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?
