justify your answer.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
17

Formative Feedback Sheet:
Name ___________________ Date____________________ # __________
Feedback from:
____Teacher _____Peer ______Self _____Other___________________
Did the student understand the problem?
Comments
Did the student make a plan? Circle any that apply – a) solve a simpler problem b) make a diagram c) make a table d) solve part of the problem
Comments
Did the student carry out the plan and attend to precision?
Comments
Did the student critique his/her own work?
Comments
Class Discussion: How did you solve these problems?
18

Lesson 1, Segment 3 continued: Challenge Board
Online activity (can be played as a 1 player or 2 player game) http://www.quia.com/cb/845397.html
19

Name___________________________________ Period____________
Unit 2, Lesson 1, Seg 3: Homework: PERCENTS
Date____________________
1. A pet store sells dog food for $26 for a 40 pound bag. If you have a 15% coupon, how much will the dog food cost?
2. Mandy has a store cash certificate for $10 to a store. She also has a 10% coupon for the purchase of a single item but it cannot be used with any other offer. If Mandy wants to buy a purse for $89.99 which way should she pay for it? Show work supporting your answer.
3. James wants to buy a gift valued at $50 for his mom. He has a coupon for 20% off. If he waits until Friday to buy the gift the store will double the coupon. How much will he pay for the gift if he buys it on Friday?
4. A survey says that 80% of the population in Harrisburg wants to build a new community center. If the population of Harrisburg is 6,780 people, how many people want the community center?
20

5. Two car dealers have the same car on their lot. Dealer A offers the car for $15,788. Dealer B offers the car for $17,590 but has a promotion discounting it by 10%. Which is the best deal? Show work to support your answer.
6. A Nike store offers Air Jordan’s for a regular price of $125 apiece. The store offers a special buy one, get one half price. You also have a coupon for 25% off your total purchase. If you buy two pairs of shoes, what will be the total cost with the special offer and the 25% off?
21

Lesson 1, Segment 4 Percent with Tape Diagrams
WARM-UP
THINK!
Represent the following situation visually:
Two-thirds of the students in Mr. Coley’s physical education class chose softball as their favorite sport.
If there are 24 students in class, how many students chose softball?
PAIR! – Turn to your partner and discuss your answers.
Remember to talk about:
Does their answer make sense to you? If not, ask them to explain.
Do you agree with their answer? Why or Why not?
Is it ok if your answers are not the same?
SHARE! – We will discuss your answers as a class
Take Notes Here (use back of page if needed):
22

Lesson 1, Segment 4 continued: Percent with Tape Diagrams
The 7 th grade basketball team won 20 of 25 games. The 8 th grade basketball team won 15 of 20 games.
Which team had a greater winning percentage? Justify your answer using a tape diagram.
Step 1: The diagrams below show 100% for each basketball team. Start by dividing each bar into 5 pieces.
Label the percent so that each section will represent 20%.
7 th grade:
100%
Games
8 th grade:
100%
Games
Step 2: Find the number that belongs in each section for the games bars. 7 th grade 25 divided by 5,
8 th grade 20 divided by 5.
Step 3: Determine how many sections to shade on each bar. Shade the sections.
Step 4: Compare bars to determine answer.
_______ grade had a greater winning percentage.
23

Lesson 1, Segment 4 continued: Percent with Tape Diagrams
SCAVENGER HUNT
 You and your partner will start at a percent problem together.
 You will each work out the problem on the next page, and compare answers.
 When you agree on an answer, find that answer somewhere else in the room.
 Complete the problem next to the answer you found.
 Repeat until all problems are completed. o HINT: If you can’t find the answer in the room, check your work!
24

Name______________________________________ Date______________
SCAVENGER HUNT: PERCENT PROBLEMS WITH TAPE DIAGRAMS
25

Name ____________________________
HOMEWORK: Percent – Tape Diagrams
1.
50 is 20% of what number? _______________
2.
What number is 70% of 250? _______________
3.
What percent of 20 is 4? _______________
4.
40% of what number is 82? _______________
5.
What percent of 90 is 36? _______________
26
Date _____________

Lesson 1, Segment 5 - Tax
Write each percent as a decimal:
1.
6.5%
2.
15%
3.
7.25%
WARM-UP
27

