Percent Foundations Guided Worksheet Percent Foundations
Core Skills • Benchmarks, Self-Guided Examples & Finding Quantities
Prerequisite Skill Builder
Student:
Date:
Period:
1 Benchmark Multiplier Toolkit Rule: In addition to divide by 100, we can move the decimal point to the left 2 times!
50% 0.50 \(\div 2\)
25% 0.25 \(\div 4\)
10% 0.10 \(\div 10\)
5% 0.05 Half of 10%
1% 0.01 \(\div 100\)
7.5% 0.075 Common Tax
a. 8% =
b. 15% =
c. 6.5% =
d. 120% =
2 Self-Guided Worked Examples • Step-by-Step Study Guide Read the model steps, then follow the pattern below
Model A: Finding the Percent Amount 15% Tip on $40.00
Step 1
Identify Values: Whole = $40.00, Percent = 15%
Step 2
Convert to Decimal: In addition to divide by 100, we can move the decimal point to the left 2 times: \(15.\% \rightarrow 0.15\)
Step 3
Multiply: \(\text{Tip} = 0.15 \times 40.00 = \$6.00\)
Calculated Tip: $6.00
Model B: Finding Total New Amount $50 Item with 8% Tax
Step 1
Find Increase: \(\text{Tax} = 0.08 \times \$50.00 = \$4.00\)
Step 2
Add to Original: \(\text{Total} = \$50.00 + \$4.00 = \$54.00\)
Alt
Multiplier: \(1.08 \times \$50.00 = \$54.00\)
Total Paid with Tax: $54.00
3 Guided Practice: Finding the Percent Amount Apply the 3-step model: \(\text{Amount} = \text{Decimal} \times \text{Original}\)
Problem 1: Sales Tax
A hoodie costs $48.00. The sales tax rate is 7%. How much is the tax?
Tax Amount: $ ________
Problem 2: Restaurant Tip
A dinner bill is $65.00. The customer leaves a 15% tip. How much is the tip?
Tip Amount: $ ________
Problem 3: Discount Savings
A pair of running shoes costs $90.00 with a 30% off coupon. How much is saved?
Discount Saved: $ ________
Problem 4: Store Markup
A store buys a basketball wholesale for $20.00 and marks it up by 45%. What is the markup amount?
Markup Amount: $ ________
Foundation Worksheet • 7th Grade Mathematics Page 1 of 2 • Flip over for Total New Amounts →
Total New Amounts & Multipliers
Connecting percent change to total new prices before multi-step problem solving.
Student: ___________________
4 The 100% Baseline: Increase vs. Decrease
Percent Increase (Tax, Tip, Markup)
Start at 100% and ADD the percent rate:
Percent Decrease (Discount, Markdown, Sale)
Start at 100% and SUBTRACT the percent rate:
6% Tax Multiplier: 1.06
15% Discount Mult:
40% Markup Mult:
5 Solving for Total New Amounts Method: Find change & adjust OR use 1-step multiplier
Scenario A: Total Cost with Tax
A skateboard costs $60.00. Sales tax is 8%. What is the total cost at checkout?
Total with Tax: $ ________
Scenario B: Sale Price after Discount
A jacket costs $75.00. The store offers a 20% discount. What is the sale price?
Sale Price: $ ________
Scenario C: Restaurant Bill with Tip
A family dinner bill is $52.00. They leave an 18% tip. What is the total paid?
Total Bill + Tip: $ ________
Scenario D: Retail Markup Price
A video game headset is bought for $40.00 wholesale and marked up 35%. What is the retail price?
Retail Price: $ ________
Weekly Probe Readiness Check Check off the skills you feel confident applying independently:
Convert % to Decimals Find Percent Amounts Calculate Total New Price
Unit: Ratios & Proportional Relationships • 7th Grade Math Ready for Weekly Multi-Step Probes
Percent Power Probes Worksheet Percent Power Probes
Weekly Progress Monitoring • Multi-Step Real-World Percents
Grade 7 • 7.RP.A.3
Student:
Date:
Period:
Self-Guided Example • Multi-Step Discount & Tax Walkthrough Tip: In addition to divide by 100, we can move the decimal point to the left 2 times!
Sample Problem: A $50.00 sweatshirt has a 20% discount and 8% sales tax. What is the final total?
Step 1: Calculate Discount
\(0.20 \times \$50 = \$10.00\)
Sale Price: \(\$50 - \$10 = \$40\)
Step 2: Calculate Tax on Sale Price
Tax = \(0.08 \times \$40 = \$3.20\)
(Always tax the discounted price!)
Step 3: Combine for Final Total
\(\$40.00 + \$3.20 = \$43.20\)
Final Cost = $43.20
PROBE 1 Level 1: Supported • Restaurant Tax & Tip
Goal: Percent of Quantity & Total Cost
Jordan and Alex eat lunch at The Corner Bistro. Their food bill totals $35.00. The city applies a 6% sales tax to the food total. They also leave an 18% tip based on the food bill. What is their total final cost for lunch?
