Percent Navigator Lesson Plan TEKS 7.4D • 5-Day Intervention Guide
Percent Navigator Teacher Plan
Targeting Multi-Step Percents: Tips, Taxes, Discounts, Commission & Simple Interest
Daily Pacing: 30–45 Min
Tier 2 / Small-Group Focus
The Core Test Misconception
"The One-Step Trap": On recent test items, over 65% of incorrect student responses were Step-1 partial calculations (e.g., selecting $11.50 tip instead of $69 total, $4,800 commission instead of $7,200 salary, or $1,950 interest instead of $4,950 balance). Students halt upon finding a number matched in the choices.
The 2-Step "Stop Sign" Anchor
Step 1: Find the change amount (\(\text{Part} = \% \times \text{Whole}\)).🛑 STOP SIGN: Ask: "Did the question ask for the fee/change, or the new total?" Step 2: ADD (Tip/Tax/Commission/Balance) or SUBTRACT (Discount/Sale).
1
Day 1: Tips & Taxes — Calculating Multi-Step Totals
Anchored on Haircuts Item
Objective
Calculate tip and sales tax amounts and sum with original bills to find final customer costs.
Direct Teaching Routine
Model \(57.50 \times 0.20 = \$11.50\). Highlight answer B ($11.50) as the "Trap". Teach labeling: Bill + Tip = Total ($69.00).
Misconception Defense
Show why Option A ($46.00) subtracted instead of added. Tips always reward workers and add to the bill.
2
Day 2: Discounts & Markdowns — The Subtraction Path
Percent Decrease
Objective
Calculate markdown amounts and subtract from original sticker prices to determine final sale prices.
Direct Teaching Routine
Use bar visual: 100% original price minus 25% discount leaves 75% payment. Compare with 2-step subtraction.
Key Questioning
"Does a discount make the price higher or lower?" If final answer is higher than original, reject immediately.
TEKS 7.4D Intervention Suite Page 1 of 2 • Days 1–2 Roadmap
Days 3–5 Instructional Sequence & Differentiation
Connecting Multi-Step Percents to Earnings, Banking, and Error Detection
Days 3–5
3
Day 3: Commission & Base Salary — Combining Pay Streams
Anchored on Hannah's SUV Item
Objective
Determine commission earnings and combine with fixed monthly base salary to find total compensation.
Direct Teaching Routine
Deconstruct prompt: Base = $2,400. Commission = \(40,000 \times 0.12 = \$4,800\). Total = \(2,400 + 4,800 = \$7,200\).
Trap Breakdown
Option A ($4,800) ignored base salary. Option B ($2,880) mistakenly took 12% of base pay instead of sales volume.
4
Day 4: Simple Interest — Interest vs. Total Account Balance
Anchored on Shania's Savings Item
Objective
Apply \(I = Prt\) to determine simple interest and calculate total balance in account (\(A = P + I\)).
Direct Teaching Routine
Convert 6.5% to decimal \(0.065\). Calculate \(I = 3,000 \times 0.065 \times 10 = \$1,950\). Balance = \(3,000 + 1,950 = \$4,950\).
Trap Breakdown
Option B ($1,950) only answers interest. The question asks "How much will she have in her account?" , requiring total.
5
Day 5: Error Detective & Assessment Mastery
Summative Check
Objective
Diagnose peer errors across all 4 problem types and independently solve 4 mixed multi-step percent items.
Student Routine
Students critique pre-made "Trap Work", identify whether the mistake was Step 1 stoppage or wrong operation, then write correct solutions.
Mastery Metric
Target 80%+ on Day 5 exit ticket, specifically showing Step 1 (\(\Delta\)) and Step 2 (Total) explicitly labeled.
Tiered Differentiation Matrix
Support (Tier 3 / Emerging)
Provide physical 2-step graphic organizer stickers with explicit boxes: Box 1 [Percent Amount], Stop Sign stamp, Box 2 [Operation: + or -], Box 3 [Final Total].
Target (Tier 2 / On-Level)
Have students annotate test prompts with two colored highlighters: yellow for the base/rate info, pink for the exact question demand (e.g., "total earnings" vs "tip only").
Extension (Advanced)
Introduce single-multiplier shortcuts: \(\times 1.20\) for 20% tip, \(\times 0.75\) for 25% discount, and ask students to mathematically prove why both methods yield identical answers.
