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Cara’s Candles & DVD Club

Kari Callier
8th grade
Sequoyah Middle School
Clayton County Schools

Contents

Task
Overview
Students are given two tasks; both require writing two equations and solving the resulting system of equations.

Illustrative Task
Cara’s Candles
Cara likes candles. She also likes mathematics and was thinking about using algebra to answer a question that she had about two of her candles. Her taller candle is 16 centimeters tall. For each hour it burns, the candle loses 2.5 centimeters in height. Her short candle is 12 centimeters tall and loses 1.5 centimeters in height for each hour that it burns.

Cara needs your help to determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. She also wants to know what height the two candles would be at that time. If it is not possible, she wants to know why it could not happen and what would need to be true in order for them to be able to reach the same height. To help Cara understand what you are doing, be sure to use multiple representations, justify your results, and explain your thinking.

DVD Club
A group of eighth-graders at your school is thinking of forming a club whose members rent DVDs. The club would also rent DVDs to non-members but at a higher price.
  • What do you think would be a reasonable amount students would be willing to pay for a year’s membership in the club?
  • What do you think would be a fair price for a member to rent one DVD for one week?
  • What do you think would be a fair price for a non-member to rent one DVD for one week?
Using the amounts you decide on, write algebraic equations that would represent the total cost “y” for a member to rent “x” DVDs in one year and another algebraic equation that would represent the cost “y” for a non-member to rent “x” DVDs in one year. How many DVDs would a person have to rent in one year in order for the cost to be the same whether one is a member or not? Show how you know.

GPS Addressed
M8A5. Students will understand systems of linear equations and inequalities and use them to solve problems.
  1. Given a problem context, write an appropriate system of linear equations or inequalities.
  2. Solve systems of equations graphically and algebraically, using technology as appropriate.
  3. Graph the solution set of a system of linear inequalities in two variables.
  4. Interpret solutions in problem contexts.

Video Information
Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.
  1. What kinds of questions does the teacher ask to promote students’ problem solving?
  2. How is the teacher gauging students’ current understandings and building from those understandings?
  3. Consider the GPS standards listed with this video.
  4. What makes this lesson different from lessons you have taught on this topic?

Classroom Materials

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