Fractions and Algebra Teacher Guide Teacher Facilitation Guide
Fractions & Algebra Bridge
Two-Period Instructional Roadmap • Low-Stress Vocabulary • Scripted Think-Alouds
Target: Grade 6–8 Reteach
No-Panic Vocabulary Decoder (Say These Plainly)
Improper Fraction: Numerator is bigger than or equal to denominator (e.g., \(\frac{7}{4}\)). It just means "more than one whole cut into equal slices."
Reciprocal ("Flipped Fraction"): Turn the fraction upside down. The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\). A number times its reciprocal always equals 1.
Unit Rate: A rate comparing an amount to exactly one unit (e.g., miles per 1 hour, dollars per 1 pound). Found by dividing top by bottom!
Inverse Operation ("Opposites"): The math action that undoes another action. Addition undoes subtraction; multiplication undoes division.
PERIOD 1: Fraction Mechanics (Mixed Numbers & KCF Division)
45–50 Minutes
Skill 1: Mixed Number to Improper Fraction (The "M-A-D" Method) 15 Min
1. Multiply (M):
Multiply the denominator by the whole number. (Gives total slice pieces in the wholes).
2. Add (A):
Add the existing numerator to that product. (Adds the leftover slices).
3. Denominator (D):
The denominator stays exactly the same! (Slice size did not change).
Script for \(2\frac{3}{4}\): "Look at \(2\frac{3}{4}\). The denominator is 4. Multiply \(4 \times 2 = 8\). Add the top: \(8 + 3 = 11\). The denominator stays 4, giving \(\frac{11}{4}\). Two whole pizzas cut in fourths is 8 slices, plus 3 extra slices is 11 slices!"
Skill 2: Dividing Fractions via Keep-Change-Flip (KCF) 25 Min
Why does KCF work? Dividing by a fraction is the same as asking: "How many of these pieces fit inside the total?" Multiplying by its flipped reciprocal finds the exact same answer faster.
KEEP Leave 1st fraction untouched
CHANGE Change \(\div\) to \(\times\)
FLIP Flip 2nd fraction (reciprocal)
Script for \(\frac{3}{5} \div \frac{2}{3}\): "We keep \(\frac{3}{5}\). We change division to multiplication. We flip \(\frac{2}{3}\) to its reciprocal \(\frac{3}{2}\). Now multiply straight across: top times top \((3 \times 3 = 9)\), bottom times bottom \((5 \times 2 = 10)\). Result: \(\frac{9}{10}\)."
Fractions and Algebra Bridge • Teacher Instructional Guide Page 1 of 2
PERIOD 2: Unit Rates with Fractions & One-Step Equations
45–50 Minutes
Skill 3: Unit Rates Involving Fractions (Complex Fractions) 20 Min
A fraction inside a fraction \(\frac{A}{B} / \frac{C}{D}\) is simply a division problem wearing a disguise!
Word Problem Script: "Marcus hikes \(\frac{3}{4}\) of a mile in \(\frac{1}{2}\) hour. What is his speed in miles per hour?"
1. Set up the ratio: \(\frac{\text{miles}}{\text{hour}} = \frac{3/4}{1/2}\)
2. Rewrite as division: \(\frac{3}{4} \div \frac{1}{2}\)
3. Apply KCF: \(\frac{3}{4} \times \frac{2}{1} = \frac{6}{4}\)
4. Simplify: \(\frac{6}{4} = 1\frac{2}{4} = 1\frac{1}{2}\) miles per hour!
Skill 4: One-Step Equations (Opposite Operations & Reciprocals) 20 Min
Goal: Isolate the variable (get \(x\) alone). Whatever we do to one side of the equal sign, we must do to the other side to keep balance.
Case A: Variable is Divided \(\frac{x}{4} = 6\)
The variable is divided by 4. The opposite of dividing by 4 is multiplying by 4 .
\(\frac{x}{4} \times 4 = 6 \times 4 \implies x = 24\)
Case B: Fraction Coefficient \(\frac{2}{3}x = 8\)
Multiply both sides by the reciprocal \(\frac{3}{2}\) to turn the coefficient into 1.
\(\frac{3}{2} \times \frac{2}{3}x = 8 \times \frac{3}{2} = \frac{24}{2} = 12\)
Red-Alert Mistakes & What to Say to Fix Them
Flipping the 1st fraction: "Only the second fraction gets flipped! The first fraction stays seated: Keep it, Change sign, Flip the next!"
