Percent Powerhouse Facilitator Guide Percent Powerhouse
Teacher Facilitator Guide
TEKS ALIGNMENT
7.4A, 7.4B, 7.4C, 7.4D, 7.4E
Reporting Category 2
Lesson Objective
Students will master proportional relationships and percent applications by analyzing real-world financial scenarios including markups, markdowns, sales tax (Texas 8.25%), tips, and simple interest. Students will use multiple strategies (proportion, equation, mental math) to solve high-rigor STAAR-formatted problems.
The "Big Rocks" (Key Concepts)
Constant of Proportionality (k): Recognizing \(k = \frac{y}{x}\) in tables and graphs.Percent Change: Distinguishing between increase (markup, tax, tip) and decrease (markdown, discount).Simple Interest: Applying \(I = prt\) with a focus on time in years.
Materials Needed
Percent Powerhouse Slides
Student Guided Practice
Texas Sales Tax Reference
Chart Paper & Markers
Basic Calculators
3-Act Math Task: The Great Sneaker Sale
ACT 1
The Hook (5-10 mins)
Instructional Prompt:
Display an image of two competing shoe store ads:
Store A: "Buy 2 pairs, get the 3rd pair 50% off!"Store B: "25% off your entire purchase when you buy 3 pairs!"
Question: "Which store is offering the better deal for a customer buying 3 pairs of shoes at the same price? What do you notice? What do you wonder?"
ACT 2
Information Gathering (15 mins)
Ask students: "What information do we need to solve this?"
Reveal the "Hidden Data":
Price per pair: $80.00
Texas Sales Tax: 8.25% (Apply to final total)
Students work in pairs to calculate the final price (including tax) for both stores. They must show their "strategy path" (Proportion, Equation, or Mental Math/Fractional Parts).
ACT 3
The Big Reveal & Discussion (10 mins)
Store A Math
2 pairs @ $80 + 1 pair @ $40 = $200
Tax: $200 × 0.0825 = $16.50
Total: $216.50
Store B Math
3 pairs @ $80 = $240
Discount: $240 × 0.25 = $60
Subtotal: $180
Tax: $180 × 0.0825 = $14.85
Total: $194.85
Debrief: Store B is better! Why? Store A only gives 50% off *one* item (effectively 16.7% off total), whereas Store B gives 25% off *everything*.
Instructional Strategies for Percents
Strategy Method When to Use The Proportion \(\frac{\text{part}}{\text{whole}} = \frac{\%}{100}\) Best for students who struggle with decimal placement. Consistent structure. The Equation \(\text{part} = \text{percent (as dec)} \times \text{whole}\) Fastest for calculators. Direct translation from English to Math. Mental Math Find 10% (move decimal), 5% (half of 10%), 1% (move twice). Best for tip (15-20%) and tax (8.25% ≈ 8%). Essential for real-world literacy.
STAAR Misconception Alert
Interest Time: Students often use months instead of years in \(I = prt\). Remind them that 6 months = 0.5 years.Tax on Discount: Students often calculate tax on the *original* price rather than the *sale* price.k vs. slope: In 7th grade, we focus on \(y = kx\) (proportional through origin). Ensure they verify the (0,0) point. Percent Powerhouse Slides %
$
y=kx
Percent Powerhouse
7th Grade Proportions & Percents
TEKS 7.4A-D • TEKS 7.4E
ACT 1
The Great Sneaker Sale
STORE A
Buy 2 pairs, get the 3rd pair 50% OFF!
STORE B
25% OFF your entire purchase when you buy 3 pairs!
Which is the better deal?
What do you notice?
What do you wonder?
ACT 2
Information Gathering
Original Price
$80.00 / pair
Texas Sales Tax
8.25%
Your Mission:
Calculate the Total Final Cost (including tax) for buying 3 pairs at each store. Which deal saves you the most money?
Three Paths to the Percent
The Proportion
\[\frac{\text{part}}{\text{whole}} = \frac{\%}{100}\]
Great for visual learners. Keeps units aligned.
The Equation
\[y = r \cdot x\]
Fastest for calculations. Turn percent into a decimal first!
Mental Math
10%: Move decimal 1 spot left
1%: Move decimal 2 spots left
5%: Half of 10%
Proportional Relationships
Constant of Proportionality (\(k\))
\(k = \frac{y}{x}\)
Hours (\(x\)) Earnings (\(y\)) 2 $30 5 $75 10 $150
What is \(k\) for this table?
x-axis
y-axis
2 Golden Rules for Graphs:
Must be a straight line
Must pass through the origin (0,0)
Percent Change
Percent Increase
Sales Tax
Tip / Gratuity
Markup
"Add the change to the original!"
Percent Decrease
Discount / Sale
Markdown
Coupon
"Subtract the change from original!"
The Interest Formula
\(I = P \cdot r \cdot t\)
I
Interest
Percent Powerhouse Worksheet Percent Powerhouse
NAME: __________________________________ DATE: ___________________
GRADE 7 MATHEMATICS
TEKS 7.4A-E
ACT 1: THE HOOK
The Great Sneaker Sale
Observations
What do you notice about the two deals?
Questions
What do you wonder about the cost?
