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

Lesson 3.4Interpreting Points on Ratio Graphs

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can graph the values from a ratio table as points on the coordinate plane.

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. (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.

x = pounds of apples, y = cost in dollars. The line passes through (4, 12). Find the cost of 6 pounds.

  1. Read it: 4 pounds cost $12.
  2. Divide: 12 ÷ 4 = 3, so the unit rate point is (1, 3).
  3. Multiply: 6 × 3 = 18, so (6, 18).

Answer: $3 per pound; 6 pounds cost $18

Say it and write itSentence starters

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

  • The point ( , ) means .
  • The unit rate is because the point ( 1 , ) is on the line.
  • The origin ( 0 , 0 ) means .
  • I know the point is on the line because .

Word bank unit rateorigininterpretcoordinatesx-valuey-valuepointlinefor eachmeanspredictflip

Watch out!A common mistake

A common mistake in Graph Ratio Tables is writing the ordered pair in the wrong order

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

Lesson 3.4Interpreting Points on Ratio Graphs

Apply Day · Version ASupported practice

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

Learning target I can graph the values from a ratio table as points on the coordinate plane.

  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.
    Packs13Pencils4?× ?× ?

    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.
    Tables14Students6?× ?× ?

    Each table seats 6 students. Tables are x and students are y. What is the y-value of the point for 4 tables?

    Show your work

    Hint Multiply the tables by 6.

    Final answer:
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
Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.4Interpreting Points on Ratio Graphs

Apply Day · Version BCore practice

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

Learning target I can graph the values from a ratio table as points on the coordinate plane.

  1. 1Circle the letter of the best answer. Show how you know.
    01234246810121416Sugar (cups)Flour (cups)(0, 0)(1, 4)
    The line starts at (0, 0) and goes through (1, 4).

    A recipe uses 4 cups of flour for every 1 cup of sugar. Sugar is x and flour is y. Which point is NOT on the graph?

    1. A(3, 7)
    2. B(2, 8)
    3. C(3, 12)
    4. D(0, 0)
    Show your work
  2. 2Complete each step, then write the final answer.
    x-value15y-value6?× ?× ?

    The points (1, 6) and (2, 12) are on a graph of equivalent ratios. What is the y-value when x = 5?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.
    Packs14Juice boxes3?× ?× ?

    Each pack has 3 juice boxes. Packs are x and juice boxes are y. What is the y-value of the point for 4 packs?

    Show your work
    Final answer:
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
Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.4Interpreting Points on Ratio Graphs

Apply Day · ChallengeExtension

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

Learning target I can graph the values from a ratio table as points on the coordinate plane.

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

    A ratio table pairs 1 hour with 45 miles, 2 hours with 90 miles, and 3 hours with 135 miles. Which ordered pair belongs on the graph of this relationship?

    1. A(4, 180)
    2. B(4, 45)
    3. C(4, 140)
    4. D(180, 4)
    Show your work
  2. 2Complete each step, then write the final answer.
    x-value6??y-value4210÷ ?÷ ?× ?× ?

    A graph of equivalent ratios goes through (0, 0) and (6, 4). Lee says the point with y = 10 is (12, 10), because he added 6 to both numbers. What is the correct x-value?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.
    x-value39y-value6?× ?× ?

    The points (3, 6) and (5, 10) are on a graph of equivalent ratios. What is the y-value when x = 9?

    Show your work
    Final answer:
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