TEKS 7.4D Intervention Suite Page 2 of 2 • Days 3–5 Roadmap & Supports
Percent Problem Slides TEKS 7.4D • 5-Day Intervention Math Problem Solving
Defeating the One-Step Trap
Mastering Multi-Step Percents: Tips, Taxes, Discounts, Commission, and Simple Interest
The Problem
Stopping after Step 1
The Strategy
2-Step Stop Sign Check
The Goal
100% Accuracy on Totals
The Universal 2-Step Routine
Core Strategy
STEP 1
Calculate Percent Part
Convert percent to decimal and multiply by original whole.
Part = Rate × Whole
STOP SIGN
Reread Question
Did it ask for just the change amount, or the final total ?
Do not pick Step 1 traps!
STEP 2
Add or Subtract
Apply change to original amount to find complete final total.
Total = Original ± Part
Tip, Tax, Commission, Interest Balance → ADD • Discount, Coupon, Sale Price → SUBTRACT
Day 1 Focus • Tips & Bills
William's Haircuts Breakdown
Missed Test Item 3
“Haircuts cost $57.50. He gave the stylist a 20% tip. What was the total cost including tip?”
Step 1: Calculate Tip
Tip = 0.20 × $57.50 = $11.50
⚠️ Option B is $11.50 — That is only the tip!
Step 2: Add to Original
Total = $57.50 + $11.50 = $69.00
✅ Correct Answer: Option C ($69.00)
Why is Option A ($46.00) wrong? Subtracted tip instead of adding! Tips always increase the total.
Day 2 Focus • Percent Decrease
Discounts: The Subtraction Path
Sale Price
A pair of basketball sneakers originally costs $120. The store is offering a 30% discount. What is the sale price?
Method: 2-Step Subtraction
Step 1: 0.30 × $120 = $36.00 discount
Step 2: $120 - $36.00 = $84.00 sale price
Trap to avoid: Answering $36 (discount amount)
Sanity Check Benchmark
• Original was $120.less .
🛑 Stop Sign Rule: Discounts ALWAYS make the final price LOWER than the starting price!
Day 3 Focus • Earnings & Commissions
Hannah's Dealership Earnings Breakdown
Missed Test Item 2
Base salary: $2,400. Sold SUV for $40,000 at 12% commission. What was Hannah's total monthly earnings?
Step 1: Commission Earned
Commission = 0.12 × $40,000
Commission = $4,800
⚠️ Option A was $4,800 — Hannah gets base salary too!
Step 2: Total Earnings
Total = Base + Commission
Total = $2,400 + $4,800 = $7,200
✅ Correct Answer: Option C ($7,200)
Key Takeaway: Total compensation combines both fixed base pay and variable sales commission.
Day 4 Focus • Simple Interest & Balances
Shania's Savings Account Breakdown
Missed Test Item 9
Deposited $3,000 at 6.5% simple interest. How much will Shania have in her savings account after 10 years?
Step 1: Interest Formula (\(I = Prt\))
\(I = 3,000 \times 0.065 \times 10\)
\(I = \$1,950\) (Interest earned)
⚠️ Option B was $1,950 — Did she lose her deposit? No!
Step 2: Total Account Balance
Balance = Principal + Interest
Balance = $3,000 + $1,950 = $4,950
✅ Correct Answer: Option A ($4,950)
Formula Alert: \(I = Prt\) ONLY calculates the interest. Total balance requires \(A = P + I\)!
Day 5 Focus • Error Detective
Spotting the Trap: Who Got It Right?
Mastery Challenge
Problem: A $50 jacket has an 8% sales tax. What is the total cost at checkout?
Student A's Work Trapped!
0.08 × $50 = $4.00
Answer: The jacket costs $4.00.
Error: Stopped at Step 1! A jacket does not cost $4 at checkout.
Student B's Work Mastery!
Tax: 0.08 × $50 = $4.00
Total: $50 + $4.00 = $54.00
Success: Followed Stop Sign and added tax to original cost.
Be an Error Detective on your test: Always label Step 1 as “Change” and Step 2 as “Total”!
The 3 Golden Questions on Every Percent Test
Test Day Armor
1
What is the question asking for?
Underline keywords: “total cost” , “sale price” , “total earnings” , or “amount in account” .
2
Did I stop after Step 1?