Step 1: 6% Sales Tax Tax = 0.06 × $35.00
Tax: $ ________
Step 2: 18% Tip Tip = 0.18 × $35.00
Tip: $ ________
Step 3: Total Paid Food + Tax + Tip
Total: $ ________
PROBE 2 Level 2: Guided • Store Discount & Sales Tax
Goal: Consecutive Percents on New Amount
A premium sports backpack is originally priced at $80.00. The outdoor store offers a 25% off clearance discount. At checkout, a state sales tax of 7.5% is calculated on the sale price. What is the customer's total final cost for the backpack?
Part A: Determine Sale Price Discount = 25% of $80
Show setup and calculation for discount & sale price:
Sale Price: $ ____________
Part B: Apply 7.5% Sales Tax Tax = 7.5% of Sale Price
Show calculation for sales tax and total final price:
Final Cost: $ ____________
Unit: Ratios & Proportional Relationships • 7th Grade Math Page 1 of 2 • Continue to Probes 3 & 4 →
Independent Probes • Week Check
Demonstrate mastery: set up equations, show calculations, and justify answers.
Student: ___________________
Score: _____ / 8
Self-Guided Model • Working Backwards to Find Original Value Reference for Probe 3
Example: A video game is on sale for $42.00 after a 30% discount. Find original price.
1. Remaining %: \(100\% - 30\% = 70\%\)
2. Set Equation: \(0.70 \times \text{Original} = \$42\)
3. Divide to Solve: \(\text{Original} = 42 \div 0.70 = \mathbf{\$60}\)
PROBE 3 Level 3: Independent • Finding Original Value
Goal: Solve for Unknown Original Value
During an annual book warehouse sale, Ms. Rivera purchased a boxed set of STEM encyclopedias on sale for $105.00. The promotional sign states that all items are discounted by 30% off the original price. What was the original price of the boxed encyclopedia set before the discount?
Show Equation & Calculation: Follow the model above: What percent is left after 30% off?
Equation:
Original Retail Price: $ ____________
PROBE 4 Level 4: Mastery • Deal Comparison & Multi-Step Reasoning
Goal: Multi-Step Real-World Decision
Two retailers sell the same graphic tablet with an original retail price of $200.00.
Option A: Tech Haven
Final Cost: $ ________
Option B: Gadget World
Final Cost: $ ________
Cheaper Store:
Difference: $ ____________ less
Weekly Progress Summary Rubric: 1 pt for mathematical setup • 1 pt for accurate computation
Probe 1 __ / 2
Probe 2 __ / 2
Probe 3 __ / 2
Probe 4 __ / 2
Total __ / 8
Scaffolded Percent Probes Worksheet Percent Power • Supported Probes
Guided Progress Monitoring • Step-by-Step Scaffolds • 7.RP.A.3
Guided Tier Support
Student:
Date:
Period:
Decimal Rule: To turn % into a decimal, divide by 100 or move the decimal point left 2 times: \(6\% = 0.06\) • \(25\% = 0.25\)
PROBE 1 Level 1: Restaurant Bill • Tax & Tip
Scaffolded 3-Step Frame
Jordan and Alex eat lunch. Their food bill is $35.00. They pay 6% sales tax and leave an 18% tip on the food bill. What is their total final cost?
Step 1: 6% Tax
6% as decimal = 0.06
Multiply: \(0.06 \times 35.00\)
Tax: $ ________
Step 2: 18% Tip
18% as decimal = 0.18
Multiply: \(0.18 \times 35.00\)
Tip: $ ________
Step 3: Total Paid
Add all 3 amounts together
$35.00 + Tax + Tip
Total: $ ________
PROBE 2 Level 2: Backpack • 25% Off & 7.5% Tax
Two-Stage Guided Plan
A sports backpack is originally priced at $80.00. It has a 25% discount. A state sales tax of 7.5% is calculated on the sale price. What is the total final cost?
Part A: Calculate Sale Price
• Discount Amount = \(0.25 \times 80.00 = \$\underline{\hspace{24px}}\)
• Sale Price = \(\$80.00 - \text{Discount} = \$\underline{\hspace{24px}}\)
Sale Price: $ ____________
Part B: Apply 7.5% Tax to Sale Price
• 7.5% as decimal = 0.075 (moved 2 places left)
• Tax = \(0.075 \times \text{Sale Price} = \$\underline{\hspace{24px}}\)
Final Cost: $ ____________
Supported Edition • 7th Grade Ratios & Proportions Page 1 of 2 • Continue to Probes 3 & 4 →
Supported Probes • Week Check
Reverse percent proportion frames and side-by-side deal organizers.
