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

Lesson 3.43.4 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

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. x across, y up
Ordered pairSpanish: Par ordenado Two numbers (x, y) that tell where a point is on a grid. (2, 14)
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 pages, 0 stickers
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 exampleturning a ratio into points on a graph

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

A sticker sheet holds 7 stickers per page. Let x = pages and y = stickers.

  1. Make a table. 1 page → 7 2 pages → 14 3 pages → 21
  2. Write each row as an ordered pair. (1, 7) (2, 14) (3, 21)
  3. Plot the points and add (0, 0) — zero pages hold zero stickers.
  4. Draw one straight line through the origin and all the points.

Answer: The points (0, 0), (1, 7), (2, 14), (3, 21) lie on one straight line.

Now you trySame steps, your turn

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

A theater has 9 seats in every row. Let x = rows and y = seats.

  1. Make a table. 1 row → 2 rows → 3 rows →
  2. Write each as an ordered pair. ( 1 , ) ( 2 , ) ( 3 , )
  3. What does the origin ( 0 , 0 ) mean here?
  4. Find the point for 5 rows. ( 5 , )
Answer:the ordered pairs and the point for 5 rows

Say it and write itSentence starters

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

  • The point ( , ) means .
  • The origin means .
  • I found y by multiplying x by .
  • The points form a straight line because .

Word bank coordinate planeordered pairoriginx-axisy-axisplotpointstraight linetablemultiplyacrossup

Watch outA common mistake

A common mistake in Graph Ratio Tables is writing the ordered pair in the wrong order — putting the second table value first instead of matching (x, y) to the table's column order. For example, if a recipe table shows 2 cups of sugar for every 4 cups of flour, a student might plot (4, 2) instead of (2, 4), landing the point in a completely different spot on the grid. Before you plot, check: which quantity goes on the x-axis, and does your ordered pair start with that number?

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

Lesson 3.43.4 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    0123456789100481216202428(2, 7)(4, 14)(8, 27)?
    Is (8, 27) in line with the other two points?

    The points (2, 7) and (4, 14) are on a graph of equivalent ratios. Is the point (8, 27) on the same line?

    1. 1What is y when x = 2?
    2. 2What scale factor takes x = 2 to x = 8?
    3. 3Multiply 7 by the same factor. What is y?
    4. 4Is (8, 27) on the line?
    Final answer:
  2. 2Complete each step, then write the final answer.
    x-value515y-value2?× ?× ?

    A graph of equivalent ratios goes through (0, 0) and (5, 2). What is the y-value when x = 15?

    1. 1What is y when x = 5?
    2. 2What scale factor takes x = 5 to x = 15?
    3. 3Multiply y by the same factor. What is y?
    4. 4Ana adds 1 to both numbers and gets (6, 3). Why is that wrong?
    Final answer:
  3. 3Complete each step, then write the final answer.
    x-valuey-value________________

    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:
  4. 4Complete each step, then write the final answer.
    012345678904812162024283236(0, 0)(3, 12)
    Would the line reach (8, 32) if you made it longer?

    A line of equivalent ratios goes through (0, 0) and (3, 12). Is the point (8, 32) on the line? Type yes or no.

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    SundaesSauce (oz)________________________

    A graph shows sundaes as x and ounces of sauce as y. It goes through (0, 0) and (8, 12). How many ounces of sauce go with 5 sundaes?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    x-valuey-value________________________

    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:

Explain your thinkingHow can you tell if a point is on a graph of equivalent ratios without drawing it? Use (8, 27) to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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