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What do you notice? What do you wonder?
2 tape diagrams. First diagram. One longer orange section, labeled 1. One smaller blue section. Second diagram. One longer green section and one smaller blue section, all labeled 1.
Complete the table to show the total distance walked in each case.
| initial distance | total distance |
|---|---|
| 10 | |
| 3 | |
| 4.5 | |
| 1 | |
Two students each wrote an equation to represent the relationship between the initial distance walked () and the total distance walked ().
Do you agree with either of them? Explain your reasoning.
Match each situation with a diagram. A diagram may not have a match.
For each diagram, write an equation that represents the relationship between and .
Diagram A:
Diagram B:
Diagram C:
Diagram D:
Using the distributive property provides a shortcut for calculating the final amount in situations that involve adding or subtracting a fraction of the original amount.
For example, one day Clare runs 4 miles. The next day, she plans to run that same distance plus half as much again. How far does she plan to run the next day?
Tomorrow she will run 4 miles plus of 4 miles. We can use the distributive property to find this in one step:
Clare plans to run 6 miles, because .
This works when we decrease by a fraction, too. If Tyler spent dollars on a new shirt, and Noah spent less than Tyler, then Noah spent dollars since .