Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3c

Lesson 3.103.4–3.10 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 3.4–3.10 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 3.4–3.10: 3.4 Determine Equivalent Ratios Using Graphs, 3.5 Compare Ratio Relationships, 3.6 Ratio Reasoning: Convert Measurements within the Same System, 3.7 Ratio Reasoning: Convert Measurements Between Systems, 3.8 Solve Problems with Unit Rates, 3.9 Equivalent Ratios, 3.10 Convert Measurement Units. Work one example from each lesson, then prove you're caught up in the mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Coordinate planeSpanish: Plano cartesiano A grid with a line going across and a line going up to plot points. A + shape made by two number lines crossing at the center point (0, 0)
Ordered pairSpanish: Par ordenado Two numbers (x, y) that tell where a point is on a grid. (3, 6) means go right 3, up 6
Linear patternSpanish: Patrón lineal Points that make a straight line on a grid. (1,2), (2,4), (3,6) all line up
ProportionalSpanish: Proporcional Two amounts that grow together at the same rate. A straight line from (0,0) through (2,6) and (4,12)
OriginSpanish: Origen The point (0, 0) where the two grid lines cross. The starting corner of the grid at (0, 0)
Ratio tableSpanish: Tabla de razones A table of equal ratios that shows a pattern. Cups of juice: 2, 4, 6 | Cups of water: 3, 6, 9

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A recipe uses 2 ounces of sauce for every 1 sundae. Write ordered pairs (sundaes, ounces) for 1, 2 and 3 sundaes.

  1. Write 1 sundae and 2 ounces in the table.
  2. Multiply both by 2, then by 3: 2 × 2 = 4; 2 × 3 = 6
  3. Write each pair as (x, y): (1, 2), (2, 4), (3, 6)
  4. The ordered pairs are (1, 2), (2, 4) and (3, 6).
  5. Store A sells 2 pens for $6. Store B sells 3 pens for $12. Which store has the better deal?
  6. Write each store in its own table: 2 : $6; 3 : $12
  7. Divide Store A's table by 2: $6 ÷ 2 = $3
  8. Divide Store B's table by 3: $12 ÷ 3 = $4
  9. Choose the lower price for 1 pen: $3 < $4
  10. Store A has the better deal at $3 per pen.
  11. A child is 4 feet tall. How many inches tall is the child?
  12. Write 1 foot and 12 inches in the table.
  13. Find the scale factor for the feet: 4 ÷ 1 = 4
  14. Multiply the inches by the same factor: 12 × 4 = 48
  15. The child is 48 inches tall.
  16. Use 1 kilometer ≈ 0.6 mile. About how many miles is 100 kilometers?
  17. Write the conversion fact in the table: 1 km : 0.6 mi
  18. Find the scale factor from 1 to 100: 100 ÷ 1 = 100
  19. Multiply the miles by the same factor: 0.6 × 100 = 60
  20. 100 kilometers is about 60 miles.
  21. Fun Supply Co. sells 500 tokens for $60. What is the cost for 1 token?
  22. Write the deal in the table: 500 tokens : $60
  23. Divide both numbers by 500: 500 ÷ 500 = 1; $60 ÷ 500 = $0.12
  24. Write the unit price: $0.12 per token
  25. The cost is $0.12 per token.
  26. A ratio is 2:5. Use a scale factor of 3 to make an equivalent ratio.
  27. Write the ratio in the table: 2 : 5
  28. Multiply the first number by 3: 2 × 3 = 6
  29. Multiply the second number by 3: 5 × 3 = 15
  30. 6:15 is equivalent to 2:5.
  31. A cabinet is 5 feet tall. How many inches tall is the cabinet?
  32. Write the conversion fact in the table: 1 foot : 12 inches
  33. Find the scale factor: 5 ÷ 1 = 5
  34. Multiply the inches by 5: 12 × 5 = 60
  35. The cabinet is 60 inches tall.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Each bag holds 5 apples. Bags are x and apples are y. What is the y-value of the point for 3 bags?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • When converting from a unit to a unit, I by the conversion factor because .

Word bank Coordinate planeOrdered pairLinear patternProportionalOriginRatio tablelargersmallermultiplydivideconversion factorratio

Watch out!A common mistake

A common mistake in Convert Measurement Units is applying the conversion factor in the wrong direction

Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3c

Lesson 3.103.4–3.10 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 3.4–3.10 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 3.4–3.10: 3.4 Determine Equivalent Ratios Using Graphs, 3.5 Compare Ratio Relationships, 3.6 Ratio Reasoning: Convert Measurements within the Same System, 3.7 Ratio Reasoning: Convert Measurements Between Systems, 3.8 Solve Problems with Unit Rates, 3.9 Equivalent Ratios, 3.10 Convert Measurement Units. Work one example from each lesson, then prove you're caught up in the mixed practice.

