Introduce Maya and Jacob's situation in Question 7. Point out to students that Maya and Jacob are finding the total volume of the marbles and water together. Ask students to complete each function table using each rule provided. When their tables are complete, ask student volunteers to add their data to a Function Table Master to represent Table A in the Student Guide. Use this display of Table A to discuss the data and how it relates to the rule.
- Look at the rule in Table A. What does the N in N × 3 + 50 represent? (number of marbles)
- Why do we multiply N × 3? (3 is the volume of one marble.)
- What was the total volume for 2 marbles? Explain how you know. (56 cc. The rule is N × 3 + 50, so I multiplied 2 marbles (N) times 3 (volume of one marble) and added 50 (the volume of water at the start) and got 56 cc as the total volume of water and marbles.)
Ask small groups of students to discuss and answer Question 7B and be prepared with their explanation.
- How can you tell which rule is for the larger marble? (Table B is for the larger marble because the marble size is multiplied by the number of marbles, and 5 cc is larger than 3 cc.)
In Questions 7C–E, students are asked to describe parts of the rule and then write the rule in words. If students are having trouble with this, have them first add units to each portion of the rule.
For example: T cc = N marbles × 3 cc + 50 cc.
Students can then transition to words: Total Volume equals the Number of Marbles times the volume of one marble plus the volume in the graduated cylinder.
Assign Check-In: Questions 8–10. Students will explore similar patterns as they complete these questions.
Use Check-In: Questions 8–10 on the Using Different Units pages in the Student Activity Book and copies of the corresponding Feedback Box in the Teacher Guide to document students' abilities to identify and extend patterns for increasing functions [E1]; make generalizations using data tables [E12]; represent patterns and functions using words, symbols, and tables [E2]; and generate a pattern from a rule [E3].
Use tasks similar to those on the Writing Rules pages in the Student Guide to provide targeted practice with representing patterns and functions [E2].
The game Guess My Rule from Unit 5 can also provide targeted practice.
