🟠 Level 0 — Most Support. Same skills as Level 1, with extra help: press then tap any text to hear it. Open every 💡 Hint — that is okay here.

Reveal Math · Unit 3 · Supplemental

Ratios & Rates

Extra support and enrichment for ratios, unit rates, equivalent ratios, ratio tables, and proportional reasoning. Standards 6.RP.A.1, 6.RP.A.2, 6.RP.A.3.

🖨️ Differentiated Practice Worksheets

Ready-to-print practice at three levels — pick the right fit for each student.

Level 0 · Extra Support Scaffolded steps, worked examples, extra space. Level 1 · Support Guided practice on the core skills. Level 2 · Enrichment Stretch problems and deeper reasoning.

Visual Vocabulary

2 : 1
Ratio
Razon
A comparison of two numbers. "2 blue to 1 orange" can be written as 2:1, 2 to 1, or 2/1.
60 miles 1 hour
Rate
Tasa
A ratio that compares two different kinds of things. Example: 60 miles per 1 hour.
$3.50 1 pound per ONE
Unit Rate
Tasa unitaria
A rate where the second number is 1. Example: $3.50 per 1 pound. Divide to find it.
1:3 = 2:6
Equivalent Ratios
Razones equivalentes
Ratios that show the same comparison. 1:3 and 2:6 are equivalent (multiply both parts by 2).
cups servings 2 4 4 8
Ratio Table
Tabla de razones
A table that lists pairs of equivalent ratios. Multiply or divide both columns by the same number.
part whole part-to-whole
Part-to-Whole
Parte al todo
A ratio comparing one part to the total. Example: 3 girls out of 10 students = 3:10.
part-to-part
Part-to-Part
Parte a parte
A ratio comparing one part to another part. Example: 3 girls to 7 boys = 3:7.
12 inches = 1 foot
Conversion Factor
Factor de conversion
A ratio that equals 1, used to change units. 12 inches = 1 foot, so 12 in./1 ft = 1.

Sentence Frames

The ratio of   to   is  .
The unit rate is   per   because I divided   by  .
These ratios are equivalent because I multiplied both parts by  .
To find the missing value, I can   both parts of the ratio by  .
The better buy is   because its unit price is  , which is less than  .
To convert   to  , I multiply by  .

Step-by-Step Visual Guides

How to Write a Ratio

A bag has 4 red marbles and 6 blue marbles.

red to blue
1 Identify the two groups: 4 red and 6 blue.
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2 Write it three ways: 4 to 6, 4:6, or 4/6.
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3 Simplify if you can. Both divide by 2: 2:3.
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! Order matters! "Red to blue" = 4:6. "Blue to red" = 6:4. Read carefully.

How to Find a Unit Rate

A car drives 150 miles in 3 hours. What is the speed?

1 Write the rate as a fraction: 150 miles / 3 hours
↓
2 Divide the top by the bottom: 150 / 3 = 50
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3 Write with units: 50 miles per hour (or 50 mph)

How to Find Equivalent Ratios with a Table

A recipe uses 2 cups of flour for every 3 eggs.

1 Start with the given ratio: Flour 2, Eggs 3.
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2 Multiply both by the same number: x2 → 4:6. x3 → 6:9. x4 → 8:12.
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3 Check: All ratios simplify back to 2:3. They are all equivalent!

Simplified Practice

  1. A class has 12 boys and 18 girls. Write the ratio of boys to girls in simplest form.
    Write 12:18. What number divides evenly into both 12 and 18?
    12:18. Both divide by 6. Simplified: 2:3.
  2. A pack of 8 pencils costs $4. What is the cost per pencil?
    Divide the total cost by the number of pencils: $4 / 8.
    $4 / 8 = $0.50 per pencil.
  3. Are these ratios equivalent? 3:5 and 9:15
    Multiply both parts of 3:5 by 3. What do you get?
    3 x 3 = 9 and 5 x 3 = 15. So 3:5 = 9:15. Yes, they are equivalent!
  4. Complete the ratio table: Apples: 3, 6, 9, __ | Oranges: 5, 10, 15, __
    The pattern: multiply the original ratio (3:5) by 1, 2, 3, and then by 4.
    3 x 4 = 12 apples, 5 x 4 = 20 oranges. The next pair is 12:20.
  5. A car drives 180 miles in 4 hours. What is the unit rate (miles per hour)?
    Divide 180 by 4 to get the miles for 1 hour.
    180 / 4 = 45 miles per hour.
  6. Which is the better buy? 6 cans for $3 or 10 cans for $4.50?
    Find the price per can for each: $3/6 and $4.50/10. Compare them.
    Option 1: $3 / 6 = $0.50/can. Option 2: $4.50 / 10 = $0.45/can. The 10-can pack is the better buy ($0.45 < $0.50).
  7. The ratio of dogs to cats at a shelter is 2:5. If there are 10 dogs, how many cats are there?
    The dogs went from 2 to 10. What did you multiply by? Do the same to the cats.
    2 x 5 = 10 dogs. So 5 x 5 = 25 cats.
  8. Convert 3 feet to inches. (1 foot = 12 inches)
    Multiply the number of feet by 12 (inches per foot).
    3 x 12 = 36 inches.
  9. A recipe for 4 servings uses 6 cups of rice. How many cups for 12 servings?
    12 servings is 3 times as many as 4 servings (12 / 4 = 3). Multiply the rice by the same number.
    6 x 3 = 18 cups of rice.
  10. Write the ratio of vowels to consonants in the word MATHEMATICS.
    Count the vowels (A, E, I, O, U) and consonants in M-A-T-H-E-M-A-T-I-C-S.
    Vowels: A, E, A, I = 4. Consonants: M, T, H, M, T, C, S = 7. Ratio: 4:7.

