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.

Start hereWords for this lesson

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

WordWhat it meansExample
Graph Ratio TablesSpanish: Representar tablas de razones en una gráfica Plot the paired values from a ratio table as ordered pairs. The ratio pairs 2:3 and 4:6 become points (2,3) and (4,6).
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)

How it worksWorked example

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

Lesson 3.4 — Determine Equivalent Ratios Using Graphs: The points from equal ratios form a straight line that passes through the origin (0, 0).

  1. Lesson 3.5 — Compare Ratio Relationships: Compare ratios fairly by making one part equal or by finding the unit rate.
  2. Lesson 3.6 — Ratio Reasoning: Convert Measurements within the Same System: Write the conversion factor as a unit ratio (12 inches : 1 foot), then multiply to go to the smaller unit and divide to go to the larger one. The amount never changes — only the unit does.
  3. Lesson 3.7 — Ratio Reasoning: Convert Measurements Between Systems: Write the conversion factor as a ratio (1 km ≈ 0.6 mi), then scale it with a ratio table until it reaches your amount. Between systems the result is approximate, so write ≈, not =.
  4. Lesson 3.8 — Solve Problems with Unit Rates: Divide the price by the number of items to get the cost per unit. The lower cost per unit is the better buy.
  5. Lesson 3.9 — Equivalent Ratios: Multiply or divide both numbers by the same amount to make an equivalent ratio.
  6. Lesson 3.10 — Convert Measurement Units: Multiply when changing to a smaller unit, and divide when changing to a bigger unit.

Now you trySame steps, your turn

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

From 3.4: A recipe uses 1 cup of sugar for every 3 cups of flour.

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 Graph Ratio TablesCoordinate planeOrdered pairLinear patternProportionalOriginlargersmallermultiplydivideconversion factorratio

Watch outA common mistake

A common mistake in Convert Measurement Units is applying the conversion factor in the wrong direction — for example, converting 4 feet to inches by dividing (4 ÷ 12 = 0.33 inches) instead of multiplying (4 × 12 = 48 inches), or converting 80 ounces to pounds by multiplying (80 × 16 = 1,280 pounds) instead of dividing (80 ÷ 16 = 5 pounds). Before you answer, ask: am I changing to a SMALLER unit (there will be MORE of them, so multiply) or a BIGGER unit (there will be FEWER of them, so divide)?

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.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 3.4) A ratio table shows (2, 6), (4, 12), and (6, 18). Which ordered pair comes next if the pattern continues?

    1. A(7, 20)
    2. B(8, 24)
    3. C(8, 22)
    4. D(10, 24)

    Hint Watch each coordinate separately: x goes 2, 4, 6, … and y goes 6, 12, 18, …

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 3.4) When you graph equivalent ratios, the points will always form what shape?

    1. AA curved line
    2. BA zigzag
    3. CA circle
    4. DA straight line through the origin

    Hint Think about what happened when you plotted equivalent-ratio points earlier in this lesson.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 3.5) Chef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?

    1. AChef B
    2. BChef A
    3. CThey use the same amount
    4. DCannot determine

    Hint You can't compare 2 cups and 3 cups directly — the chefs use different numbers of crackers.

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 3.5) Which ratio is greater: 3:4 or 5:8?

    1. A5:8
    2. BThey are equal
    3. C3:4
    4. DCannot determine

    Hint The second numbers (4 and 8) don't match, so the ratios aren't ready to compare yet.

    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 3.6) There are 12 inches in 1 foot. How many inches are in 5 feet?

    1. A7 inches
    2. B17 inches
    3. C50 inches
    4. D60 inches

    Hint Write the unit ratio first: 12 inches : 1 foot.

    Show your work

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 ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help