Patterns of Growth

5 min

Narrative

This Warm-up prompts students to compare four tables. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Launch

Arrange students in groups of 2–4. Display the tables for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three tables that go together and can explain why. Next, tell students to share their response 

Student Task

Which three go together? Why do they go together?

Table A

xx yy
1 8
2 16
3 24
4 32
8 64

Table B

xx yy
0 0
2 16
4 32
6 48
8 64

Table C

xx yy
0 1
1 4
2 16
3 64
4 256

Table D

xx yy
0 4
1 8
2 12
3 16
4 20

 

Sample Response

Sample responses:

  • A, B, and C go together because they include a yy-value of 64.
  • A, B, and D go together because the differences between values in the rows are constant.
  • A, C, and D go together because they include at least 1 odd value for xx.
  • B, C, and D go together because they show the yy-intercept.

Synthesis

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.

During the discussion, ask students to explain the meaning of any terminology they use, such as “common differences” or “common factors.”

Standards
Building Toward
  • F-BF.A·Build a function that models a relationship between two quantities
  • F-BF.A·Build a function that models a relationship between two quantities
  • F-BF.A·Build a function that models a relationship between two quantities
  • F-BF.A·Build a function that models a relationship between two quantities
  • F-BF.A·Build a function that models a relationship between two quantities
  • F-BF.A·Build a function that models a relationship between two quantities
  • F-LE.2·Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  • F-LE.2·Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  • F-LE.2·Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  • HSF-BF.A·Build a function that models a relationship between two quantities.
  • HSF-LE.A.2·Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

20 min

10 min