Lesson 1, Segment 5 continued - Tax
Think-Pair-Share: Tax
Answer these questions on your own.
1. Why do people pay tax?
2. When/who collects tax? Explain.
3. How do you determine how much money to give as tax?
Turn to your partner and share your answers.
Ask your partner questions about his or her answers.
Write down anything you would like to add here:
Class Discussion
Why do we pay tax?
Who collects tax?
How do you determine tax?
28

Lesson 1, Segment 5 continued - Tax
Performance Task:
Work in your groups to answer the following questions.
29

Lesson 1, Segment 5 continued - Tip
Think-Pair-Share: Tip
Answer these questions on your own.
1. Why do people give money as a tip?
2. When/to whom should you give a tip to? Explain.
3. How do you determine how much money to give as a tip?
4. Is it important to give an exact amount as a tip? Why or why not?
Turn to your partner and share your answers.
Ask your partner questions about his or her answers.
Who gets a tip? Why?
How do you determine tip?
Should tip be exact? Why?
Write down anything you would like to add here:
Class Discussion
**Tip Tricks**
30

Lesson 1, Segment 5 continued: Sales Tax and Tip Activity
How to play:
Draw a Card and display a dollar amount for all to see.
Spin for a sale tax or tip percentage.
15%
$65.00
Solve the problem.
15% of $65.00
Show your work and record your answers on the following page.
31

Name__________________________
Amount from
Card Drawn
Percent Tax or
Tip from Spinner
Sales Tax & Tip Activity Answer Document
Show work and Circle Answer
32

Name_________________________________
Homework: Tax and tip
1.
Date:_________
John buys a new video game for $19.99. Sales tax is 7.5%. What is the amount of sales tax he will pay?
5.
6.
4.
2. Patty would like to leave a 15% tip on her $62 dinner order. How much will she leave for a tip?
3. You lunch bill is $19.75. A 5% sales tax will be added, and you want to give a tip of 20% on the
$19.75. How much total will you pay for lunch?
Your neighbor pays $40 to have her lawn mowed and always adds a 15% tip. You and your friend decide to mow the lawn together and split the earnings evenly. How much will each of you make?
If Linda pays $160.50 for a new phone and paid 7% tax, what was the cost of the phone?
Michael purchased a car for $23,081.10. The sticker price was $21,982. What was the percent of tax charged on the purchase?
33

Lesson 1, Segment 6 Commission and Fees
WARM-UP
1. The price of a coat is $114 before sales tax. The sales tax is 7%. Find the total cost of the coat.
2. You wait tables in a restaurant. You consider a tip of %15 or more to be a good tip. A family has a bill of
$86.29. They leave you a $12 tip. Is that a good tip? Explain.
Try this: Commission
For some sales jobs, the employee earns a commission. This is a percent of the amount of sales. The sales go to the company, and the company pays commission to the employee.
Example 1:
At Larry's Auto Dealership, Larry earns 7% commission on every Rambler SUV he sells.
Each Rambler sells for $33,000.
Last month Larry sold 4 Rambler SUV's.
How much commission did he make last month?
How much money did Larry make for his company in sales, if he sold 4 Rambler SUV’s?
How much is his commission, based on that amount?
If Larry makes $2000 plus commission each month, how much money did he make last month?
34

Example 2:
Howard sold $3500 worth of jewelry this past week. If he earns an 8% commission, how much did he earn in commission??
If Howard makes $1,500 a month plus commission. If he continues to sell $3,500 worth of jewelry each week, how much did he make this month (assume 4 weeks in a month)?
Example 3:
Anthony receives a 9% commission on magazine subscription sales. Last week, his total sales were $1,800.
How much commission did he earn?
If Anthony’s weekly sales remain constant and he makes $900 a month plus commission, how much did he make during the months of January and February (assume 4 weeks in a month)?
35

Fees
Some businesses charge a restocking fee when their customers return merchandise for a refund of the selling price. The amount can range from 1% to over 50% of the full retail cost of the item.
Example 1:
Juan’s business has a 5% restocking fee for any jewelry returned. If a customer returns an item purchased for $875, how much money will the customer be reimbursed?
Example 2:
A track coach ordered medals from a trophy store, paying $540 for the order. The track meet was rained out and the coach returned the medals. The coach was reimbursed $496.80. What is this trophy store’s stocking fee as a percent?
36