Real-World Connections

Cooking & Recipes

A pancake recipe says: 2 cups of mix for every 1 cup of milk. If you want to make pancakes for 8 people instead of 4, you double everything. Ratios keep the flavor the same no matter how much you make!

$2.49/lb

Grocery Shopping

Store A sells 5 pounds of chicken for $15. Store B sells 3 pounds for $8.40. Which is cheaper? Find the unit rate: Store A = $3/lb, Store B = $2.80/lb. Store B is the better deal!

Speed & Travel

Your family drives 240 miles in 4 hours. The unit rate is 60 miles per hour. At that speed, how far can you go in 6 hours? Multiply: 60 x 6 = 360 miles. Rates help you plan trips!

Sports

A soccer player scores 8 goals in 20 games. That is a rate of 8/20 = 0.4 goals per game. Another player scores 6 goals in 12 games = 0.5 goals per game. Unit rates help compare players fairly!

Challenge Problems

  1. The ratio of cats to dogs at a pet store is 3:4. There are 35 animals total (only cats and dogs). How many cats are there? Medium
    The ratio 3:4 means there are 3+4 = 7 parts total. Divide 35 by 7 to find the value of one part.
    7 parts = 35 animals. 1 part = 5. Cats = 3 x 5 = 15 cats.
  2. A map scale says 1 inch = 25 miles. Two cities are 3.5 inches apart on the map. How far apart are they in real life? Medium
    Multiply the map distance by the scale factor: 3.5 x 25.
    3.5 x 25 = 87.5 miles apart.
  3. Runner A finishes a 5K race in 22 minutes. Runner B finishes a 10K race in 48 minutes. Who has the faster pace (minutes per kilometer)? Medium
    Find minutes per km for each: 22/5 and 48/10. Lower is faster.
    Runner A: 22/5 = 4.4 min/km. Runner B: 48/10 = 4.8 min/km. Runner A is faster (lower time per km).
  4. A paint mixture uses red, blue, and white in the ratio 2:3:5. If you need 40 gallons total, how many gallons of each color? Hard
    Total parts = 2+3+5 = 10. Find what one part equals: 40/10 = 4 gallons per part.
    Red: 2 x 4 = 8 gallons. Blue: 3 x 4 = 12 gallons. White: 5 x 4 = 20 gallons. Check: 8+12+20 = 40.
  5. A faucet leaks 3 cups of water every 2 hours. At this rate, how many gallons leak in one week? (16 cups = 1 gallon) Hard
    First find cups per hour: 3/2 = 1.5. Then multiply by hours in a week: 24 x 7 = 168. Then convert cups to gallons.
    Rate: 1.5 cups/hour. Hours in a week: 168. Total cups: 1.5 x 168 = 252 cups. Gallons: 252 / 16 = 15.75 gallons.
  6. Car A gets 32 miles per gallon and gas costs $3.50/gallon. Car B gets 24 mpg and gas costs $3.20/gallon. Which car costs less to drive 480 miles? Hard
    Find gallons needed for each: 480/mpg. Then multiply gallons by price.
    Car A: 480/32 = 15 gal, cost = 15 x $3.50 = $52.50. Car B: 480/24 = 20 gal, cost = 20 x $3.20 = $64.00. Car A costs less.
  7. The ratio of boys to girls in a school is 5:6. If 24 more girls join, the ratio becomes 5:8. How many boys are in the school? Expert
    Let boys = 5x, original girls = 6x. After 24 more girls: 5x/(6x+24) = 5/8. Cross multiply to solve.
    5x/(6x+24) = 5/8. Cross multiply: 40x = 30x + 120. 10x = 120. x = 12. Boys = 5 x 12 = 60.
  8. You can buy pens in packs of 5 for $3.75 or packs of 12 for $8.40. You need exactly 60 pens. What is the cheapest way to buy them? Hard
    Unit price: $3.75/5 = $0.75/pen vs $8.40/12 = $0.70/pen. But you need exactly 60 — check different combinations.
    5-packs: 60/5 = 12 packs, cost = 12 x $3.75 = $45.00. 12-packs: 60/12 = 5 packs, cost = 5 x $8.40 = $42.00. Cheapest: five 12-packs for $42.00.
  9. A recipe calls for flour and sugar in the ratio 4:1. Maria accidentally put in 3 cups of sugar. How much flour does she need to keep the ratio correct? Medium
    If sugar is 1 part and she used 3 cups, each part = 3 cups. Flour is 4 parts.
    4 x 3 = 12 cups of flour.
  10. A gear with 20 teeth is connected to a gear with 50 teeth. When the small gear makes 10 full turns, how many turns does the large gear make? Expert
    The teeth mesh, so total teeth engaged must be equal. Small gear: 20 teeth x 10 turns = 200 teeth. Large gear: 200 / 50 teeth per turn.
    Small gear pushes 20 x 10 = 200 teeth. Large gear: 200 / 50 = 4 turns.

