Lesson 3

Gzorp

Est. Class Sessions: 2–3

Developing the Lesson

Part 2: Doubling Growth Patterns

One-Eyed Double Worm Growth Patterns. Explain to students that some creatures on Gzorp grow really fast. One of these creatures is the double worm. There are many kinds of double worms on Gzorp. Every kind of double worm doubles its length each year. Use a display of the first Double Worm page in the Student Activity Book to introduce the One-Eyed Double Worm. Have students use square-inch tiles to model the One-Eyed Double Worm.

  • If the One-Eyed Double Worm doubles its length every year, how long will it be in one year? (2 squares)

Have students add 1 square to the worm to show its length after one year.

  • How long will the One-Eyed Double Worm be after two years? (4 squares)

Have students add 2 more squares to the One-Eyed Double Worm so that it has 4 squares. Create a data table showing this growth pattern. See Figure 4.

Continue to tell lengths for the One-Eyed Double Worm for various years. Each time, record the length in the data table. See Figure 4. Have student pairs complete Questions 1–3 on the Double Worm pages in the Student Activity Book.

Five-Eyed Double Worm. Display five adjoining square tiles in a row. Explain to students that this is a newborn Five-Eyed Double Worm that starts with 5 squares.

  • If the Five-Eyed Double Worm has 5 squares when it is born and it doubles in length every year, how long will it be in one year? (10 squares)

Add 5 squares to the worm to show its length after one year and encourage students to do the same.

  • How long will the Five-Eyed Double Worm be after two years? (20 squares)
  • How long will it be after five years? (160 squares)

Have students work in pairs to develop strategies for solving the problems. Possible strategies include:

  • Draw squares to make the worm.
  • Use a data table.
  • Use the compact method.
  • Use a calculator.

Have students demonstrate their strategies for finding the length of a Five-Eyed Double Worm after five years.

  • Which strategy do you think is the most efficient? (Possible response: The data table because it’s easier to keep track of the number of squares for each age.)
  • Is the length of a One-Eyed Double Worm the same as the length of a Five-Eyed Double Worm after 5 years? (No.) Why not? (Possible response: They start out with a different number of squares at birth.)

Assign Double Worm Check-In: Questions 4–7 in the Student Activity Book to assess students’ abilities to find the length of a Three-Eyed Double Worm at different ages.

Use Double Worm Check-In: Questions 4–7 with the Feedback Box in the Student Activity Book to assess students’ abilities to identify and extend patterns represented in numbers and in geometric patterns [E1]; represent patterns and functions using words and tables [E2]; find a strategy for solving a problem [MPE2]; and show or tell how to solve a problem [MPE5].

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One-Eyed Double Worm growth pattern
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