Cross-multiplying too soon: "Cross-multiplication is only for proportions with an equal sign in the middle (\(\frac{a}{b} = \frac{c}{d}\)). For division, write out KCF first!"
Dividing by whole numbers: "Always put a 1 under any whole number before flipping (e.g., \(4\) becomes \(\frac{4}{1}\), and its flip is \(\frac{1}{4}\))."
Daily Routine Anchor
Start each class with 2 warm-up problems on the board. Emphasize that algebra is just a balance scale: whatever you multiply or divide on the left side, you copy on the right side.
Fractions and Algebra Bridge • Teacher Instructional Guide Page 2 of 2
Fractions and Algebra Slides Math Toolkit Reteach 2-Period Masterclass
Fractions & Algebra
Unlock mixed numbers, master Keep-Change-Flip, conquer unit rates, and solve one-step equations with confidence.
Period 1: Fraction Mechanics Period 2: Rates & Equations
Rule #1: Fractions are not monsters—they are just pieces of wholes! Slide 1 of 6
Skill 1 • Period 1
The "M-A-D" Method
Mixed \(\rightarrow\) Improper
M
Multiply
Multiply the bottom denominator by the whole number.
\(3 \times 2 = 6\)
A
Add
Add the top numerator to your product.
\(6 + 1 = 7\)
D
Denominator
Keep the exact same denominator on the bottom!
\(2\frac{1}{3} = \frac{7}{3}\)
Example: \(2\frac{1}{3}\) \(\rightarrow\) \((3 \times 2) + 1 = 7\) over \(3\) \(\rightarrow\) \(\frac{7}{3}\)
Skill 2 • Period 1
Dividing Fractions: K-C-F
Multiplying by Reciprocal
KEEP
First fraction stays identical
\(\frac{3}{4}\)
CHANGE
Change \(\div\) into \(\times\)
\(\times\)
FLIP
Flip second fraction upside-down
\(\frac{5}{2}\)
Problem: \(\frac{3}{4} \div \frac{2}{5}\) → KCF: \(\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}\) → \(1\frac{7}{8}\)
Never divide fractions directly—always turn it into a multiplication problem!
Skill 3 • Period 2
Fractional Unit Rates
Per 1 Single Unit
Real-World Scenario
"A chef uses \(\frac{3}{4}\) cup of flour to make \(\frac{1}{3}\) of a cake. How much flour per 1 whole cake?"
Unit Rate = \(\frac{\text{Flour}}{\text{Cake}} = \frac{3/4}{1/3}\)
1 Write as division: \(\frac{3}{4} \div \frac{1}{3}\)
2 Apply KCF: \(\frac{3}{4} \times \frac{3}{1}\)
3 Multiply: \(\frac{9}{4} = 2\frac{1}{4}\) cups per cake
Key Takeaway: A complex fraction is simply a fraction division problem written top-over-bottom!
Skill 4 • Period 2
One-Step Equations with Opposites
Keep the Balance!
Case 1: Variable is Divided
\(\frac{x}{5} = 4\)
Opposite of \(\div 5\) is multiply by 5 on both sides!
Fractions and Algebra Practice Packet Period 1 • Skills Practice
Fractions & Algebra: Day 1 Mechanics
Name:
Date:
Period:
M-A-D: M ultiply bottom by whole • A dd top • D enominator stays
K-C-F: K eep 1st • C hange (\(\div \to \times\)) • F lip 2nd
1 Part A: Mixed Numbers to Improper Fractions (Use M-A-D)
Show your multiplication & addition
\(2\frac{3}{5}\)
Answer:
\(4\frac{1}{2}\)
Answer:
\(3\frac{2}{7}\)
Answer:
\(5\frac{3}{4}\)
Answer:
2 Part B: Dividing Fractions with Keep-Change-Flip (K-C-F)
Simplify final answers when possible
\(\frac{2}{3} \div \frac{4}{5}\) K • C • F Setup
Flipped multiplication: Final:
\(\frac{5}{6} \div \frac{1}{3}\) K • C • F Setup
Flipped multiplication: Final:
\(\frac{3}{8} \div 6\) Tip: Write \(6\) as \(\frac{6}{1}\)
Flipped multiplication: Final:
\(1\frac{1}{2} \div \frac{3}{4}\) Tip: Use MAD first!