Student: ___________________
PROBE 3 Level 3: Working Backwards • Original Price
Proportion Organizer
Ms. Rivera buys books on sale for $105.00 after a 30% discount. What was the original price before the discount?
Think: Percent Paid
\(100\% - 30\% = \mathbf{70\%}\)
($105 represents 70% of original)
Guided Proportion Frame
\(\frac{70}{100} = \frac{105}{x}\) or \(0.70 \times x = 105\)
Solve for \(x\) (original price) by dividing: \(\text{Original} = 105 \div 0.70\)
Original Price: $ ____________
PROBE 4 Level 4: Comparing Deals • Tablet $200 List Price
Side-by-Side Organizer
Both stores sell a $200 tablet and apply 8% tax to their final price. Which store is cheaper, and by how much?
Store A: Tech Haven
1. 20% off $200 = \(\$200 - \$40 = \$160\)
2. Subtract $15 coupon = \(\$160 - \$15 = \$145\)
3. Add 8% tax: \(0.08 \times \$145 = \$\underline{\hspace{20px}}\)
Total A: $ ________
Store B: Gadget World
1. 30% off $200 = \(0.70 \times 200 = \$140\)
2. No extra coupon needed
3. Add 8% tax: \(0.08 \times \$140 = \$\underline{\hspace{20px}}\)
Total B: $ ________
The cheaper store is
by $ ____________ less.
Weekly Growth Tracker Record score: 1 pt for guided setup • 1 pt for accurate answer
P1 __ / 2
P2 __ / 2
P3 __ / 2
P4 __ / 2
Total __ / 8
Percent Power Exit Ticket Percent Power • Exit Ticket 7.RP.A.3 Formative Check
Name:
Period:
1. Multi-Step Total (Discount & Tax) Show both steps
Wireless earbuds cost $50.00. The store offers a 20% discount. A 6% sales tax is added to the sale price. What is the final total cost?
Sale Price: $ ________ Final Total Cost: $ ____________
2. Finding Original Value (Working Backwards) Set up an equation
After a 25% discount, a school hoodie costs $36.00. What was the original price before the discount?
Equation: __________________________ Original Price: $ ____________
Confidence Check:
1: Need Help 2: Getting It 3: Got It Down!
Cut Along Line • 2 Tickets Per Page
Percent Power • Exit Ticket 7.RP.A.3 Formative Check
Name:
Period:
1. Multi-Step Total (Discount & Tax) Show both steps
Wireless earbuds cost $50.00. The store offers a 20% discount. A 6% sales tax is added to the sale price. What is the final total cost?
Sale Price: $ ________ Final Total Cost: $ ____________
2. Finding Original Value (Working Backwards) Set up an equation
After a 25% discount, a school hoodie costs $36.00. What was the original price before the discount?
Equation: __________________________ Original Price: $ ____________
Confidence Check:
1: Need Help 2: Getting It 3: Got It Down!
Percent Power Answer Key Teacher Answer Key & Guide
Weekly Progress Probes • Complete Solutions & Error Diagnostics
Standard 7.RP.A.3
Mastery Benchmark: 7 / 8 points (87.5%+) Scoring Scale: 1 pt for mathematical setup • 1 pt for computational accuracy
PROBE 1 KEY Food Bill $35.00 • 6% Sales Tax • 18% Tip
Total: $43.40 (2 pts)
Step 1: 6% Tax
0.06 × 35 = $2.10
Tax = $2.10
Step 2: 18% Tip
0.18 × 35 = $6.30
Tip = $6.30
Step 3: Total Paid
35 + 2.10 + 6.30
= $43.40
Common Error: Students calculating tip on top of tax (\(0.18 \times \$37.10\)). Emphasize tip is traditionally based on original food subtotal.
PROBE 2 KEY Backpack $80.00 • 25% Off • 7.5% Tax
Final Cost: $64.50 (2 pts)
Part A: Sale Price (1 pt)
Discount: \(0.25 \times 80 = \$20.00\)
Sale Price: \(\$80 - \$20 = \mathbf{\$60.00}\)
Alt: \(0.75 \times 80 = \$60.00\)
Part B: Apply 7.5% Tax (1 pt)
Tax: \(0.075 \times 60 = \$4.50\)
Final Total: \(\$60 + \$4.50 = \mathbf{\$64.50}\)
Alt: \(1.075 \times 60 = \$64.50\)
Common Error: Subtracting 25% then adding 7.5% net (\(-17.5\%\)), or taxing original $80 instead of sale price $60.
