Illustrative Mathematics Grade 8, Unit 4, Lesson 10: On or Off the Line?

Learning Targets:

  • I can identify ordered pairs that are solutions to an equation.
  • I can interpret ordered pairs that are solutions to an equation.

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Illustrative Math
Grade 8

Lesson 10: On or Off the Line?

Let’s interpret the meaning of points in a coordinate plane.

Illustrative Math Unit 8.4, Lesson 10 (printable worksheets)

Lesson 10 Summary

The following diagram show how to identify and interpret ordered pairs that are solutions to an equation. Points On or Off the Line

Lesson 10.1 Which One Doesn’t Belong: Lines in the Plane

Which one doesn’t belong? Explain your reasoning.

Lesson 10.2 Pocket Full of Change

Jada told Noah that she has $2 worth of quarters and dimes in her pocket and 17 coins all together. She asked him to guess how many of each type of coin she has.

  1. Here is a table that shows some combinations of quarters and dimes that are worth $2. Complete the table.
  2. Here is a graph of the relationship between the number of quarters and the number of dimes when there are a total of 17 coins. a. What does Point A represent? b. How much money, in dollars, is the combination represented by Point A worth?
  3. Is it possible for Jada to have 4 quarters and 13 dimes in her pocket? Explain how you know.
  4. How many quarters and dimes must Jada have? Explain your reasoning.

Lesson 10.3 Making Signs

Clare and Andre are making signs for all the lockers as part of the decorations for the upcoming spirit week. Yesterday, Andre made 15 signs and Clare made 5 signs. Today, they need to make more signs. Each person’s progress today is shown in the coordinate plane.
Based on the lines, mark the statements as true or false for each person.

Are you ready for more?

  • 4 toothpicks make 1 square
  • 7 toothpicks make 2 squares
  • 10 toothpicks make 3 squares
    Do you see a pattern? If so, how many toothpicks would you need to make 10 squares according to your pattern? Can you represent your pattern with an expression?
    • Show Answer

      The pattern is
      Number of toothpicks = 3n + 1
      10 squares would need 3(10) + 1 = 31

Lesson 10 Practice Problems

  1. a. Match the lines m and n to the statements they represent:
    i. A set of points where the coordinates of each point have a sum of 2
    ii. A set of points where the y-coordinate of each point is 10 less than its x-coordinate
    b. Match the labeled points on the graph to statements about their coordinates:
    i. Two numbers with a sum of 2
    ii. Two numbers where the y-coordinate is 10 less than the x-coordinate
    iii. Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate
  2. Here is an equation: 4x - 4 - 4x + . What could you write in the blank so the equation would be true for:
    a. No values of x
    b. All values of x
    c. One value of x
  3. Mai earns $7 per hour mowing her neighbors' lawns. She also earned $14 for hauling away bags of recyclables for some neighbors. Priya babysits her neighbor’s children. The table shows the amount of money m she earns in h hours. Priya and Mai have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of work hours.
    a. How many hours do they have to work before they go to the movies?
    b. How much will they have earned?
    c. Explain where the solution can be seen in tables of values, graphs, and equations that represent Priya’s and Mai’s hourly earnings.
  4. For each equation, explain what you could do first to each side of the equation so that there would be no fractions. You do not have to solve the equations (unless you want more practice).

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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