  1. 1Complete each step, then write the final answer.
    01234512345678910BikesWheels(1, 2)(2, 4)
    Each bike adds 2 wheels. Where is the point for 4 bikes?

    Each bike has 2 wheels. Bikes are x and wheels are y. What is the y-value of the point for 4 bikes?

    Show your work

    Hint Multiply the bikes by 2.

    Final answer:
  2. 2Complete each step, then write the final answer.
    PacksPencils________________

    Each pack has 4 pencils. Packs are x and pencils are y. The point for 3 packs is (3, ?). What is the missing number?

    Show your work

    Hint The missing number is y. Multiply the packs by 4.

    Final answer:
  3. 3Complete each step, then write the final answer.
    CookiesCost ($)________________________________
    Shop A: first two columns. Shop B: last two.

    Shop A sells 2 cookies for $4. Shop B sells 3 cookies for $9. What is the lower price for 1 cookie?

    Show your work

    Hint Divide each cost by the number of cookies.

    Final answer:
  4. 4Complete each step, then write the final answer.
    Juice (cups)Water (cups)________________________________
    Drink A: first two columns. Drink B: last two.

    Drink A uses 1 cup of juice for 2 cups of water. Drink B uses 2 cups of juice for 3 cups of water. Scale both to 6 cups of water. Which drink has more juice?

    Show your work

    Hint With the same water, the drink with more juice wins.

    Final answer:
  5. 5Complete each step, then write the final answer.
    FeetInches________________

    How many inches are in 2 feet?

    Show your work

    Hint Each foot is 12 inches. Find 2 × 12.

    Final answer:
  6. 6Complete each step, then write the final answer.
    KilometersMeters________________

    There are 1,000 meters in 1 kilometer. How many meters are in 6 kilometers?

    Show your work

    Hint Meters are smaller than kilometers, so multiply by 1,000.

    Final answer:
  7. 7Complete each step, then write the final answer.
    Kilometers (km)Miles (mi)________________

    Use 1 kilometer ≈ 0.6 mile. About how many miles is 60 kilometers?

    Show your work

    Hint Find the scale factor from 1 to 60. Multiply 0.6 by the same factor.

    Final answer:
  8. 8Complete each step, then write the final answer.
    Kilograms (kg)Pounds (lb)________________

    Use 1 kilogram ≈ 2.2 pounds. About how many pounds is 3 kilograms?

    Show your work

    Hint Find the scale factor from 1 to 3. Multiply 2.2 by the same factor.

    Final answer:
  9. 9Complete each step, then write the final answer.
    ApplesCost ($)________________

    6 apples cost $3. What is the cost for 1 apple?

    Show your work

    Hint Divide the price by the number of apples: $3 ÷ 6.

    Final answer:
  10. 10Complete each step, then write the final answer.
    Shop A pensShop A cost ($)Shop B pensShop B cost ($)________________

    Shop A sells 2 pens for $3. Shop B sells 5 pens for $6. Which shop has the lower cost for 1 pen?

    Show your work

    Hint Find the cost for 1 pen at each shop. Then compare.

    Final answer:
  11. 11Complete each step, then write the final answer.
    First amountSecond amount________________

    A ratio is 1:4. Multiply both numbers by 3. The new ratio is 3 : ?. What is the missing number?

    Show your work

    Hint Multiply the second number by 3: 4 × 3.

    Final answer:
  12. 12Complete each step, then write the final answer.
    First amountSecond amount________________

    A ratio is 3:2. Use a scale factor of 5. The new ratio is ? : 10. What is the missing number?

    Show your work

    Hint Multiply the first number by 5: 3 × 5.

    Final answer:
  13. 13Complete each step, then write the final answer.
    YardsFeet________________

    There are 3 feet in 1 yard. How many feet are in 7 yards?

    Show your work

    Hint The scale factor from 1 yard to 7 yards is 7. Multiply the feet by 7.

    Final answer:
  14. 14Complete each step, then write the final answer.
    MetersCentimeters________________

    There are 100 centimeters in 1 meter. How many centimeters are in 6 meters?

    Show your work

    Hint The scale factor from 1 meter to 6 meters is 6. Multiply the centimeters by 6.

    Final answer:

Explain your thinkingHow do you decide whether to multiply or divide when converting units?

Sentence starter When converting from a ___ unit to a ___ unit, I ___ by the conversion factor because ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help