PROBE 3 KEY Reverse Percent • Sale Price $105.00 after 30% Off
Original Price: $150.00 (2 pts)
1. Percent Paid: \(100\% - 30\% = 70\% = 0.70\)
2. Equation Setup (1 pt): \(0.70 \times x = 105.00\) or \(\frac{70}{100} = \frac{105}{x}\)
3. Solve for Original (1 pt): \(x = 105 \div 0.70 = \mathbf{\$150.00}\)
Fatal Misconception: Taking 30% of $105 ($31.50) and adding it back ($136.50). Remind students: 30% was of the *original* amount, which was larger!
PROBE 4 KEY Tablet $200 • Tech Haven vs Gadget World
Gadget World by $5.40 (2 pts)
Option A: Tech Haven
20% off: \(200 - 40 = \$160\)
Coupon: \(\$160 - \$15 = \$145\)
8% Tax: \(0.08 \times 145 = \$11.60\)
Total: \(\$145 + \$11.60 = \mathbf{\$156.60}\)
Option B: Gadget World
30% off: \(0.70 \times 200 = \$140\)
8% Tax: \(0.08 \times 140 = \$11.20\)
Total: \(\$140 + \$11.20 = \mathbf{\$151.20}\)
Difference: \(\$156.60 - \$151.20 = \mathbf{\$5.40}\)
Teacher Guide • Unit: Ratios & Proportions 7.RP.A.3 Page 1 of 2 • Flip over for Foundations Worksheet Key →
Foundations Worksheet Answer Key
Benchmark conversions, multipliers, and single-step practice solutions.
Part 1 Solutions
Section 1: Quick Decimal Conversions
a. 8% 0.08
b. 15% 0.15
c. 6.5% 0.065
d. 120% 1.20
Section 3: Guided Practice (Finding Percent Amounts)
Problem 1: Sales Tax
7% of $48.00 = \(0.07 \times 48.00\)
Tax = $3.36
Problem 2: Restaurant Tip
15% of $65.00 = \(0.15 \times 65.00\)
Tip = $9.75
Problem 3: Discount Savings
30% of $90.00 = \(0.30 \times 90.00\)
Savings = $27.00
Problem 4: Store Markup
45% of $20.00 = \(0.45 \times 20.00\)
Markup = $9.00
Section 4: Multiplier Practice
6% Tax Multiplier 1.06
15% Discount Multiplier 0.85 (1.00 - 0.15)
40% Markup Multiplier 1.40 (1.00 + 0.40)
Section 5: Total New Amounts
Scenario A: Skateboard ($60 + 8% Tax)
Tax = $4.80 • Total = \(\$60 + \$4.80 = \mathbf{\$64.80}\)
Scenario B: Jacket ($75 - 20% Discount)
Discount = $15.00 • Sale Price = \(\$75 - \$15 = \mathbf{\$60.00}\)
Scenario C: Dinner ($52 + 18% Tip)
Tip = $9.36 • Total Bill = \(\$52 + \$9.36 = \mathbf{\$61.36}\)
Scenario D: Headset ($40 + 35% Markup)
Markup = $14.00 • Retail = \(\$40 + \$14 = \mathbf{\$54.00}\)
Diagnostic Intervention Guide
Struggles with Probe 1/2:
Confusion between addition vs multiplication. Revisit 100% baseline: 7% tax means multiplying by 1.07 or adding tax to original.
Struggles with Probe 3:
Multiplying by 0.30 instead of dividing by 0.70. Have student check: "Should the original price before discount be bigger or smaller?"
Struggles with Probe 4:
Order of operations in store promotions: coupon applies *after* percent discount, and tax applies to the final out-of-pocket sale price.
Unit: Ratios & Proportions • Teacher Master Key Classroom-Ready Grading Resource
Unit Rate Probes Worksheet Unit Rate Probes
Rate Mastery • Integers, Decimals & Fractions • Standard 7.RP.A.1
6-Probe Weekly Check
Student:
Date:
Period:
Self-Guided Toolkit • Calculating Unit Rates \(\text{Unit Rate} = \frac{\text{Quantity A}}{\text{Quantity B}} = A \div B\)
Model A: Decimals & Unit Price
\(5\text{ pounds of apples for } \$7.50\)
\(\frac{\$7.50}{5\text{ lbs}} = 7.50 \div 5 = \mathbf{\$1.50\text{ per pound}}\)
• Always divide cost by quantity for unit price.
Model B: Unit Fractions & Reciprocal
\(\frac{1}{2}\text{ mile in } \frac{1}{6}\text{ hour}\)
\(\frac{1}{2} \div \frac{1}{6} = \frac{1}{2} \times \frac{6}{1} = \frac{6}{2} = \mathbf{3\text{ miles per hour}}\)
• Dividing by a fraction = multiply by its reciprocal!
PROBE 1 Level 1: Integer Direct Rate • Distance & Time
Direct Numeric Setup
A passenger train travels 240 miles in 4 hours at constant speed. What is the unit rate in miles per hour?