Lesson 1, Segment 6 Commission and Fees continued: Commission and Fee Activity
How to play:
Draw a Card and display a dollar amount for all to see.
Spin for a commission or fee percentage.
$12,500
7.5%
Solve the problem.
7.5% of $12, 500
Show your work and record your answers on the following page.
37

Name__________________________
Amount from
Card Drawn
Percent
Commission or
Fee from Spinner
Sales Tax & Tip Activity Answer Document
Show work and Circle Answer
38

Name_____________________________ Homework: Commission
MONEY, MONEY, MONEY... MONEY!!
Show all work on a separate sheet of paper and staple to the worksheet.
COMMISSION
Commission is money earned as a percent of the amount made for the company.
For example: Joe sells cars. He earns 15% commission. If he sells 3 cars in a week for a total of$43,557, his commission is $6,533.55.
You find this by multiplying the total sales by the percent of commission (as a decimal).
43,557 x 0.15 = 6,533.55
You work for Wireless Cell Company. You earn 8% commission on all minute packages you sell. On Fridays, you earn 12% commission! The following table shows all the packages you sold last week. Find your total commission.
Package &
Price/month
Package 1
$11.99
Package 2
$14.99
Package 3
$24.99
Package 4
$39.99
Package 5
$74.99
Package 6
$99.99
DAY’S
TOTAL
DAY’S
COMMISSION
MONDAY
2
0
1
1
0
0
$88.96
TUESDAY
1
3
0
0
2
1
WEDNESDAY THURSDAY
0
1
2
4
1
0
2
3
1
5
2
1
FRIDAY
3
4
3
6
3
2
39

On Monday you sold 2 of Package #1 at $11.99 each, 1 of Package #3 at $24.99, and 1 of
Package #4 at $39.99. You had total sales of $88.96. Find your commission for Monday, and put it in the last box under MONDAY.
Now complete the table for the rest of the week.
What was the total commission for the whole week?_____________________
Your weekly salary is $350.00. What was your total earnings for the week?_______________
1. A credit card company gives a 1.5% fee on late payments balances. If you are late paying your bill and have a credit card balance of $1,342 last month, how much will they charge you in late fees?
2. The library has a policy of charging a 25% fee plus the cost of a book when it is returned damaged or it is lost. You lost a book costing $12.25. What is the total amount you will be charged for the book?
3. Your brother needs a tux for a wedding. A formal shop charges $120 plus a 20% cleaning fee on top of their rental if you have any stains on the tux. Your brother spills his dinner on the front shirt. What will be the total cost for the tux rental including the fee?
4. Michael loses his iPhone. His mom orders him a new one off Amazon for $150. While it is being delivered Michael finds his iPhone and wants to cancel the order. Amazon has already shipped it so they say there will be a $100 restocking fee. What percent of the order is the restocking feel.
40

Lesson 1, Segment 7: Simple Interest
WARM-UP
1. Great Bank Corp has free ATM usage for its customers but charges other people 2% for withdrawals. If a noncustomer withdraws $240, how much will they be charged for the ATM fee?
2. Jacob works at an appliance store. He gets paid $12 an hour plus a 5% commission on his weekly sales. How much did Jacob get paid last week if he worked 30 hours and sold $860 of merchandise?
Definitions:
1.
Principal –
2.
Simple Interest –
3.
Annual –
Formula:
I = prt
I - interest in dollars and cents p – principal r – rate as a decimal t- time in years
Examples:
1.
You borrow $300 for 5 years at an annual interest rate of 4%. What is the simple interest you pay in dollars?
2.
You deposit $500 into a 5.5% simple interest account. How long before the total amount is $665?
41

Segment 7 continued: Practice: In the computer lab
Simple Interest Game: http://www.math-play.com/Simple-Interest/Simple-Interest.html
Simple Interest Practice: http://www.aaamath.com/mny84x10.htm
42

