Illustrative Mathematics Unit 6.7, Lesson 11: Points on the Coordinate Plane

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Illustrative Math
Grade 6

Lesson 11: Points on the Coordinate Plane

Let’s explore and extend the coordinate plane.

Illustrative Math Unit 6.7, Lesson 11 (printable worksheets)

Lesson 11 Summary

The following diagram shows how to plot points on a coordinate plane that has four quadrants and negative coordinates

Lesson 11.1 Guess My Line

1. Choose a horizontal or a vertical line on the grid. Draw 4 points on the line and label each point with its coordinates.
2. Tell your partner whether your line is horizontal or vertical, and have your partner guess the locations of your points by naming coordinates.
   If a guess is correct, put an X through the point. If your partner guessed a point that is on your line but not the point that you plotted, say, “That point is on my line, but is not one of my points.”
   Take turns guessing each other’s points, 3 guesses per turn.
   

• See Video for Whole Lesson

Scroll down the page for the solutions to the “Are you ready for more?” section.

Lesson 11.2 The Coordinate Plane

1. The colored points on the coordinate plane are like targets. Hit each point by entering its coordinates as an ordered pair in the Input Bar, like this:
   See Coordinate Plane
   
   
2. What do you notice about the locations and ordered pairs of B, C, and D? How are they different from those for point A?
3. Plot a point at (-2,5). Label it E. Plot another point at (3,-4.5). Label it F.
4. The coordinate plane is divided into four quadrants, I, II, III, and IV, as shown here.
   a. In which quadrant is G located? H? I?
   b. A point has a positive y-coordinate. In which quadrant could it be?
   
   

Lesson 11.3 Coordinated Archery

Here is an image of an archery target on a coordinate plane. The scores for landing an arrow in the colored regions are:
Yellow: 10 points, Red: 8 points, Blue: 6 points, Green: 4 points, White: 2 points
Name the coordinates for a possible landing point to score:

1. 6 points
   
2. 10 points
   
3. 2 points
   
4. No points
   
5. 4 points
   
6. 8 points
   Type the coordinates for each point in a separate line, using parentheses. Like this:
   
   See Archery Target
   
   

Are you ready for more?

Pretend you are stuck in a coordinate plane. You can only take vertical and horizontal steps that are one unit long.

1. How many ways are there to get from the point (-3,2) to (-1,-1) if you will only step down and to the right?
   
   • Show Answers

     Let R means move one step right.
     Let D means move one step down.
     To move from the point (-3,2) to (-1,-1) we can move two steps right and three steps down which can be represented by RRDDD.
     Other ways are
     RDRDD
     RDDRD
     RDDDR
     DRRDD
     DRDRD
     DRDDR
     DDRRD
     DDRDR
     DDDRR
     Altogether, there are 10 ways.

   
   
2. How many ways are there to get from the point (-1,-2) to (4,0) if you can only step up and to the right?
   
   • Show Answers

     21

   
   
3. Make up some more problems like this and see what patterns you notice.
   

Glossary Terms

quadrant
The coordinate plane is divided into 4 regions called quadrants. The quadrants are numbered using Roman numerals, starting in the top right corner.

Lesson 11 Practice Problems

1. a. Graph these points in a coordinate plane: (-2,3),(2,3),(-2,3),(2,-3).
   b. Connect all of the points. Describe the figure.
   
2. Write the coordinates of each point.
   
3. These three points form a horizontal line: (-3.5,4),(0.4),and (6.2,4). Name two additional points that fall on this line.
   
4. One night, it is 24°C warmer in Tucson than it was in Minneapolis. If the temperatures in Tucson and Minneapolis are opposites, what is the temperature in Tucson?
   A. -24°C
   B. -12°C
   C. 12°C
   D. 24°C
   
5. Noah is helping his band sell boxes of chocolate to fund a field trip. Each box contains 20 bars and each bar sells for $1.50.
   a. Complete the table for values of m
   b. Write an equation for the amount of money, m, that will be collected if b boxes of chocolate bars are sold. Which is the independent variable and which is the dependent variable in your equation?
   c. Write an equation for the number of boxes, b, that were sold if m dollars were collected. Which is the independent variable and which is the dependent variable in your equation?
   
6. Lin ran 29 meters in 10 seconds. She ran at a constant speed.
   a. How far did Lin run every second?
   b. At this rate, how far can she run in 1 minute?
   

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

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