Real-World Investigations

Best Value Grocery Challenge

Compare unit prices at two different stores or brands to find the best deals.

  1. Choose 5 common products (juice, cereal, pasta, etc.)
  2. Find two different sizes or brands for each product
  3. Calculate the unit price for every option
  4. Create a comparison table showing product, size, total price, and unit price
  5. Determine the best buy for each and calculate how much you save per year if you buy that product weekly

Scale Model Project

Create a scale drawing of your classroom, bedroom, or dream house.

  1. Measure the real dimensions of the room (length, width, furniture)
  2. Choose a scale ratio (e.g., 1 inch = 2 feet)
  3. Convert all real measurements to scale measurements using your ratio
  4. Draw the scale model on graph paper, including furniture
  5. Calculate the real area and the scale area — how do they compare?

Party Planning with Ratios

Plan a class party for 30 people using ratio reasoning for all quantities.

  1. A punch recipe serves 6 people. Scale it up for 30 people (multiply by 5)
  2. Pizza comes in boxes of 8 slices. If each person eats 3 slices, how many boxes?
  3. Decorations come in packs of 12. You want 2 per person. How many packs?
  4. Budget: $150 total. Create a ratio for food vs. decorations vs. supplies
  5. Present your complete plan with all ratio calculations shown

Brain Teasers

The Shrinking Ratio

A bag has red and blue marbles in the ratio 3:2. You add 5 red marbles and the ratio becomes 4:2. How many blue marbles are in the bag?

Let blue = 2x. Original red = 3x. After adding 5 red: (3x+5)/(2x) = 4/2 = 2. So 3x+5 = 4x. x = 5. Blue marbles = 2 x 5 = 10.

The Speed Puzzle

You drive to school at 30 mph and drive home at 50 mph on the same route. Is your average speed for the round trip 40 mph? (Careful!)

No! Average speed = total distance / total time. If the distance is d miles each way: Time to school = d/30. Time home = d/50. Total time = d/30 + d/50 = 5d/150 + 3d/150 = 8d/150. Average speed = 2d / (8d/150) = 300/8 = 37.5 mph. The average is less than 40 because you spend more time at the slower speed.

The Lemonade Dilemma

Mix A is lemon juice and water in ratio 1:4. Mix B is 1:6. You combine equal amounts of Mix A and Mix B. What is the ratio of lemon juice to water in the combined mix?

Take 1 cup of each mix. Mix A (1 cup): 1/5 lemon, 4/5 water. Mix B (1 cup): 1/7 lemon, 6/7 water. Combined lemon: 1/5 + 1/7 = 12/35. Combined water: 4/5 + 6/7 = 28/35 + 30/35 = 58/35. Ratio: 12:58 = 6:29.

The Growing Garden

A garden has flowers and vegetables in the ratio 2:3. If you triple the number of flowers and double the number of vegetables, what is the new ratio?

Start with flowers = 2x, vegetables = 3x. After changes: flowers = 3(2x) = 6x, vegetables = 2(3x) = 6x. New ratio: 6x:6x = 1:1. They are equal!

Extension Topics

Where This Leads: Proportional Relationships (7th Grade)

In 7th grade, you will study proportional relationships in depth. You will learn that y = kx represents a proportional relationship where k is the constant of proportionality (the unit rate). Every ratio table, unit rate, and equivalent ratio you learn now is building toward this big idea.

Where This Leads: Scale Factor & Similar Figures

When you use a map scale like 1 inch = 10 miles, you are using a scale factor. In geometry, similar figures have the same shape but different sizes, connected by a constant ratio. Architects, engineers, and artists all use scale factors daily.

Where This Leads: Slope & Linear Equations

The unit rate in a ratio (like 50 mph) becomes the slope of a line in algebra. The equation y = 50x means distance = 50 x time. Understanding rates now means you already understand slope — the steepness of a line on a graph.

Self-Assessment

Rate your confidence: 1 = Need help, 2 = Getting there, 3 = Got it, 4 = Can teach it

  • I can write a ratio in three forms (a to b, a:b, a/b)
  • I can simplify ratios to lowest terms
  • I can find a unit rate by dividing
  • I can determine if two ratios are equivalent
  • I can use a ratio table to generate equivalent ratios
  • I can solve "better buy" problems by comparing unit prices
  • I can use ratios to convert between measurement units
  • I can solve ratio problems in real-world contexts