Lesson 1, Segment 7 continued:
Let’s Practice! Simple interest: Matching
Write the number of the problem in the blank next to the correct answer. Round to the nearest cent.
Principal Yearly Interest Rate Years Simple Interest
7.
8.
9.
5.
6.
3.
4.
1.
2.
$398.75
$420.10
$875.00
$1,342.38
$2,134.77
$986.50
$880.25
$699.99
$3,000.00
10. $719.30
11. $556.78
12. $410.50
13. $315.00
14. $600.00
15. $443.62
16. $1,050.00
17. $812.20
18. $5,000.00
19. $113.17
20. $386.49
21.
22.
$78.00
$2046.00
23. $525.15
17.35%
18.15 %
25 ¼ %
20 %
19.3 %
7 ¼ %
11 %
16.05 %
13 %
19 ½ %
28 %
8 5/8 %
23 %
16 %
18 %
12 1/8 %
6 ¾ %
11.6 %
9 %
6.8125 %
22 %
7 %
10 7/8 %
43
_____ $79.03
_____ $881.99
_____ $226.88
_____ $383.83
_____ $77.86
_____ $589.45
_____ $407.81
_____ $309.19
_____ $1,326.42
_____ $960.65
_____ $2,252.89
_____ $967.81
_____ $790.69
_____ $235.33
_____ $99.38
_____ $151.21
_____ $800.11
_____ $968.96
_____ $3,704.40
_____ $504
_____ $516.80
_____ $452.21
_____ $60.04
1.67
0.25
28
4
5.25
0.67
39
3.917
8
0.75
42
7.417
13
3
13.5
19
8.75
0.5
5
2.25
4.083
18
1.25

Name______________________________________
Homework: Simple Interest
1.
Find the simple interest on $2000 at 10% for 6 years.
2.
Find the simple interest on $340 loan at 7% interest for 3 years.
Date___________
3.
You invest $2000 in a simple interest account. The balance after 8 years was $2,720. What is their interest rate?
4.
Money Market: You deposit $5000 in an account earning 7.5% simple interest. How long will it take for the balance of the account to be $6500?
5.
Critical Thinking: You put $500 in an account that earns 4% annual interest. The interest earned each year is added to the principal to create a new principal. Find the total amount in your account after each year for 3 years
44

Lesson 1, Segment 8: Where in the Room?
Work with a partner to solve each problem. To check your answer, find it somewhere in the classroom.
Write the location of the answer on the answer document. You must show all your work, as well as your answer, and “Where in the Room” your answer is for each problem.
Problem Show your work Where in the room is it?
1. In a mayoral election, Ron Harris received 56% of the votes. There were
825 votes cast. How many votes did
Ron Harris receive?
2. Morris treated his friends to lunch.
The total bill for lunch was $32.60. He left a 15% tip for the waitress. How much money did he leave as a tip?
3. The skeleton accounts for about
12% of a person’s total body weight. If
Aaron weighs 150 pounds, what would you expect his skeleton to weigh?
4. Lakeisha buys a bicycle that costs
$200. With sales tax, she pays a total of $212.50. What is the rate of sales tax?
5. This week there is a 30% off sale at
Just Books. Vikram wants to buy a book that normally costs $16.40. How much will he pay for the book on sale?
6. Manuela has $800 in a savings account that earns 0.95% annual simple interest. If she makes no withdrawals or deposits, how much simple interest will her account earn in
4 years?
45

Problem Show your work
7. Mr. Harris sold a house for
$200,000. His commission for the sale was $8,000. What is the rate of commission that Mr. Harris received?
8. You order items from a menu that total $7.85. Your bill comes to $8.30, including tax. What is the percent of the tax? Round to the nearest tenth of a percent.
9. The price of a new version of a computer game is 120% of the price of the original version. The original version cost $48. What is the cost of the new version?
10. You go to a restaurant with four
other people. The total for the food is
$43.85. You need to add 5% for tax and 15% for tip. If you decide to split the bill evenly, how much will you pay?
11. Find the commission on a diamond that is sold for $6,700 when the commission paid is 4%.
12. A sales person receives a salary of
$300 per week and a 6% commission on all sales. How much does this salesperson earn in a week with
$2,540 in sales?
13. You buy a sweater for $18.75, which is 25% off the original price.
What was the original price?
Segment 9: Assessment
46
Where in the room is it?