ACT 2: DATA & DOLLARS
Essential Data
Original Price: $80.00 / pair
Quantity: 3 pairs
Texas Sales Tax: 8.25%
STORE A
Buy 2, Get 3rd Pair 50% Off
Show calculations here...
Total with Tax
$ _________________
STORE B
25% Off Entire Purchase
Show calculations here...
Total with Tax
$ _________________
Proportional Power-Up
The table below shows the cost of buying multiple pairs of socks at a shop. Does this relationship represent a constant of proportionality? If so, what is \(k\)?
Pairs (\(x\)) Total Cost (\(y\)) Ratio (\(y/x\)) 3 $13.50 5 $22.50 8 $36.00
The Constant of Proportionality (\(k\)) is:
___________________
Graph the Relationship
Label your axes and identify the point (1, \(k\)).
Financial Literacy: Texas Style
1. The Houston Family dinner bill was $54.00. They want to leave a 20% tip. What is the total cost including tip?
Final Answer:
$ _________________
2. A bicycle in Austin is priced at $240.00. If the sales tax is 8.25%, how much total tax will be paid?
Final Answer:
$ _________________
3. Simple Interest: You deposit $1,000 into a savings account with a 5% simple interest rate. How much interest will you earn after 6 months?
WATCH THE TIME UNIT!
Final Answer:
$ _________________
Percent Powerhouse Assessment Powerhouse Practice
7th Grade Mathematics
Reporting Category 2: Proportionality
NAME: _________________________________________
DATE: _______________________
Read each question carefully. For multiple-choice questions, select the best answer. For constructed-response questions, show your work and write your final answer in the provided space.
1
The table below shows the relationship between the number of gallons of gas used and the number of miles driven by a truck. Which equation represents the relationship between the miles driven, \(y\), and the gallons of gas used, \(x\)?
Gallons (\(x\)) Miles (\(y\)) 4 72 7 126 12 216
A \(y = 18x\)
B \(y = x + 68\)
C \(y = 4x\)
D \(y = 0.05x\)
2
A grocery store sells 5 pounds of apples for $12.50. What is the constant of proportionality that relates the total cost, \(y\), to the weight in pounds, \(x\)?
A $0.40 per pound
B $2.50 per pound
C $5.00 per pound
D $12.50 per pound
3
A graph represents a proportional relationship if it passes through which point?
A (0, 1)
B (1, 0)
C (0, 0)
D (1, 1)
4
A collector bought a vintage poster for $120. Two years later, the value of the poster increased by 15%. What was the value of the poster after two years?
A $102
B $135
C $138
D $150
5
A department store is having a clearance sale. All winter coats are marked down by 40%. If the original price of a coat is $85.00, what is the sale price?
A $34.00
B $45.00
C $51.00
D $119.00
6
Marisol had lunch at a restaurant in Dallas. Her meal cost $18.50. She must pay 8.25% sales tax and wants to leave a 20% tip on the cost of the meal *before* tax. What is the total amount Marisol will pay for her lunch?
A $23.73
B $24.05
C $22.20
D $25.22
7
A student opens a savings account with an initial deposit of $500. The account earns 3% simple interest annually. If no other deposits or withdrawals are made, how much interest will the student earn after 4 years?
Percent Powerhouse Answer Key Percent Powerhouse
Assessment Answer Key
Teacher Resource
TEKS 7.4A-E Alignment
Multiple Choice Solutions
1
A \(y = 18x\)
Calculation: \(k = \frac{72}{4} = 18\); \(k = \frac{126}{7} = 18\). Correct equation is \(y = 18x\).
2
B $2.50 per pound
Calculation: \(\frac{12.50}{5} = 2.50\). This is the unit rate and constant of proportionality.
3
C (0, 0)
Concept: Proportional graphs must be straight lines passing through the origin (0,0).
4
C $138
Calculation: \(120 \times 0.15 = 18\). New value: \(120 + 18 = 138\).
5
C $51.00
Calculation: \(85 \times 0.40 = 34\). Sale price: \(85 - 34 = 51\).
6
A $23.73
Calculation: Tax \( = 18.50 \times 0.0825 = 1.52625 \approx 1.53\). Tip \( = 18.50 \times 0.20 = 3.70\). Total: \(18.50 + 1.53 + 3.70 = 23.73\).
7
B $60
Calculation: \(I = prt \rightarrow I = 500 \times 0.03 \times 4 = 60\).
8
B $180
Calculation: \(t = \frac{18}{12} = 1.5\) years. \(I = 2000 \times 0.06 \times 1.5 = 180\).
Constructed Response Solutions
Question 9 Solution
Correct Answer: $40.00
Step 1: Find the markup amount. \(25.00 \times 0.60 = 15.00\).
Step 2: Add markup to original price. \(25.00 + 15.00 = 40.00\).
Grading Note: Students must show the addition step to receive full credit.
Question 10 Solution
Correct Answer: 5 cups
Method 1 (Ratio Table): 2 OJ : 5 Soda. Multiplier is \(12.5 / 5 = 2.5\). \(2 \times 2.5 = 5\).
Method 2 (Proportion): \(\frac{2}{5} = \frac{x}{12.5}\). \(5x = 25\). \(x = 5\).
Grading Note: Accept any work showing a scale factor of 2.5 or cross-multiplication.