Improper division: Final:
Fractions and Algebra Bridge • Student Practice Packet Page 1 of 2
Period 2 • Applications
Fractions & Algebra: Day 2 Rates & Equations
Name:
Date:
3 Part C: Unit Rates with Fractions (Divide via KCF)
Remember: Unit Rate = \(\frac{\text{Numerator}}{\text{Denominator}}\)
9. Leo bikes \(\frac{4}{5}\) mile in \(\frac{1}{4}\) hour. What is his speed in miles per hour?
Rate: \(\frac{\text{miles}}{\text{hour}}\) Unit Rate:
10. A painting crew paints \(\frac{2}{3}\) of a room using \(\frac{1}{2}\) gallon of paint. How many gallons per 1 full room?
Rate: \(\frac{\text{gallons}}{\text{room}}\) Unit Rate:
4 Part D: One-Step Equations (Opposite Operations & Reciprocals)
Show the balance step on both sides
\(\frac{x}{6} = 7\)
Solution:
\(\frac{m}{3} = \frac{4}{5}\)
Solution:
\(\frac{3}{4}y = 9\)
Solution:
\(\frac{2}{5}w = \frac{6}{7}\)
Solution:
Part E: Detective Check • Find the Flaw!
Samantha was solving \(\frac{2}{3} \div \frac{4}{7}\). She wrote: \(\frac{3}{2} \times \frac{4}{7} = \frac{12}{14} = \frac{6}{7}\).
Fractions and Algebra Exit Ticket Period 1 Quick Check
Exit Ticket • Fraction Mechanics
Name:
Date: Period:
1. Convert the mixed number to an improper fraction using M-A-D:
\(3\frac{4}{7}\)
Improper:
2. Solve using Keep • Change • Flip:
\(\frac{4}{9} \div \frac{2}{3}\)
Answer:
How confident do you feel about Keep-Change-Flip?
Need Help Almost Got It Got It!
Cut Along Line for Distribution
Period 2 Quick Check
Exit Ticket • Rates & Equations
Name:
Date: Period:
1. Maya reads \(\frac{5}{6}\) of a chapter in \(\frac{1}{3}\) of an hour. What is her unit rate in chapters per hour?
Setup: \(\frac{\text{chapters}}{\text{hour}}\)
Rate:
2. Solve the equation for \(y\) using opposite operations:
\(\frac{3}{5}y = 6\)
Solution: \(y = \)
How confident do you feel with fractional equations?
Need Help Almost Got It Got It!
Fractions and Algebra Answer Key Teacher Solution Key • Day 1
Period 1 Solutions: Fraction Mechanics
Complete Worked Steps
Part A: Mixed Numbers to Improper Fractions (M-A-D) 4 pts total (1 pt each)
1. \(2\frac{3}{5}\) \(\frac{13}{5}\)
M: \(5 \times 2 = 10\) • A: \(10 + 3 = 13\) • D: Denominator stays \(5\).
2. \(4\frac{1}{2}\) \(\frac{9}{2}\)
M: \(2 \times 4 = 8\) • A: \(8 + 1 = 9\) • D: Denominator stays \(2\).
3. \(3\frac{2}{7}\) \(\frac{23}{7}\)
M: \(7 \times 3 = 21\) • A: \(21 + 2 = 23\) • D: Denominator stays \(7\).
4. \(5\frac{3}{4}\) \(\frac{23}{4}\)
M: \(4 \times 5 = 20\) • A: \(20 + 3 = 23\) • D: Denominator stays \(4\).
Part B: Dividing Fractions with Keep-Change-Flip (K-C-F) 8 pts total (2 pts each)
5. \(\frac{2}{3} \div \frac{4}{5}\) \(\frac{5}{6}\)
KCF: \(\frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}\)
Accept unsimplified \(\frac{10}{12}\) for 1.5 pts.
6. \(\frac{5}{6} \div \frac{1}{3}\) \(\frac{5}{2}\) or \(2\frac{1}{2}\)
KCF: \(\frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2}\)
Both improper and mixed formats receive full credit.
7. \(\frac{3}{8} \div 6\) \(\frac{1}{16}\)
Write \(6\) as \(\frac{6}{1}\) • KCF: \(\frac{3}{8} \times \frac{1}{6} = \frac{3}{48} = \frac{1}{16}\)
Common error: forgetting to write 6 over 1 before flipping.
8. \(1\frac{1}{2} \div \frac{3}{4}\) \(2\)
MAD: \(1\frac{1}{2} = \frac{3}{2}\) • KCF: \(\frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2\)
Notice reciprocals cancel out to clean whole number 2.