Lesson 2 of 4:
Percent change (increase/decrease), percent error and scale factor
I Can…
 Use proportional relationships to solve percent increase, percent decrease, and percent (margin of) error.
Purpose: Students will be able to solve problems that contain percent increase, percent decrease and percent error.
47

Segment 1: Finding Percent of Change
WARM-UP
Solve each proportion.
1.
2
20
= n
100
2.
1
8
= n
100
3.
3
7
= n
100
4.
4
20
= n
100
Questions to think about…
What does it mean to be proportional?
What is percent?
Vocabulary
Percent of Change _______________________________________________________________
______________________________________________________________________________
Amount of Change_______________________________________________________________
______________________________________________________________________________
Percent of Increase________________________________________________________________
______________________________________________________________________________
Percent of Decrease______________________________________________________________
______________________________________________________________________________
48

Lesson 2, Segment 1 continued:
Consider the following question (Think, pair, share):
Paige needs your help! She wants to convince her grandmother to let her sign up for a rock-climbing class.
The class normally costs $50, but the school is offering a special price of $34. Paige’s grandmother wants to know what percent of the cost of the class she would save.
1) Without calculating, estimate the percent of the discount.
2) Determine the percent change in the price of the class. Use the prompts below to help guide you. a.
Draw a diagram that represents the situation. b.
What is the original (whole) value? Indicate this on your diagram. c.
What percent is the change? Find and indicate this on your diagram. d.
Does this situation represent an increase or decrease?
49

Lesson 2, Segment 1 continued:
Discussion: The percent change is a comparison of the amount of change to the original amount. If a number increases from the original amount, it is called percent increase. If the number decreases from the original, it is called a percent decrease.
1) What is the percent change from $30 to $33? Is this a percent increase or decrease? To answer this question: a.
Draw a diagram to represent the problem. b.
Determine if it is a percent increase or decrease. c.
Calculate the percent change.
2) What is the percent change from $33 to $30? Is this a percent increase or decrease? To answer this question: a.
Draw a diagram to represent the problem. b.
Determine if the percent increase or decrease. c.
Calculate the percent change.
3) If both parts (1 and 2) above have a change of $3, why are the percent changes different?
Explain.
50

Lesson 2, Segment 1 continued:
Work with a partner…
Develop a proportion to find percent of change:
Example 1: Look at the business sign below, would you still do business with this company?
Joe is concerned about how many customers he will lose. He heard that if he increases his prices more than
30%, he will lose customers. Look at the letter that he wrote to his customers. Do you think he will lose a lot of customers? Explain.
1.
How did you solve this problem? Think about proportions.
2.
What does your proportion look like?
3.
After looking at this problem, what do you think the proportion should look like to solve percent of change problems?
Percent of Change Proportion
51

Example 2:
A loaf of bread increased in price from $0.29 to $2.89 in the past 50 years. What was the percent increase?
Example 3:
Calculator prices decreased from $59 to $9.95. What was the percent decrease?
52

Lesson 2, Segment 1 continued
53

54

Finish for Homework, if needed.
55

Lesson 2, Segment 2
WARM-UP
Why would you need to know a PERCENT OF CHANGE, instead of just how much the amount changed?
For example: The cost of perfume changed from $40 to $35, which is a $5 change, but the PERCENT
OF CHANGE is a12.5% increase.
Percent Change Scavenger Hunt: Find the card with the proportion setup on the left. Setup the proportion for the next question and find that somewhere else in the classroom.
56

