Growing Patterns Lesson 3
In this lesson, students use the idea of what comes next to determine the relationship between the pattern number and number of objects in the pattern (explicit rule).
Project the Trinumbers Overhead.
Revisit the I see, I think, I wonder activity to activate prior knowledge. Connect to previous day's lesson by having students draw a picture of the 5th term in this pattern. Ask students:
Explain that we have been working on figuring out how many objects will be needed for the next term, in this case the next triangle.
Today we are going to explore these questions!
Distribute the How Many Beans Student Page. Students complete the table, record the Triangle Pattern, and solve the first three questions.
If students finish early, have them try to find another strategy for finding the number of beans for the 10th design.
Students exchange their work with a partner and discuss similarities and differences in solutions and strategies for generating solutions. Engage in whole class discussion. Focus students' attention on the pattern across their tables and ask them to determine a rule for getting from the pattern number to the number of beans. Have students complete the remainder of the student activity page.
Note: This same exploration can be done (with growing beans) that generate squares, pentagons, and other polygons.
These other patterns can be used for differentiation (giving different groups different patterns to explore or having students choose the one they want to explore), and it can be done as a challenge for early finishers or students who need an additional challenge.
Explore the different polygon growing patterns, as briefly mentioned above. Students can then generalize how the rules themselves are changing with each new polygon rule.
Close the lesson by having students work with a partner. The partner to the right tells how to find the "what comes next" rule to the person on the left. Trade and have the person on the left tell the person on the right how to find the rule for the relationship between pattern number and number of beans.
It is important to focus attention on the difference between the pattern going down the table, which is the "what comes next" pattern and the pattern or rule going across the table, which is the "relationship between corresponding terms" (in this case pattern number and number of beans). Have students make an Exit Slip demonstrating their understanding.
Leave your thoughts in the comments below.
Students explore growing patterns using the actual pattern and tables and determine a rule to tell what comes next.
Students continue to explore growing patterns and rules to determine what comes next. They analyze, describe, and justify their rules for naming patterns. Since students are likely to see growing patterns in a different way compared to their classmates, this is an opportunity to engage them in communicating about mathematics. This lesson requires students to explain correspondences among their verbal descriptions of the patterns, tables, and graphs that will help them eventually build an equation to solve the problem.
Students explore a toothpick staircase problem to apply their skills of finding the rule to describe the relationship between corresponding terms.
Continue to explore relationships between terms by exploring a growing pattern that involves several rules.
Pose interesting, but more difficult-to-generalize growing patterns.
CCSS, Content Standards to specific grade/standard
CCSS, Standards for Mathematical Practices
PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS