The purpose of this activity is for students to generate two patterns from rules and then graph them on the coordinate grid. Students first identify a point on the coordinate grid with one of the pairs of numbers from the patterns and then plot the rest of the points. Students may notice that the points on the graph are regularly spaced. They are invited to share this and other observations in the Activity Synthesis.

• “How did you decide where to place the points on the grid?” (I used the top row to decide how far over to go on the horizontal axis and the second rule to decide how far up to go on the vertical axis.)
• Invite students to share completed graphs for parts A and B.
• “How are the two graphs the same?” (There is a point at the bottom left, , on each graph. The points are regularly spaced and go up and to the right. They all lie at the intersection of grid lines.)
• “How are the two graphs different?” (The numbers on the axes are different. The ones for Partner B get bigger really quickly.)

• The numbers in the second pattern are double the numbers in first pattern and half more.
• The numbers in the second pattern are  times the numbers in the first pattern.

• Invite previously selected students to share.
• “What does point D represent in terms of the two rules? How do you know?” (When Rule 1 is 6, Rule 2 is 15. The coordinates are and the horizontal coordinate is Rule 1 and the vertical coordinate is Rule 2.)
• Display:
• “10 is a number in Rule 1 and 20 is a number in Rule 2. Is the point with coordinates on your graph?” (No, the points that represent the two rules are or . The 10 from Rule 1 and the 20 from Rule 2 don’t match up with each other.)