Proportions Teacher Guide Teacher Guide
Price Tag Proportions
Grade 7
Learning Objective
Students will use proportional relationships to solve multi-step ratio and percent problems, specifically focusing on cross-multiplication and unit rates in real-world contexts.
Standards Alignment
CCSS.MATH.CONTENT.7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems.
Materials Needed
Lesson Slides
Proportion Puzzle Worksheet
Discussion Cards
Exit Ticket
YouTube Access
Instructional Sequence
5 MIN
Warm-up: Fraction Match-up
Quick review of equivalency. Students verify if \( \frac{1}{2} = \frac{4}{8} \) and \( \frac{3}{4} = \frac{9}{12} \). Focus on the concept that ratios represent the same relationship even with different numbers.
15 MIN
Guided Video Investigation
Watch segments of "Unit Rates, Ratios & Proportions."
1:51-3:19: Method 2 (Proportions). Pause at 2:15 to let students try the cross-multiplication setup.3:20-5:15: Proportions with Decimals. Pause at 3:50 to discuss converting "quarter pound" to 0.25.
20 MIN
The Proportion Puzzle
Students work in pairs using the Discussion Cards and Proportion Puzzle Worksheet . They must set up the proportion first, show the cross-multiplication step, and solve for the unknown value.
5 MIN
Closure: Exit Ticket
Individual assessment of one money-based proportion problem to gauge mastery of the day's objective.
Watch Out For...
Misaligned Units
Students may put pounds in the numerator on one side and the denominator on the other. Remind them: "Units must be neighbors!" (Matching spots on both sides).
Division Order
When solving \( 8x = 4888 \), students sometimes divide 8 by 4888. Emphasize that we divide by the coefficient attached to the variable.
Answer Key
Proportion Puzzle Worksheet
1. Baking Flour
\( \frac{2 \text{ cups}}{24 \text{ cookies}} = \frac{x \text{ cups}}{60 \text{ cookies}} \)
\( x = 5 \text{ cups} \)
2. Road Trip
\( \frac{3 \text{ gallons}}{90 \text{ miles}} = \frac{x \text{ gallons}}{225 \text{ miles}} \)
\( x = 7.5 \text{ gallons} \)
3. Sugar Cost (Video Style)
\( \frac{\$0.85}{0.25 \text{ lbs}} = \frac{x}{5 \text{ lbs}} \)
\( x = \$17.00 \)
4. Phone Charging
\( \frac{15\%}{10 \text{ mins}} = \frac{100\%}{x \text{ mins}} \)
\( x = 66.67 \text{ mins} \)
Exit Ticket
Scenario: 12 oranges cost $4.80. How much do 5 oranges cost?
Proportion: \( \frac{4.80}{12} = \frac{x}{5} \)
Step 1: \( 12x = 4.80 \times 5 \)
Step 2: \( 12x = 24.00 \)
Step 3: \( x = 24 / 12 \)
Answer: $2.00
Price Tag Slides Price Tag
Proportions
Solving Multi-Step Ratio Problems
7th Grade Mathematics
Warm-up
Fraction Equivalency
Are these equal?
\( \frac{1}{2} \) ? \( \frac{4}{8} \)
Try this one:
\( \frac{3}{4} \) ? \( \frac{9}{12} \)
Key Idea: Different numbers can represent the same relationship!
Video Case Study: John's Typing
Embedded media
"Problem 1b: How many words can he type in 13 minutes?"
Pause & Solve
John types 376 words in 8 minutes. How many words (\(x\)) can he type in 13 minutes?
Step 1: Setup
\( \frac{376}{8} = \frac{x}{13} \)
Step 2: Cross-Multiply
8x = ?
WORK ON YOUR WHITEBOARDS NOW!
Video Case Study: Sugar Prices
Embedded media
"A quarter pound costs $0.85. How much for 5 lbs?"
Proportion Puzzle
Partner up! You are now Grocery Analysts.
Grab your **Discussion Cards**
Set up the proportions on your **Worksheet**
Cross-multiply to find the "Missing Price"
!
Golden Rule
"Keep your units in the same neighborhood!"
\( \frac{\text{Price}}{\text{lbs}} = \frac{\text{Price}}{\text{lbs}} \)
Exit Ticket
A supermarket sells 12 oranges for $4.80. How much would 5 oranges cost?
1. Set up Proportion
2. Show your Work
Turn in your paper before you leave the store!
Proportion Puzzle Worksheet Proportion Puzzle
Become a Grocery Analyst
Name
Date
Mission Instructions
Work with your partner to solve each "Grocery Case." For every problem, you must (1) Set up the proportion, (2) Show the cross-multiplication equation, and (3) Solve for \(x\).
01
The Cookie Crisis
Setup: Cups / Cookies
A baker uses 2 cups of flour to make 24 cookies . How many cups of flour are needed to make a batch of 60 cookies ?
Proportion Setup
Cross-Multiply Step
Final Answer
02
The Gas Gauge
Setup: Gallons / Miles
Your family car uses 3 gallons of gas to travel 90 miles . At this rate, how many gallons will you use for a 225-mile road trip?
Proportion Setup
Cross-Multiply Step
Final Answer
03
Phone Power
Setup: Percent / Minutes
A phone charges 15% in 10 minutes . If it continues at this exact same rate, how many minutes would it take to charge from 0% to 100% ?
Proportion Setup
Cross-Multiply Step
Final Answer
04
The Bulk Buy
Setup: Cost / Pounds
Just like in the video, 0.25 pounds of gourmet coffee beans cost $3.50 . What is the total cost of a 2-pound bag of these beans?
Proportion Setup
Cross-Multiply Step
Final Answer
Remember: If you put pounds on top, keep pounds on top! Neighborhood units stay together.
Shopping Math Discussion Cards Grocery Gossip
Discussion Cards for Partners
01
The Pause & Ponder
"The video shows John can type 376 words in 8 minutes. Before the narrator reveals the answer, discuss with your partner: Why is it easier to use a proportion than just finding the unit rate first?"
Video Reflection 1:51 - 3:19
02
The Fraction Flip
"If I set up my proportion as minutes over words, but my partner sets theirs up as words over minutes, will we get the same answer? Prove your thinking."
Method Discussion Critical Thinking
03
Decimal Danger
"In Problem 2 of the video, the narrator changes 'a quarter pound' into 0.25. Why do you think he did that instead of leaving it as 1/4? Discuss how decimals make cross-multiplication easier."
Video Reflection 3:20 - 5:15
04
Real World Reality
"Think of a time you were at a store or a fast food place. When would setting up a proportion in your head actually help you save money or make a better choice?"
Practical Application Connection
Cut along the lines to separate cards for partner pairs
Grocery Checkout Exit Ticket Sale!
Final Checkout
Exit Ticket
Customer Name
Date
The Citrus Deal
"A supermarket sells a bag of 12 oranges for $4.80. If the rate stays exactly the same, how much would 5 oranges cost?"
1 Setup Proportion
2 Show your Math
Total Cost for 5 Oranges
$
MATH-7-RP-PROPORTIONS
