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

Lesson 3.43.4 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can graph the values from a ratio table as points on the coordinate plane — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can graph the values from a ratio table as points on the coordinate plane — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    Pizzas123Slices6??× ?× ?
    Each column is a point (pizzas, slices).

    Each pizza has 6 slices. Pizzas are x and slices are y. Write ordered pairs for 1, 2 and 3 pizzas.

    1. 1How many slices go with 1 pizza?
    2. 2What scale factor takes 1 pizza to 2 pizzas?
    3. 3Multiply the slices by 2. What is the y-value for 2 pizzas?
    4. 4Now scale 1 pizza by 3. What is the y-value for 3 pizzas?
    Final answer:
  2. 2Complete each step, then write the final answer.
    012345678910012345678Juice (cups)Ice (cups)(3, 2)
    Plot (3, 2). Where do 6 and 9 cups go?

    A ratio table shows 3 cups of juice for every 2 cups of ice. Juice is x and ice is y. Find the points for 3, 6 and 9 cups of juice.

    1. 1How many cups of ice go with 3 cups of juice?
    2. 2What scale factor takes 3 cups of juice to 6 cups?
    3. 3Do the same to the ice. What is the y-value for x = 6?
    4. 49 is 3 × 3. What is the y-value for x = 9?
    Final answer:
  3. 3Complete each step, then write the final answer.
    BoxesBalls________________

    Each box holds 2 balls. Boxes are x and balls are y. What is the y-value of the point for 6 boxes?

    Show your work

    Hint Each box adds 2 balls. Multiply the boxes by 2.

    Final answer:
  4. 4Complete each step, then write the final answer.
    Ears of cornCheese (oz)________________

    A street corn recipe uses 3 ounces of cheese for every 1 ear of corn. Ears are x and ounces are y. What is the y-value of the point for 5 ears?

    Show your work

    Hint Each ear needs 3 ounces. Multiply the ears by 3.

    Final answer:
  5. 5Complete each step, then write the final answer.
    0123456081624324048HoursDollars(0, 0)(1, 8)(2, 16)(3, 24)

    Mia babysits. Hours are x and dollars are y. The points (1, 8), (2, 16) and (3, 24) are on her graph. How many dollars does she earn in 5 hours?

    Show your work

    Hint Look at the point for 1 hour. That is her pay for each hour.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.
    012340246810121416Sugar (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)

    Hint On this graph, y is always 4 times x. Test each point.

    Show your work

Explain your thinkingWhy does the graph of pizzas and slices go through (0, 0)? Why do the points make a straight line?

Sentence starter The line goes through (0, 0) because ___ pizzas have ___ slices. · The points make a straight line because each pizza adds ___.

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