Setup Fraction / Division:
Calculate Unit Rate (include units):
Unit Rate: ________ miles / hour
PROBE 2 Level 2: Integer Word Problem • Printing Rate
Contextual Problem
Marcus uses the school library printer to print 168 flyers in 6 minutes. At this constant rate, how many flyers does the printer produce per minute?
Show Mathematical Setup:
Unit Rate Solution:
Unit Rate: ________ flyers / minute
PROBE 3 Level 3: Decimal Real-World • Unit Cost per Ounce
Cost per Unit Rate
A supermarket sells a 16-ounce family box of cereal for $4.48. What is the unit cost per ounce?
Show Division Setup:
Unit Cost with Proper Units:
Unit Cost: $ ________ per ounce
Unit Rate Assessment • Grade 7 Standard 7.RP.A.1 Page 1 of 2 • Turn over for Probes 4, 5 & 6 →
Advanced Probes • Decimals & Fractions
Solve direct decimal and complex fraction unit rate problems with correct units.
Student: ___________________
Fraction Division Reminder: To divide by a fraction, multiply by its reciprocal: \(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\)
PROBE 4 Level 4: Decimal Direct Numeric • Speed
Decimal Measurement
A science research drone flies 31.5 meters in 4.5 seconds. Calculate the drone's speed as a unit rate in meters per second.
Show Decimal Division:
Unit Rate with Proper Units:
Speed: ________ meters / second
PROBE 5 Level 5: Unit Fraction Rate • Distance & Time
Complex Fraction Setup
A cyclist rides \(\frac{3}{4}\) of a mile in \(\frac{1}{8}\) of an hour. What is the cyclist's average speed in miles per hour?
Show Complex Fraction & Reciprocal:
Unit Rate with Proper Units:
Speed: ________ miles / hour
PROBE 6 Level 6: Contextual Fraction • Cooking Recipe
Independent Challenge
Elena uses \(\frac{2}{3}\) cup of strawberry puree to prepare \(\frac{1}{4}\) batch of fruit smoothies. How many cups of puree are required per 1 full batch?
Show Complete Mathematical Work:
Final Answer with Units:
Puree Rate: ________ cups / batch
Weekly Unit Rate Score Tracker 1 pt for rate setup • 1 pt for accurate unit rate with correct units
P1 __ / 2
P2 __ / 2
P3 __ / 2
P4 __ / 2
P5 __ / 2
P6 __ / 2
Total __ / 12
Scaffolded Unit Rate Worksheet Unit Rate • Supported Probes
Guided Frames • Integers, Decimals & Fractions • Standard 7.RP.A.1
Guided Tier Edition
Student:
Date:
Period:
Unit Rate Formula: \(\text{Unit Rate} = \frac{\text{Numerator}}{\text{Denominator}} = \text{Numerator} \div \text{Denominator}\) (The second quantity is always 1!)
PROBE 1 Level 1: Integer Direct Rate • Train Speed
Guided Fraction Frame
A passenger train travels 240 miles in 4 hours. Find the unit rate in miles per hour.
1. Set Up Fraction & Divide:
\(\frac{\text{Miles}}{\text{Hours}} = \frac{240}{4} = 240 \div 4\)
2. Sentence Solution:
The train travels
miles per hour.
PROBE 2 Level 2: Integer Word Problem • Library Printer
Breakdown Frame
Marcus prints 168 flyers in 6 minutes. How many flyers does he print per 1 minute?
1. Division Setup:
\(\frac{168\text{ flyers}}{6\text{ minutes}} = 168 \div 6\)
2. Sentence Solution:
Marcus prints
flyers per minute.
PROBE 3 Level 3: Decimal Real-World • Cereal Box Price
Money Rule Frame
A 16-ounce box of cereal costs $4.48. What is the unit cost per ounce?
1. Money ALWAYS Goes on Top:
\(\frac{\text{Price (\$)}}{\text{Ounces}} = \frac{\$4.48}{16} = 4.48 \div 16\)
2. Sentence Solution:
The unit price is
$ per ounce.
Supported Edition • Grade 7 Standard 7.RP.A.1 Page 1 of 2 • Continue to Probes 4, 5 & 6 →
Supported Probes • Advanced Levels
Decimal shifts and 'Keep-Change-Flip' reciprocal scaffolds.
Student: ___________________
Keep • Change • Flip: Keep 1st fraction • Change \(\div\) to \(\times\) • Flip 2nd fraction to reciprocal (\(\frac{1}{8} \rightarrow \frac{8}{1}\))
PROBE 4 Level 4: Decimal Speed • Drone Flight
Decimal Clear Frame
A research drone flies 31.5 meters in 4.5 seconds. Find speed in meters per second.