Period 1 Scoring Guide (12 Points Total)
10–12 Points: Mastery. Ready for fractional unit rates & equations.
7–9 Points: Minor arithmetic slips or forgot to simplify. Reinforce KCF steps.
0–6 Points: Conceptual confusion. Review MAD and flipping the 2nd fraction.
Fractions and Algebra Bridge • Teacher Solutions & Grading Guide Page 1 of 2
Teacher Solution Key • Day 2
Period 2 Solutions & Exit Tickets
Complete Solutions
Part C: Unit Rates 2 Problems
9. Leo's Biking Speed \(3\frac{1}{5}\) mph
\(\frac{4/5}{1/4} = \frac{4}{5} \times \frac{4}{1} = \frac{16}{5} = 3\frac{1}{5}\) (or 3.2 mph)
Rate Problems Teacher Guide Teacher Instructional Script
Cracking Mixed Number Rate Problems
Step-by-Step Blueprint • "Per Means Fraction Bar" • Scripted Think-Aloud
Target: Word Problem Mastery
The Golden Rule: "PER" is the Fraction Bar!
Students freeze because they do not know which number goes on top. Teach them this exact visual chant:
"Miles PER Hour" →
Miles (Numerator) Hours (Denominator)
"The word before 'per' goes on top. The word after 'per' goes on bottom."
The 5-Step Problem-Solving Blueprint
Step 1: Words Write the target rate as words with a fraction bar (\(\frac{\text{miles}}{\text{hours}}\)).
Step 2: M-A-D Convert all mixed numbers into improper fractions. Never divide mixed numbers!
Step 3: Setup Place improper fractions into the ratio, then rewrite as a horizontal division (\(\div\)).
Step 4: K-C-F Keep 1st fraction, change to multiply, flip 2nd fraction (reciprocal), then multiply.
Step 5: Units Simplify to a mixed number or integer, and attach the exact unit label!
Classroom Script Anchor Problem: "Brandon's Run"
5 1/4 miles in 1 1/2 hours
Teacher Says: "Let’s read the problem: 'Brandon ran \(5\frac{1}{4}\) miles in \(1\frac{1}{2}\) hours. Determine Brandon's speed in miles per hour.' Notice that question asks for miles per hour . That is our mission clue!"
Step 1: "Write the word ratio on your board: \(\frac{\text{miles}}{\text{hours}}\). Miles is on top, hours is on bottom."
Step 2: "Look at \(5\frac{1}{4}\). Use MAD: \(4 \times 5 = 20\), plus \(1 = 21\). That is \(\frac{21}{4}\). Now look at \(1\frac{1}{2}\): \(2 \times 1 = 2\), plus \(1 = 3\). That is \(\frac{3}{2}\)."
Step 3: "Write the division: \(\frac{21}{4} \div \frac{3}{2}\)."
Step 4: "Now use K-C-F! Keep \(\frac{21}{4}\). Change \(\div\) to \(\times\). Flip \(\frac{3}{2}\) to \(\frac{2}{3}\). Let's multiply: \(\frac{21 \times 2}{4 \times 3} = \frac{42}{12}\)."
Step 5: "Divide 42 by 12: 12 goes into 42 three times with 6 left over, so \(3\frac{6}{12} = 3\frac{1}{2}\). Never stop at the number—add the unit label: \(3\frac{1}{2}\) miles per hour !"
Rate Problems • Teacher Facilitation Guide Page 1 of 2
Intervention & Diagnostics
Rate Problems Slides Real-World Math Mastery Word Problem Strategy
Cracking Fractional Rate Word Problems
Conquer mixed numbers, decode "miles per hour", and master the 5-step blueprint with zero confusion.
Step 1: Words • Step 2: MAD • Step 3: Setup • Step 4: KCF • Step 5: Units
Key Secret: Fractions in word problems are just division problems telling a story! Slide 1 of 6
Secret Weapon
"PER" Means Fraction Bar!
Never Guess Which Goes on Top
In The Problem
Miles per Hour
→
In Your Math
Miles (Top) Hours (Bottom)
"Cost per Pound" \(\frac{\text{Dollars}}{\text{Pounds}}\)
"Cups per Cake" \(\frac{\text{Cups}}{\text{Cakes}}\)
"Pages per Minute" \(\frac{\text{Pages}}{\text{Minutes}}\)
The word BEFORE "per" is numerator (top). The word AFTER "per" is denominator (bottom)!