If your answer is only the tip, tax, commission, or interest, you are likely falling into the test trap.
3
Does my final answer make sense?
Tips, taxes, commissions, and interest make amounts increase . Discounts and coupons make amounts decrease .
You have the tools to conquer TEKS 7.4D!
Percent Detective Student Workbook TEKS 7.4D Intervention Workbook
Percent Detective: Defeating the One-Step Trap
Name:
Date:
Step 1: Calculate Percent Change (\(\text{Part} = \text{Rate} \times \text{Whole}\)) 🛑 STOP SIGN: Total or Part? Step 2: Add (Tip/Tax) OR Subtract (Discount)
1 Day 1: Tips & Bills — Test Item Analysis
Test Review • Haircuts Problem
Item 1: William took his three kids to get haircuts. The haircuts cost $57.50. He also gave the stylist a 20% tip. What was the total cost, including tip, for William's three kids to get haircuts?
Step 1: Calculate Tip Amount
Step 2: Add to Haircut Cost
A. $46.00
B. $11.50
C. $69.00
D. $77.50
🛑 Detective Reflection: Which answer choice above was the "Step 1 Trap"? Explain why:
2 Day 2: Discounts & Markdowns — The Subtraction Path
Percent Decrease
Item 2: A backpack has an original price tag of $45.00. The store is having a weekend promotion offering a 25% discount. What is the final sale price of the backpack before tax?
Step 1: Calculate Discount Dollars
Step 2: Subtract from Original
A. $11.25
B. $33.75
C. $56.25
D. $20.00
Final Answer: $_________________ Sanity Check: Is final price less than $45.00? Yes / No
Percent Detective Workbook • TEKS 7.4D Page 1 of 3
Days 3 & 4: Earnings & Financial Literacy
Navigating Commission and Simple Interest Multi-Step Problems
Name:
3 Day 3: Commission & Base Salary — Test Item Analysis
Test Review • Hannah's SUV Problem
Item 3: Hannah works as a sales representative at a vehicle dealership. She receives a base salary of $2,400 each month. In addition to her base salary she earns commission on the final sale price of each vehicle she sells. This month, she sold a brand new SUV for a price of $40,000 and earned 12% commission. What was Hannah's total earnings for the month from her base salary and the commission earned from selling this SUV?
Step 1: Calculate Commission (12% of $40,000)
Step 2: Add Monthly Base Salary ($2,400)
A. $4,800
B. $2,880
C. $7,200
D. $6,400
🛑 Detective Reflection: Why did many students choose Option A ($4,800)? What did they forget?
4 Day 4: Simple Interest — Test Item Analysis
Test Review • Shania's Savings Account
Item 4: Shania deposited $3,000 into a savings account that earns 6.5% simple interest. How much will Shania have in her savings account after 10 years?
Step 1: Interest Formula (\(I = P \cdot r \cdot t\))
P = $3,000, r = 0.065, t = 10 yrs
Step 2: Total Account Balance (\(A = P + I\))
Original Deposit + Interest Earned
A. $4,950
B. $1,950
C. $3,875
D. $4,125
🛑 Detective Reflection: Does the formula \(I = Prt\) give the account balance or only the interest? Explain:
Percent Detective Workbook • TEKS 7.4D Page 2 of 3
Day 5 Summative Check
Day 5: Error Detective Mastery Check
Score: / 100
Part 1: Spot the Peer Error (Explain & Correct)
The Problem: A tablet costs $240. The sales tax rate is 8.5%. What is the total cost?"\(240 \times 0.085 = 20.40\). The total cost of the tablet is $20.40."
What error did Devon make?
Correct 2-Step Solution:
Part 2: Independent Problem Solving (Show Both Steps)
1. Restaurant Bill: Food total is $42.00. Tax is 8% and tip is 15%. What is the grand total?
Step 1: Tax + Tip
Step 2: Add to Bill
Final Answer:
2. Skateboard Sale: Regular price is $80.00 with a 35% discount. What is the sale price?
Step 1: Discount $
Step 2: Subtract
Final Answer:
3. Bank Certificate: Marcus deposits $1,500 at 4% simple interest for 5 years. Total in account?
Step 1: \(I = Prt\)
Step 2: \(A = P + I\)
Final Answer:
Mastery Checklist: □ Labeled Step 1 & Step 2 □ Avoided Step 1 Trap Choice □ Checked + / - Logic Ready for Retest!