1. Multiply Both by 10 to Clear Decimals:
\(\frac{31.5 \times 10}{4.5 \times 10} = \frac{315}{45} = 315 \div 45\)
2. Sentence Solution:
The drone flies
meters per second.
PROBE 5 Level 5: Unit Fraction Rate • Cyclist Speed
Reciprocal Frame
A cyclist rides \(\frac{3}{4}\) of a mile in \(\frac{1}{8}\) of an hour. Find speed in miles per hour.
1. Multiply by Reciprocal of \(\frac{1}{8}\):
\(\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times \frac{8}{1} = \frac{3 \times 8}{4 \times 1} = \frac{24}{4}\)
2. Sentence Solution:
The cyclist rides
miles per hour.
PROBE 6 Level 6: Contextual Fraction • Fruit Smoothie Recipe
Smoothie Frame
Elena uses \(\frac{2}{3}\) cup of strawberry puree for \(\frac{1}{4}\) batch. How many cups per 1 full batch?
1. Multiply by Reciprocal of \(\frac{1}{4}\):
\(\frac{2}{3} \div \frac{1}{4} = \frac{2}{3} \times \frac{4}{1} = \frac{2 \times 4}{3 \times 1} = \frac{8}{3}\)
2. Sentence Solution:
Elena needs
cups per batch.
Supported Growth Tracker 1 pt for guided setup • 1 pt for accurate sentence solution
P1 __ / 2
P2 __ / 2
P3 __ / 2
P4 __ / 2
P5 __ / 2
P6 __ / 2
Total __ / 12
Unit Rate Exit Ticket Unit Rate • Exit Ticket 7.RP.A.1 Formative Check • Decimals & Fractions
Name:
Period:
1. Decimal Unit Price Include units in answer
A grocery store sells a 12-pack of sparkling water for $7.20. What is the unit cost per can?
Show Division: Cost ÷ Cans Unit Cost: $ ________ per can
2. Complex Fraction Rate Multiply by reciprocal
A riding lawnmower cuts \(\frac{2}{5}\) of an acre in \(\frac{1}{10}\) of an hour. What is the mowing speed in acres per hour?
Reciprocal Multiplication: Mowing Rate: ________ acres / hour
Confidence Check:
1: Need Help 2: Getting It 3: Got It Down!
Cut Along Line • 2 Tickets Per Page
Unit Rate • Exit Ticket 7.RP.A.1 Formative Check • Decimals & Fractions
Name:
Period:
1. Decimal Unit Price Include units in answer
A grocery store sells a 12-pack of sparkling water for $7.20. What is the unit cost per can?
Show Division: Cost ÷ Cans Unit Cost: $ ________ per can
2. Complex Fraction Rate Multiply by reciprocal
A riding lawnmower cuts \(\frac{2}{5}\) of an acre in \(\frac{1}{10}\) of an hour. What is the mowing speed in acres per hour?
Reciprocal Multiplication: Mowing Rate: ________ acres / hour
Confidence Check:
1: Need Help 2: Getting It 3: Got It Down!
Unit Rate Answer Key Unit Rate Answer Key & Guide
6-Probe Assessment • Step-by-Step Solutions • Standard 7.RP.A.1
Teacher Edition
Mastery Benchmark: 10 / 12 points (83%+) Scoring: 1 pt for mathematical setup • 1 pt for unit rate with correct units
PROBE 1 KEY Integer Direct • 240 miles in 4 hours
60 miles / hour (2 pts)
Setup & Calculation (1 pt):
\(\frac{240\text{ miles}}{4\text{ hours}} = 240 \div 4 = \mathbf{60}\)
Divide numerator miles by denominator hours.
Unit Rate with Units (1 pt):
60 miles per hour (or 60 mph)
Deduct 1 pt if student writes "60" without units.
Common Misconception: Inverting the division (\(4 \div 240 = \frac{1}{60}\) hours per mile). Prompt student: "We want miles for *each* hour."
PROBE 2 KEY Integer Contextual • 168 flyers in 6 minutes
28 flyers / minute (2 pts)
Setup & Calculation (1 pt):
\(\frac{168\text{ flyers}}{6\text{ minutes}} = 168 \div 6 = \mathbf{28}\)
Division: \(6 \times 20 = 120\), \(168 - 120 = 48\), \(48 \div 6 = 8\).
Unit Rate with Units (1 pt):
28 flyers per minute (or 28 flyers/min)
Must include both "flyers" and "minute".
Error Check: Arithmetic errors during long division (e.g. writing 26 or 27). Check basic division facts.
PROBE 3 KEY Decimal Unit Price • $4.48 for 16 ounces
$0.28 / ounce (2 pts)
Setup & Calculation (1 pt):
\(\frac{\$4.48}{16\text{ oz}} = 4.48 \div 16 = \mathbf{0.28}\)
Long division with decimal: \(16 \times 2 = 32\), \(128 \div 16 = 8\).