Anchor Model • Steps 1 & 2
Brandon's Run
Word Clues & MAD
"Brandon went for a run after school. He ran for \(5\frac{1}{4}\) miles in \(1\frac{1}{2}\) hours. Determine Brandon's speed in miles per hour."
1
Write Word Rate
\(\frac{\text{Miles}}{\text{Hours}}\)
Target is "miles per hour", so Miles stays on top!
2
M-A-D (Convert Both)
\(5\frac{1}{4} = \frac{(4 \times 5) + 1}{4} = \frac{21}{4}\) miles
\(1\frac{1}{2} = \frac{(2 \times 1) + 1}{2} = \frac{3}{2}\) hours
Never divide mixed numbers directly—always turn them into improper fractions first!
Anchor Model • Steps 3, 4 & 5
Dividing & Labeling
KCF to Final Answer
3
Setup Division
Put top over bottom, then rewrite horizontally:
\(\frac{21}{4} \div \frac{3}{2}\)
4
Apply K-C-F
Keep, change, flip the second fraction:
\(\frac{21}{4} \times \frac{2}{3} = \frac{42}{12}\)
5
Simplify & Unit
Convert to mixed number & attach label:
\(3\frac{1}{2}\) mph
Brandon runs at an average speed of \(3\frac{1}{2}\) miles per hour (or \(3.5\) mph).
Try Together
Guided Practice: Chef Marcus
Follow The 5 Steps
"Chef Marcus uses \(4\frac{1}{2}\) cups of sugar to bake \(3\) batches of cookies. What is the unit rate in cups of sugar per batch?"
1. Word Rate \(\frac{\text{Cups}}{\text{Batch}}\)
Rate Problems Practice Packet 5-Step Problem Solving
Fractional Rate Word Problems
Name:
Date:
The 5 Steps:
1. Word Ratio (\(\frac{\text{top}}{\text{bottom}}\)) • 2. M-A-D • 3. Setup Division • 4. K-C-F • 5. Label Units!
1. Anchor Problem: Brandon went for a run after school. He ran for \(5\frac{1}{4}\) miles in \(1\frac{1}{2}\) hours. Determine Brandon's speed in miles per hour. Show all steps and include units in your answer.
Guided Model
Step 1: Word Ratio
\(\frac{\text{word}}{\text{word}}\)
Step 2: M-A-D
Convert both
Step 3: Setup (\(\div\))
Rewrite \(\div\)
Step 4: K-C-F
Multiply
Step 5: Final Unit
Number + Unit
2. Cycling Distance: Maya rode her bicycle \(8\frac{3}{4}\) miles on the rail trail in \(1\frac{1}{4}\) hours. What was Maya's average speed in miles per hour?
Show 5 Steps
1. Word Ratio
2. M-A-D
3. Setup (\(\div\))
4. K-C-F
5. Final Unit
Fraction Rate Word Problems • Student Practice Packet Page 1 of 3
Independent Applications
Rate Problem Applications
Name:
Cooking
3. A recipe for homemade salsa uses \(3\frac{1}{3}\) cups of crushed tomatoes to make \(2\frac{1}{2}\) jars. How many cups of tomatoes are needed per 1 jar?
Final Unit Rate:
Summer Work
4. Andre mowed \(4\frac{1}{2}\) lawns in \(2\frac{1}{4}\) hours. What is Andre's mowing rate in lawns per hour?
Final Unit Rate:
5. Fuel Mileage: A trail motorbike uses \(2\frac{2}{5}\) gallons of fuel to travel \(18\) miles. What is the fuel efficiency in miles per gallon? (Remember: 18 can be written as \(\frac{18}{1}\)).
Miles ÷ Gallons
Show KCF steps: Efficiency:
6. Error Detective: Stop Carlos's Shortcut!
Carlos looked at the Brandon problem (\(5\frac{1}{4}\) miles in \(1\frac{1}{2}\) hours) and argued:
Why is Carlos's method mathematically incorrect? What is the correct speed?
Fraction Rate Word Problems • Student Practice Packet Page 2 of 3
Rate Problems Exit Ticket Quick Check • Slip A
Exit Ticket • Fractional Unit Rates
Name:
Date: Period:
Kendrick is training for a cross-country meet. He ran \(3\frac{3}{4}\) miles in \(1\frac{1}{4}\) hours. Determine Kendrick's speed in miles per hour. Show all steps and include units in your answer!