5.
7.
Name______________________________________
Write the proportion for each problem here:
1. 2.
3. 4.
6.
8.
Homework: Take the proportions created and solve them. Decide if the percent of change is an increase or a decrease.
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Lesson 2, Segment 2
Percent Game Directions
Work in Groups of 2-4.
There are three piles of cards. One pile has percentages, one pile has an action (such as mark up, mark down, increase, decrease), and one pile has a starting amount. Draw one card from each pile, and then perform the indicated operation to calculate the new quantity.
For example: You draw a 30% card, an increase card, and a starting amount of 50 ounces.
30%
Calculate 30% of 50 ounces. Then add the amount to the starting amount to determine the new quantity.
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Lesson 2, Segment 3: Percent Error
WARM-UP
Find each percent of change. Indicate if it is an increase or decrease.
1.
60 to 75
2.
$9 discounted to $4
3.
35 to 15
4.
$22 marked up to $33
Questions to think about…
Is it increasing or decreasing?
What is it changing from?
By how much did it change?
Percent error - Discovery education: 4 Videos
Link: http://app.discoveryeducation.com/search?Ntt=percent+error&N=18343
Introduction: Error in Foam Mixing
Example 1: Absolute and Relative Error – Construction
Example 2: Importance of Errors – Emergency Room
Example 3: Low tolerance for Error – Drag Racing
Finding the percent error is the process of expressing the size of the error (or deviation) between two measurements.
To calculate the percent error, students determine the absolute deviation (positive difference) between an actual measurement and the accepted value and then divide by the accepted value. Multiplying by 100 will give the percent error. (Note the similarity between percent error and percent of increase or decrease)
| Estimated value - Actual value | x
Actual value
100 = Percent error
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Lesson 2, Segment 3 of 4 continued:
Example:
Jamal needs to purchase a countertop for his kitchen. Jamal measured the countertop as 5 ft. The actual measurement is 4.5 ft. What is Jamal’s percent error?
Solution:
Percent error = | 5 ft – 4.5 ft | x
4.5
Percent error = 0.5 ft
4.5 x
100
100
Percent error about 11%
On your own…
1. The report said the parking lot held 240 cars, but we counted only 200 parking spaces.
2. They forecast 20 mm of rain, but we really got 25 mm.
*****************************************************************************************************************
EXIT SLIP
1. You buy a punch bowl expecting it to hold enough punch for 12 people. Because of the design it only holds enough for 10 people. Find percent of error.
2. A $20 book was discounted to $16, find percent of change. Is it increase or decrease?
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HOMEWORK
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Segment 4: Assessment on Percent of Change and Percent Error
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Lesson 3 of 4: Solving Multi-Step Problems
I Can…
 Calculate tax
 Calculate tip
 Calculate discount & markup
 Calculate simple interest
 Find percent of change
 Find percent error
Purpose: Students will be able to solve multi-step problems using proportional relationships.
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Lesson 3, Segment 1: Use proportions to solve multistep problems.
WARM-UP
1.
If you estimate 846 jelly beans in a jar but it turns out there were only 822, what is the percent of error?
2.
Mrs. Smith ordered enough pencils for 80 students. Turns out she only has 78 students in her class. What is her percent of error?
Questions to think about…
What is a proportion?
What is a proportional relationship?
Let’s think about how we can use proportions to solve more complex problems.
A proportion is when two ratios are set equal to each other.
Example 1:
5
=
1
2 10
3
When one of the parts is missing, you can find the missing number by using cross products.
Example 2:
= 𝑥
12 4
3 • 12 = 4 x
36 = 4 x
9 = x
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Lesson 4, Segment 1: continued
Proportional relationships can be used to solve for unknown quantities in many different problems. Use a proportion somehow in each problem in order to find its solution. (May be used as class examples and/or homework.)
1. A family goes out to dinner. The cost of each of the meals is as follows: $8.50, $7.25, $11.00, and $6.25. The tax is 7%. Find the amount of tax the family will pay for their dinner.
2. The family from the previous problem would like to leave a 15% tip. How much will their tip be?
3. A hardware store buys hammers from a warehouse for $6. They sell the hammers for $21. What is the percent markup on the hammers?
4. The hardware store puts out a 20% coupon for any item in their hardware store. What is the new cost of the $21 hammer be after the discount.
5. A new employee is able to cleanup and close a store in 1 hour 10 minutes. With practice he is able to perform his task more quickly. After 4 weeks his supervisor notices that it only takes him 48 minutes to cleanup and close the store. What is the percent decrease in the time it takes to close the store?
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Lesson 3, Segment 1:
6. A machine shop creates bolts for steel beams. The width of each bolt should be 20 mm. The margin of error must be less than 1% for the bolt to be used. If the bolt measures 19 mm can it be used? Show your work to support your answer.
7. You are looking for a multi-year bank loan in the amount of $15,000 with simple interest rate less than
5%. BankTwo advertises a simple interest loan for $15,000 will only cost you $1,3560 over the course of 3 years. What percent is BankTwo charging for a loan? Is this lender a good choice for a loan? Show your work to support your answer.
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Lesson 3, Segment 1
Review: Multistep Problems Carousel Activity
Objective: To practice solving different types of percent problems using percent proportion, percent equation, percent error, markups, discounts, and simple interest.
Directions:
Work together to complete each problem around the room. Be sure to show your work and record your answers on the following page.
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5.
9.
13.
17.
Name: Date:
Percent Review Carousel
Use the following boxes to SHOW ALL WORK from the carousel and circle your final answer.
1. 2. 3. 4.
6.
10.
14.
18.
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7.
11.
15.
19.
8.
12.
16.
20.