Unit Rate with Units (1 pt):
$0.28 per ounce (or 28¢/oz)
Accept either dollar or cent notation.
Crucial Rule: Unit price is ALWAYS \(\frac{\text{Dollars}}{\text{Units}}\). Students dividing \(16 \div 4.48 \approx 3.57\) calculated ounces per dollar, not price per ounce.
Teacher Guide • Unit Rates 7.RP.A.1 Page 1 of 2 • Turn over for Probes 4, 5 & 6 →
Advanced Probes Key & Diagnostics
Decimal rates, complex fractions, and intervention tips.
Part 2 Solutions
PROBE 4 KEY Decimal Measurement • 31.5 meters in 4.5 seconds
7 meters / second (2 pts)
Setup & Calculation (1 pt):
\(\frac{31.5}{4.5} = \frac{315}{45} = 315 \div 45 = \mathbf{7}\)
Shift decimal 1 place right in both numbers: \(45 \times 7 = 315\).
Unit Rate with Units (1 pt):
7 meters per second (or 7 m/s)
Accept standard abbreviations: m/s or mps.
PROBE 5 KEY Unit Fraction • 3/4 mile in 1/8 hour
6 miles / hour (2 pts)
Complex Fraction & Reciprocal (1 pt):
\(\frac{\frac{3}{4}}{\frac{1}{8}} = \frac{3}{4} \times \frac{8}{1} = \frac{24}{4} = \mathbf{6}\)
Multiply by reciprocal of denominator (\(\frac{8}{1}\)).
Unit Rate with Units (1 pt):
6 miles per hour (or 6 mph)
Common Error: Multiplying \(\frac{3}{4} \times \frac{1}{8} = \frac{3}{32}\).
PROBE 6 KEY Contextual Fraction • 2/3 cup for 1/4 batch
2 2/3 cups / batch (2 pts)
Complex Fraction Setup (1 pt):
\(\frac{\frac{2}{3}}{\frac{1}{4}} = \frac{2}{3} \times \frac{4}{1} = \frac{8}{3} = \mathbf{2\frac{2}{3}}\)
Reciprocal of \(\frac{1}{4}\) is \(\frac{4}{1}\). Product is \(\frac{8}{3}\).
Final Solution (1 pt):
\(2\frac{2}{3}\) cups per batch (or \(\frac{8}{3}\) cups/batch)
Accept \(2.67\) cups if rounded to hundredths.
Unit Rate Targeted Interventions
Inverting Terms:
If students write "hours per mile" or "ounces per dollar", have them circle the target unit: "per [what?]" is always the denominator.
Decimal Division:
For Probe 4, remind students that divisor must become a whole number by multiplying both numerator and denominator by 10.
Fraction Division:
Reinforce "Keep, Change, Flip": Keep numerator fraction, change \(\div\) to \(\times\), flip denominator to its reciprocal.
Teacher Guide • Unit Rates Master Key Classroom-Ready Grading Resource
Percent Rate Showdown Activity Rate & Percent Showdown
Partner Review Board • Connect 4 or Highest Point Total • Standards 7.RP.A.1 & 7.RP.A.3
2-Player Activity
Player 1 (O):
Player 2 (X):
How to Play: Take turns picking a square. Solve on your Scorecard (Page 2). If partner verifies answer is correct, initial & claim the square!
Goal: 4 in a Row or Most Points
#1 • TAX 100 pts
A $40 hoodie has 7% tax. What is the tax amount?
Claim: _____ Ans: $2.80
#2 • DISCOUNT 100 pts
A $60 game is 25% off. What is the sale price?
Claim: _____ Ans: $45.00
#3 • UNIT RATE 100 pts
180 miles in 3 hours. Find the miles per hour.
Claim: _____ Ans: 60 mph
#4 • REVERSE % 150 pts
Item costs $70 after 30% off. What was the original price?
Claim: _____ Ans: $100.00
#5 • TIP 100 pts
A $50 bill with 18% tip. What is the tip amount?
Claim: _____ Ans: $9.00
#6 • UNIT PRICE 150 pts
$3.60 for 12 eggs. What is the cost per egg?
Claim: _____ Ans: $0.30/egg
#7 • MULTI-STEP 200 pts
$100 shoes, 20% off, then 8% tax on sale price. Final cost?
Claim: _____ Ans: $86.40
#8 • FRACTION RATE 200 pts
\(\frac{1}{2}\) mile in \(\frac{1}{10}\) hour. Find speed in miles per hour.
Claim: _____ Ans: 5 mph
#9 • REVERSE % 200 pts
Sale price is $80 after 20% discount. Find original price.
Claim: _____ Ans: $100.00
#10 • MARKUP 150 pts
Wholesale $30, marked up 40%. What is the retail price?
