Student Page 1.3.3 Growing Pattern of Dots
Now consider a pattern related to Figure 1.3.2.2. See the student page, Growing Pattern of Dots.
Spend at least 5 minutes thinking about the problem on your own.
When everyone in your group is ready, share your solutions to Growing Pattern of Dots with each other. Try to resolve any differences you have in your understandings. If you and your group members are still uncertain about something after your discussion, write a question or two to ask the full class.
Consider the pattern of dot arrangements in Figure 1.3.3.1.
1.
How are these dots related to the dots you counted in the Pattern Talk: Dot Pattern?
2.
(a)
How is each arrangement of dots related to the arrangement in the step before it?
(b)
How is each arrangement of dots related to the arrangement in the step after it?
3.
(a)
Is this pattern of dots related to Making Introductions? How?
4.
Consider the strategies you and classmates used to count the arrangement of dots in the Pattern Talk: Dot Pattern. Choose one strategy that works to count the dots in each of the arrangements.
(a)
Describe the strategy.
(b)
Use the strategy, show how you used it for each step, and record the number of dots in each arrangement in the bottom row of Figure 1.3.3.1.
5.
How many dots will there be in step 10? How do you know?
Share your responses with the full class:
Which strategy did you use to count the dots in each of these arrangements? Show how you used the same strategy to count the dots in Student Page Exercise 1.3.3.4 and Student Page Exercise 1.3.3.5.
Does the strategy you used to count each dot arrangement help you determine the number of introductions that were made in our class? Explain.
What questions do you still have? (Resolve these as a class.)