Lesson 3, Segment 2
Assessment: Solving Multi-Step Problems
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Lesson 4 of 4: Maps and Scale Drawings
I Can…
 Compute actual lengths and areas from a scale drawing
 Solve problems involving scale drawings using ratios and proportions
 Reproduce a proportional scale drawing using a different scale
Purpose: Students will be able to use proportional reasoning to find scale factor and missing lengths of scale drawings, scale models and maps.
Segment 1: PRE-ASSESSMENT – Scale Drawing
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Class Discussion:
Why do we have scale drawings?
What does a scale on a map or blueprint represent?
What is scale factor?
OTHER NOTES (use back if needed):
Start in class and then send home for homework:
Create or find examples of scale. Real life examples may include advertisements, blueprints, diagrams, descriptions, etc. These can be problems out of a math book, other books like science, social studies, or library books. Some can be off the internet or maps they may have at home or in their cars.
EXIT SLIP:
List 3 things you learned about scale drawings.
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NAME:________________________

Lesson 4, Segment 2: Scale Factor
WARM-UP
THINK!
Draw a triangle.
Draw another triangle larger but similar to the first.
PAIR! – Turn to your partner and discuss your answers.
Remember to talk about:
What things did you have to consider to make sure your triangles are similar?
Do you agree with their answer? Why or Why not?
Is it ok if your answers are not the same?
SHARE! – We will discuss your answers as a class.
Take Notes Here:
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Lesson 4, Segment 2: Scale Factor and Similar Figures
MUG WUMP ACTIVITY
Adapted from: http://conwaymathte.pbworks.com/f/Stretching+and+Shrinking+Student+Edition.pdf
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74

75

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Hat’s Off to the Wumps!
Now it’s time to equip the Wumps with magic hats. Here is a hat that will fit Mug on the coordinate graph below. However, the location of the hat will not fit on Mug’s head. Using this drawing of the hat, find the coordinates of Mug’s hat so that it will be on Mug’s head in your original drawing of Mug from day 1. Draw the hat on Mug using your coordinates in the table. Then create coordinates for each of the other Wumps and plot each new magic hat on the appropriate Wump or imposter drawing.
Point
A
B
C
D
E
F
G
Mug’s Hat Hat 1 (Zug) Hat 2 (Lug) Hat 3 (Bug) Hat 4 (Glug)
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Discussion Questions:
1.
Compare the angles and side lengths of the hats. Which hats are similar to Mug’s hat? Explain why.
2.
Write a rule for a hat that would be half as large as Mug’s hat.
Wumps Mouthing Off and Nosing Around
In order for two figures to be similar, there must be the following correspondence between the figures.
 Side lengths of one figure are multiplied by the same number to get the corresponding side lengths in the second figure
 The corresponding angles are the same size
The number that the side lengths of one figure can be multiplied by to give the corresponding side lengths of the other figure is called the scale factor.
Example:
The number that each side is multiplied by creates the scale factor.
This number doesn’t always have to be a whole number, sometimes it will be a fraction or decimal.
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The diagram below shows a collection of Mouths (rectangles) and Noses (triangles) from the Wump family and some imposters. Answer the discussion questions below.
1.
Decide which mouths and noses belong to each of the Wumps.
2.
Decide which mouths and noses are similar to Mug’s mouth and nose.
3.
Find the scale factor of those mouths and noses which are similar.
4.
Can you use the scale factors you found in Question 3 to predict the relationship between the perimeters for Mug’s mouth and the similar mouths?
5.
Find the perimeter of Mug’s mouth and the similar mouths. Describe the relationship.
6.
Can you use the scale factors you found in Question 3 to predict the relationship between the areas for Mug’s mouth and the similar mouths?
7.
Find the area of Mug’s mouth and the similar mouths. Describe the relationship.
8.
Design a Mug-Like character of your own on graph paper. He/she can either be a Wump or an imposter. Create a name for your character. Give the rule for your character. Check your rule by finding the coordinates and graphing the character. Graph your character.
*Use the tables below to help organize the information to answer #1-7
WUMP
MUG
ZUG
Width of
Mouth
1
Length of
Mouth
4
Perimeter of Mouth
10
Area of Mouth
4
Ratio of
Perimeters
Mug : ____
Ratio of
Areas
Mug : ____
Scale
Factor to
MUG
WUMP
LUG
BUG
GLUG
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WUMP
Width of
Nose
Height of
Nose
Perimeter of Nose
Area of Nose
Ratio of
Perimeters
Mug : ____
Ratio of
Areas
Mug : ____
MUG
ZUG
LUG
BUG
GLUG
More to think about…
1.
Is there a scale factor from Mug to Glug’s nose? Why or why not?
2.
What would be the dimensions of the mouth of a new Wump named “Pug” if his scale factor is “9”?
3.
Why does the perimeter grow the same way as the lengths of the sides of a rectangle?
4.
If the perimeter of the mouth of a new similar Wump named “Slug” is 150, what are the length, width, and area of his mouth? What scale factor was used to grow this new Wump from Mug?
Scale
Factor to
MUG
WUMP
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Name_______________________________________ Date:_________
Homework: Similar Figures Review/Intro to Scale Factor
Write a paragraph on similarity. In your own words, define what it means for two geometric figures to be similar. What are all the geometric features that must be considered in order to say that two figures are similar? If two figures are similar, what can you say about how their perimeters compare? How their areas compare? Name three real-world examples (other than the ones mentioned in class) that could be used with your class in a discussion of similarity. You do not have to write up a description of an activity, just identify what kinds of things might provide good examples of similarity.
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Lesson 4, Segment 3: Scale Factor
WARM-UP
What is a scale?
What is a scale factor?
How could you find a scale factor?
82