Claim: _____ Ans: $42.00
#11 • FRACTION RATE 200 pts
\(\frac{3}{4}\) cup sugar for \(\frac{1}{2}\) batch. Find cups per batch.
Claim: _____ Ans: \(1\frac{1}{2}\) cups
#12 • MULTI-STEP 200 pts
$30 meal, 6% tax ($1.80) and 20% tip ($6.00). What is total?
Claim: _____ Ans: $37.80
#13 • DECIMAL SPEED 150 pts
25 meters in 5 seconds. Find speed in meters per second.
Claim: _____ Ans: 5 m/s
#14 • REVERSE % 250 pts
After 10% discount, jacket is $45. Find original price.
Claim: _____ Ans: $50.00
#15 • DEALS 250 pts
Store A: 30% off $100 ($70). Store B: $25 off coupon ($75). Which cheaper?
Claim: _____ Ans: Store A
#16 • COMPLEX RATE 250 pts
\(\frac{2}{5}\) acre in \(\frac{1}{10}\) hour. Find acres per hour.
Claim: _____ Ans: 4 acres/hr
7th Grade Math • Collaborative Showdown Page 1 of 2 • Solve all turns on Scorecard (Page 2) →
Showdown Scorecard & Work Area
Show step-by-step mathematical work for every square you attempt.
Player Log
Player 1 Work Log Total Points: _______
Square #: _____ (____ pts) Partner Verified: [ ]
Square #: _____ (____ pts) Partner Verified: [ ]
Square #: _____ (____ pts) Partner Verified: [ ]
Square #: _____ (____ pts) Partner Verified: [ ]
Player 2 Work Log Total Points: _______
Square #: _____ (____ pts) Partner Verified: [ ]
Square #: _____ (____ pts) Partner Verified: [ ]
Square #: _____ (____ pts) Partner Verified: [ ]
Square #: _____ (____ pts) Partner Verified: [ ]
Showdown Champion:
Winning Condition: Connect 4 Highest Score
7th Grade Math • Standards Review Game Showdown Complete • Turn in with your partner
Showdown Game Answer Key Showdown Game Master Key
16-Square Solution Grid • Point Values & Mathematical Steps • 7.RP.A.1 & 7.RP.A.3
Teacher Reference
Facilitation: Post at station or use for rapid peer referee checks. Total Board Points: 2,750 pts across all 16 squares
#1: 7% Tax on $40 100 pts
\(0.07 \times 40 = 2.80\)
Answer: $2.80
#2: 25% Off $60 100 pts
\(60 - 15 = 45\)
\(0.75 \times 60 = 45\)
Answer: $45.00
#3: 180 mi in 3 hr 100 pts
\(180 \div 3 = 60\)
Answer: 60 mph
#4: $70 at 30% Off 150 pts
\(70\% \text{ left}\)
\(70 \div 0.70 = 100\)
Answer: $100.00
#5: 18% Tip on $50 100 pts
\(0.18 \times 50 = 9.00\)
Answer: $9.00
#6: $3.60 / 12 Eggs 150 pts
\(3.60 \div 12 = 0.30\)
Answer: $0.30/egg
#7: $100 • 20% + 8% 200 pts
Sale: \(\$80.00\)
Tax: \(80 \times 0.08 = 6.40\)
Answer: $86.40
#8: 1/2 mi in 1/10 hr 200 pts
\(\frac{1}{2} \times \frac{10}{1} = \frac{10}{2} = 5\)
Answer: 5 mph
#9: $80 at 20% Off 200 pts
\(80\% \text{ left}\)
\(80 \div 0.80 = 100\)
Answer: $100.00
#10: Wholesale $30 + 40% 150 pts
\(30 \times 1.40 = 42\)
Answer: $42.00
#11: 3/4 c in 1/2 batch 200 pts
\(\frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = 1.5\)
Answer: 1 1/2 cups
#12: $30 + 6% + 20% 200 pts
\(30 + 1.80 + 6.00\)
Answer: $37.80
#13: 25 m in 5 sec 150 pts
\(25 \div 5 = 5\)
Answer: 5 m/s
#14: $45 at 10% Off 250 pts
\(90\% \text{ left}\)
\(45 \div 0.90 = 50\)
Answer: $50.00
#15: Deals: 30% vs $25 250 pts
A: \(\$70\) vs B: \(\$75\)
Diff: \(\$5\) cheaper
Answer: Store A
#16: 2/5 ac in 1/10 hr 250 pts
\(\frac{2}{5} \times \frac{10}{1} = \frac{20}{5} = 4\)
Answer: 4 acres/hr
Referee Rules:
• Partners verify both numeric answer AND required units. • If work is missing on Scorecard, square cannot be claimed!
Teacher Resource • Standards Review Game Master Key Page 1 of 1 • Complete Solution Matrix