1. Word Ratio
2. M-A-D Both
3. K-C-F Division
4. Final Unit Rate
How confident do you feel solving mixed-number word problems?
Need Help Pretty Good Crushed It!
Cut Line for Printing
Quick Check • Slip B
Exit Ticket • Fractional Unit Rates
Name:
Date: Period:
A hiking trail guide notes that Jordan hiked \(4\frac{2}{3}\) miles in \(1\frac{1}{3}\) hours. Determine Jordan's hiking speed in miles per hour. Show all steps and include units in your answer!
1. Word Ratio
2. M-A-D Both
3. K-C-F Division
4. Final Unit Rate
How confident do you feel solving mixed-number word problems?
Need Help Pretty Good Crushed It!
Rate Problems Answer Key Teacher Solution Key
Rate Problems Practice Solutions
Full 5-Step Steps
1. Anchor Problem: Brandon's Run (\(5\frac{1}{4}\) mi in \(1\frac{1}{2}\) hr) \(3\frac{1}{2}\) miles per hour
1. Word Ratio: \(\frac{\text{Miles}}{\text{Hours}}\)
2. M-A-D: \(5\frac{1}{4} = \frac{21}{4}\)
3. Setup: \(\frac{21}{4} \div \frac{3}{2}\)
4. K-C-F: \(\frac{21}{4} \times \frac{2}{3} = \frac{42}{12}\)
5. Final: \(\frac{7}{2} = \mathbf{3\frac{1}{2}\text{ mph}}\)
2. Maya's Cycling (\(8\frac{3}{4}\) mi in \(1\frac{1}{4}\) hr) \(7\) miles per hour
1. Word Ratio: \(\frac{\text{Miles}}{\text{Hours}}\)
2. M-A-D: \(8\frac{3}{4} = \frac{35}{4}\)
3. Setup: \(\frac{35}{4} \div \frac{5}{4}\)
4. K-C-F: \(\frac{35}{4} \times \frac{4}{5} = \frac{140}{20}\)
5. Final: \(\mathbf{7\text{ mph}}\)
3. Carmen's Salsa Recipe \(1\frac{1}{3}\) cups/jar
• Word Ratio: \(\frac{\text{Cups of Tomatoes}}{\text{Jars}}\)
• MAD: \(3\frac{1}{3} = \frac{10}{3}\) and \(2\frac{1}{2} = \frac{5}{2}\)
• KCF: \(\frac{10}{3} \times \frac{2}{5} = \frac{20}{15} = \frac{4}{3}\)
• Final Answer: \(1\frac{1}{3}\) cups per jar.
4. Andre's Lawns \(2\) lawns/hour
• Word Ratio: \(\frac{\text{Lawns}}{\text{Hours}}\)
• MAD: \(4\frac{1}{2} = \frac{9}{2}\) and \(2\frac{1}{4} = \frac{9}{4}\)
• KCF: \(\frac{9}{2} \times \frac{4}{9} = \frac{36}{18} = 2\)
• Final Answer: \(2\) lawns per hour.
5. Trail Motorbike Fuel Mileage \(7\frac{1}{2}\) miles per gallon (or 7.5 mpg)
Steps: Ratio \(= \frac{\text{Miles}}{\text{Gallons}} = 18 \div 2\frac{2}{5} = \frac{18}{1} \div \frac{12}{5}\).
Rate Problems • Teacher Solutions & Grading Guide Page 1 of 2
Diagnostics & Assessments
Error Analysis & Exit Ticket Keys
Grading Benchmarks
Problem 6: Why Carlos's Shortcut Fails
Rate Problems Task Cards Practice Stations • 10 Problem Set
Rate Word Problem Task Cards
Solve each problem on your laminated 5-step dry-erase workspace mat.
Cards 1–5
Card #1 • Track & Field Target: Miles per Hour
Mateo ran \(4\frac{1}{2}\) miles around the school track in \(1\frac{1}{2}\) hours. Determine Mateo's average running speed in miles per hour. Show all 5 steps on your mat.
Mat Setup: Miles (top) ÷ Hours (bottom) Answer format: ______ mph
Card #2 • Bakery Kitchen Target: Cups per Loaf
Jasmine used \(3\frac{3}{4}\) cups of flour to bake \(2\frac{1}{2}\) loaves of artisan bread. How many cups of flour were used per 1 whole loaf?