83

84

85

Let’s Practice! Work with a partner to solve the following problems.
Find Scale Factor:
1.
Car (hint, change to common units): Scale Factor __________________________.
8 in
5 in ft
Work:
8 ft
5 ft
Setup and solve the proportion. Identify the scale factor.
2. Sticker: Find the value of y ____________________. Scale Factor _____________________________.
Actual Picture Sticker
4 cm
60 cm y
Work:
90 cm
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Work:

4.
3.
Setup and solve the proportion. Identify the scale factor.
Triangle: Find the value of w ____________________. Scale Factor _____________________________. w w
32 m
Work:
Length m
Picture:
48 m
_________________________________
24 m 24 m
Dog House: Enlarge using 2:5 scale factor. Find the length of the front of the actual dog house.
Actual size:
Work:
1.5 m
87 m

Homework:
The scale of a drawing is 5 cm : 1 mm.
1.
Is the scale drawing larger or smaller than the actual figure? Explain.
The scale of a map is 1 inch: 5 miles. Find each distance.
2.
A road is 3 in. long on the map. Find the actual length of the road.
3.
A lake is 35 miles long. Find the length of the lake on the map.
The blueprint below is a scale drawing of an apartment.
4.
The scale is ¼ in. : 4 ft. Write the actual dimensions in place of the scale dimensions.
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5.
You are making a scale drawing with a scale of 2 in. = 17 ft. Explain how you find the length of the drawing of an object that has an actual length of 51 ft.
6.
A special-effects artist has made a scale model of a dragon for a movie. In the movie, the dragon will appear to be 16 ft. tall. The model is 4 in. tall. a.
What scale has the artist used? b.
The same scale is used for a model of a baby dragon, which will appear to be 2 ft. tall. What is the height of the model?
7.
Challenge Question: A building is drawn with a scale of 1 in. : 3 ft. The height of the drawing is 1 ft.
2in. After a design change, the scale is modified to be 1 in. : 4 ft. What is the height of the new drawing?
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Lesson 4, Segment 4: Scale Drawing Activity
In this activity, you will be redrawing a picture at a different scale.
1.
Browse the internet and select and print a logo, symbol, cartoon character, etc. that you would like to recreate. The logo must be approved by your teacher.
2.
You will have to decide on a scale factor. For example, 1:2, 1:3, 1:4, 1:5, etc. Then, choose a unit of measure inches, centimeters, or both. Select a scale factor and unit of measure that will allow you to easily recreate your picture on paper. For example, if you choose a scale factor of 1:4, you might use a grid that has ¼ inch squares on your printed picture and 1 inch squares on your drawing; or a factor of 1:3 with 1 centimeter squares on the picture and 3 inch squares on your drawing.
3.
After cutting out and gluing the picture to the grid paper, choose a straight edge tool and trace the grid over the top of the original picture.
4.
Label the rows of the grids with numbers, and the columns of the grids with letters.
5.
Recreate your picture on a large piece of paper!
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Name ________________________________ Date ______________
Lesson 4, Segment 5: Lesson Assessment (New Flooring Problem)
Segment 6: UNIT 2 SUMMATIVE ASSESSMENT
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