7th Grade Task: The Leader of the Pack

7th Grade Task: The Leader of the Pack

Standards & Objectives

Essential and guiding questions: 

Solving the Equation

  • In part a), did anyone use an equation to complete the table?
  • If you did not use an equation, how did you find the times for each speed?
  • Can someone show me how you got one of the times using the equation?
  • Can someone else tell me how you got the same time without using the equation?
  • How are these approaches the same?
  • What operation was used? Why?
  • Why do you think that we use formulas and equations to solve problems, when they can be done without them?

Rounding Choices

  • As you found the times for the table, were they “nice” decimal numbers? What was not nice about them?
  • Can a few people tell me how they handled these unruly decimals?
  • Why did you choose to do it that way?
  • Did anyone do it differently?
  • What seems to be the best approach when solving a real-world problem?
  • Do these numbers represent exact answers?
  • Why is it okay in this context that they do not?

Dividing by Large Numbers

  • As you filled out the table in part b), how did you choose the speeds?
  • How do the speeds change as you move down the table?
  • How do the times change?
  • How is the distance changing?
  • What operation is occurring between the distance and the speed in order to give you the time?
  • Can you make a general observation about what happens when we divide a constant by larger and larger numbers?
  • Will this value ever reach zero? [This provides a good place to discuss the limitations of calculators and why users must always reason
  • about appropriateness of answers.]

Dividing by Zero

  • What is an equation that would represent what happens when t=0 ?
  • Are there any other distances that could be covered in 0 seconds?
  • Are there any other rates that would satisfy the formula?
  • What observations can you make about D and r when t=0?

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can't get started...

  • If I told you someone was traveling 70 mph for 2 hours, how would you calculate the distance covered?
  • How are distances, speeds, and the time it takes to travel them related?
  • How would you use this relationship to complete the table?
Extension suggestions: 

If students fnish early:

  • What concept that we have learned about integers was illustrated in this activity?
  • Can you write a paragraph explaining how this activity illustrates division concepts?
  • Under what conditions is D=rt a proportional relationship?