Mat Setup: Cups (top) ÷ Loaves (bottom) Answer format: ______ cups/loaf
Card #3 • Home Improvement Target: Sq Yards per Hour
A painter stained \(6\frac{2}{3}\) square yards of wood deck fencing in \(1\frac{1}{3}\) hours. Find the staining rate in square yards per hour.
Mat Setup: Square Yards (top) ÷ Hours (bottom) Answer format: ______ sq yd/hr
Card #4 • Swim Training Target: Miles per Hour
Chloe swam \(2\frac{1}{4}\) miles during morning swim practice in \(\frac{3}{4}\) of an hour. Determine Chloe's average swimming speed in miles per hour.
Mat Setup: Miles (top) ÷ Hours (bottom) Answer format: ______ mph
Card #5 • Landscaping Gig Target: Acres per Hour
Darius mowed \(3\frac{1}{2}\) acres of sports fields in \(1\frac{3}{4}\) hours using a commercial mower. What was his mowing rate in acres per hour?
Mat Setup: Acres (top) ÷ Hours (bottom) Answer format: ______ acres/hr
Fraction Rate Word Problems • 10 Problem Task Set Page 1 of 2 • Cards 1 to 5
Practice Stations • 10 Problem Set
Rate Word Problem Task Cards
Show all steps on your mat: Word Ratio • MAD • Setup • KCF • Units.
Cards 6–10
Card #6 • Fuel Efficiency Target: Miles per Gallon
An SUV traveled \(22\frac{1}{2}\) miles across town on \(1\frac{1}{4}\) gallons of gasoline. Determine the vehicle's fuel efficiency in miles per gallon.
Mat Setup: Miles (top) ÷ Gallons (bottom) Answer format: ______ mpg
Card #7 • Scarf Knitting Target: Inches per Hour
Grandma Rosa knitted \(5\frac{5}{8}\) inches of a wool winter scarf in \(1\frac{1}{2}\) hours. Find her knitting speed in inches per hour.
Rate Problems Display Slides Card #1 Track & Field Practice
1 of 10
Mateo ran \(4\frac{1}{2}\) miles around the school track in \(1\frac{1}{2}\) hours. Determine Mateo's average running speed in miles per hour.
Mat Setup:
\(\frac{\text{Miles (Top)}}{\text{Hours (Bottom)}}\)
Target: Miles per Hour (mph)
Use Your Laminated Mat: 1. Words • 2. MAD • 3. Setup • 4. KCF • 5. Units Rate Problem Display
Card #2 Bakery Kitchen
2 of 10
Jasmine used \(3\frac{3}{4}\) cups of flour to bake \(2\frac{1}{2}\) loaves of artisan bread. How many cups of flour were used per 1 whole loaf?
Mat Setup:
\(\frac{\text{Cups of Flour (Top)}}{\text{Loaves of Bread (Bottom)}}\)
Target: Cups per Loaf
Use Your Laminated Mat: 1. Words • 2. MAD • 3. Setup • 4. KCF • 5. Units Rate Problem Display
Card #3 Home Improvement
3 of 10
A painter stained \(6\frac{2}{3}\) square yards of wood deck fencing in \(1\frac{1}{3}\) hours. Find the staining rate in square yards per hour.
Mat Setup:
\(\frac{\text{Square Yards (Top)}}{\text{Hours (Bottom)}}\)
Target: Sq Yards per Hour
Use Your Laminated Mat: 1. Words • 2. MAD • 3. Setup • 4. KCF • 5. Units Rate Problem Display
Card #4 Swim Training
4 of 10
Chloe swam \(2\frac{1}{4}\) miles during morning swim practice in \(\frac{3}{4}\) of an hour. Determine Chloe's average swimming speed in miles per hour.
Mat Setup:
\(\frac{\text{Miles (Top)}}{\text{Hours (Bottom)}}\)
Target: Miles per Hour (mph)
Use Your Laminated Mat: 1. Words • 2. MAD • 3. Setup • 4. KCF • 5. Units Rate Problem Display
Card #5 Landscaping Gig
5 of 10
Darius mowed \(3\frac{1}{2}\) acres of sports fields in \(1\frac{3}{4}\) hours using a commercial mower. What was his mowing rate in acres per hour?
Mat Setup:
\(\frac{\text{Acres (Top)}}{\text{Hours (Bottom)}}\)
Target: Acres per Hour