Percent Detective Answer Key Teacher Resource • TEKS 7.4D
Percent Detective Answer Key & Error Guide
Intervention Diagnostic Key
Days 1–3 Item Breakdown
1 Day 1: William's Haircuts ($57.50 + 20% Tip)
Correct: C ($69.00)
Worked Steps:
Step 1: Tip = 0.20 × $57.50 = $11.50
Step 2: Total = $57.50 + $11.50 = $69.00
Student Trap Distractor Breakdown:
A ($46.00): Subtracted tip instead of adding.
B ($11.50): 🛑 Step 1 Trap! Only found tip amount.
D ($77.50): Added 20 directly to $57.50 without % math.
Detective Reflection Key: Option B is the trap because $11.50 is only the stylist's tip, not the total bill.
2 Day 2: Backpack Sale Price ($45.00 - 25% Discount)
Correct: B ($33.75)
Worked Steps:
Step 1: Discount = 0.25 × $45.00 = $11.25
Step 2: Sale Price = $45.00 - $11.25 = $33.75
Student Trap Distractor Breakdown:
A ($11.25): 🛑 Step 1 Trap! Found savings, not sale price.
C ($56.25): Added discount to original price.
D ($20.00): Subtracted 25 directly from 45.
Sanity Check: Final price MUST be lower than $45.00 because discounts reduce the customer cost.
3 Day 3: Hannah's Dealership Earnings ($2,400 + 12% on $40,000)
Correct: C ($7,200)
Worked Steps:
Step 1: Commission = 0.12 × $40,000 = $4,800
Step 2: Total Pay = $2,400 + $4,800 = $7,200
Student Trap Distractor Breakdown:
A ($4,800): 🛑 Step 1 Trap! Only commission; omitted base.
B ($2,880): Took 12% of base pay ($288) and added to $2,400 (or arithmetic error).
D ($6,400): Subtraction/addition arithmetic error.
Detective Reflection Key: Option A was tempting because $4,800 is the exact result of the multiplication.
Percent Detective Answer Key • TEKS 7.4D Page 1 of 2
Days 4 & 5 Solutions & Retest Protocol
Simple Interest, Error Analysis Critique & Independent Mastery
Page 2 of 2
4 Day 4: Shania's Savings Account ($3,000 at 6.5% for 10 Years)
Correct: A ($4,950)
Worked Steps:
Step 1: \(I = 3,000 \times 0.065 \times 10 = \$1,950\)
Step 2: Balance = \(3,000 + 1,950 = \$4,950\)
Distractor Diagnosis:
B ($1,950): 🛑 Step 1 Trap! Only the interest accrued.
C ($3,875): Calculated using 5% rate instead of 6.5%.
D ($4,125): Failed to multiply by 10 years accurately.
Key Formula Note: \(I = Prt\) calculates only the growth interest. The prompt asked how much she will HAVE in the account (total balance).
Day 5: Error Detective & Mastery Assessment Key
Part 1: Devon's Tablet Error Critique
Identified Error: Devon stopped at Step 1. He calculated 8.5% of $240 ($20.40) and assumed that was the final cost of the tablet, rather than adding it to the $240 base price.
Correct Solution: \(\text{Tax} = \$20.40\); \(\text{Total} = \$240 + \$20.40 = \mathbf{\$260.40}\).
1. Restaurant Bill
Tax (8%): \(42 \times 0.08 = \$3.36\)
Tip (15%): \(42 \times 0.15 = \$6.30\)
Total add-ons: \(\$9.66\)
Total: $51.66
2. Skateboard Sale
Discount: \(80 \times 0.35 = \$28.00\)
Subtract: \(\$80.00 - \$28.00\)
Or \(80 \times 0.65\)
Sale Price: $52.00
3. Bank Certificate
\(I = 1500 \times 0.04 \times 5 = \$300\)
Balance: \(P + I\)
\(\$1,500 + \$300\)
Total: $1,800.00
Retest Readiness Rubric
Students scoring 3/4 or 4/4 on Day 5 and successfully identifying the "Step 1 Trap" in Devon's problem are cleared for the retest. If a student still stops at Step 1, provide the physical Stop Sign desktop tent card and 2 additional guided pairing problems.
Percent Detective Answer Key • TEKS 7.4D Page 2 of 2
