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Focus 1: Proportional ReasoningPowerPoint Presentation

Focus 1: Proportional Reasoning

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### Focus 1: Proportional Reasoning

Standards: 7.RP.1, 7.NS.2d, 7.NS.3, 7.EE.4a, 7.G.1

Resource: Connected Math Program 2

Comparing and Scaling: Investigation 3.2

Mathematical & Problem-SolvingLearning Goals for Comparing & Scaling Rates

Examine & Connect the idea of unit rate to what you already know about ratios and about linear relationships (3.1)

Further develop understanding of unit rates and how to compute and interpret them (3.2)

Work with the important application of rates to miles per hour (speed) (3.2)

Introduce the concept of “average” or “steady” rate of progress (3.2)

Introduce and formalize the meaning of unit rate and computation strategies for computing unit rates

Relate unit rate to the slope of the line representing the equation of the underlying relationship

Confront the issue of what it means to divide in rate situations

Investigation 3.2Learning Target

Further develop understanding of unit rates and how to compute and interpret them

Work with the important application of rates to miles per hour (speed)

Introduce the concept of “average” and “steady” rate of progress

Getting Ready for Problem 3.2

Consider your own experiences riding a bike

Did You Know?

The highest rate ever recorded on a pedal-powered bicycle was 166.944 miles per hour. Fred Rompelberg performed this amazing feat on October 3, 1995, at the Bonneville Salt Flats in Utah. He was able to reach this rate by following a vehicle. The vehicle acted as a windshield for him and his bicycle.

3.2 Time, Rate, and Distance

Sascha cycled on a route with different kinds of conditions. Sometimes he went uphill, sometimes he went mostly downhill. Sometimes he was on flat ground. He stopped three times to record his time and distance.

- Stop 1: 5 miles in 20 minutes
- Stop 2: 8 miles in 24 minutes
- Stop 3: 15 miles in 40 minutes

3.2 Finding Rates

Show your work in your math workbook. Label any rate that you find with appropriate units.

Find Sascha’s rate in miles per hour for each part of the route.

On which part was Sascha cycling fastest? On which part was he cycling slowest?

Suppose you can maintain a steady rate of 13 miles per hour on a bike. How long will it take you to travel the same distance Sascha traveled in 1 hour and 24 minutes?

Suppose you were racing Sascha. What steady rate would you have to maintain to tie him?

Explore 3.2 on a bike. How long will it take you to travel the same distance Sascha traveled in 1 hour and 24 minutes?Have you thought about?

What exactly do you know about Sascha’s trip?

Tell me in your own words what Question C or D is asking you to figure out.

If I send two of you out of the room to go to the library to get a book, is it possible for you to each walk at different rates and get there at the same time? If so, give an example.

Could one of you walk at a steady rate over the entire distance and get there at the same time as someone walking for part of the time at a faster rate? If so, how?

This situation is an interesting one since both the time and the distance have to be considered in answering Questions C and D. Each has to cover 28 miles in 84 minutes.

Explore 3.2 on a bike. How long will it take you to travel the same distance Sascha traveled in 1 hour and 24 minutes?Have you thought about?

How did you compute the rates in Question A? on a bike. How long will it take you to travel the same distance Sascha traveled in 1 hour and 24 minutes?

What do you answers to Question A tell you?

Do you think that his speed was constant throughout each time interval? Why or why not?

Say in your own words what “average” rate of speed means.

What does a steady rate of speed mean?

Did you know? That the idea of a steady rate is sometimes referred to as a constant speed.

How can you tell when he is going faster if you compute miles per minute?

Class Discussion & Sharing- How can you tell when he is going faster if you compute minutes per miles?
- What computation did you perform to find how long if would take you to travel the 28 mi Sascha traveled if you are going 13 mi/h? Why?
- What strategy did you use to find a steady rate that would tie Sascha?
- How can you match the parts of the trip to the conditions of the path?

Pre-Algebra Homework minutes per miles

A.C.E

Applications, Connections, & Extensions

#4- 8, 10a, 10b, 10c

Copy your answers in your math workbook

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