IM: 7.4.2: Ratios and Rates With Fractions (Lesson)

Posljednje ažuriranje over 1 year ago

2.1: Number Talk: Division

2.2: A Train is Traveling at . . .

A train is traveling at a constant speed and goes 7.5 kilometers in 6 minutes. At that rate:

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How far does the train go in 1 minute?

2.3: Comparing Running Speeds

Are you ready for more?

2.4: Scaling the Mona Lisa

IM: 7.4.2: Ratios and Rates With Fractions (Lesson)

Posljednje ažuriranje over 1 year ago

2.1: Number Talk: Division

Find each quotient mentally.

5 \div \frac{1}{3}

2 \div \frac{1}{3}

\frac{1}{2} \div \frac{1}{3}

2\frac{1}{2} \div \frac{1}{3}

2.2: A Train is Traveling at . . .

A train is traveling at a constant speed and goes 7.5 kilometers in 6 minutes. At that rate:

null

How far does the train go in 1 minute?

How far does the train go in 100 minutes?

2.3: Comparing Running Speeds

Lin ran 23/4 miles in 2/5 of an hour. Noah ran 82/3 miles in 4/3 of an hour.

Questions to consider:

Who ran faster, Noah or Lin?
How far would Lin run in 1 hour?
How far did Noah run in 1 hour?
How long would it take Lin to run 1 mile at that rate?
How long would it take Noah to run 1 mile at that rate?

Pick one of the questions that was displayed, but don’t tell anyone which question you picked. Find the answer to the question.

When you and your partner are both done, share the answer you got (do not share the question) and ask your partner to guess which question you answered. If your partner can’t guess, explain the process you used to answer the question.

Switch with your partner and take a turn guessing the question that your partner answered.

Are you ready for more?

Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible?

Traveling a billion meters in 5 seconds.

Traveling a meter in 2.5 nanoseconds. (A nanosecond is a billionth of a second.)

Traveling a parsec in a year. (A parsec is about 3.26 light years and a light year is the distance light can travel in a year.)

2.4: Scaling the Mona Lisa

In real life, the Mona Lisa measures 2\frac{1}{2} feet by 1\frac{3}{4} feet. A company that makes office supplies wants to print a scaled copy of the Mona Lisa on the cover of a notebook that measures 11 inches by 9 inches.

The applet is here to help you experiment with the situation. (It won't solve the problems for you.) Use the sliders to scale the image and drag the red circle to place it on the book. Measure the side lengths with the Distance or Length tool.

https://curriculum.illustrativemathematics.org/MS/students/2/4/2/index.html

[Scroll to the tool under "2.4: Scaling the Mona Lisa"]

IM: 7.4.2: Ratios and Rates With Fractions (Lesson)

How far does the train go in 1 minute?

IM: 7.4.2: Ratios and Rates With Fractions (Lesson)

5 \div \frac{1}{3}

2 \div \frac{1}{3}

\frac{1}{2} \div \frac{1}{3}

2\frac{1}{2} \div \frac{1}{3}

How far does the train go in 1 minute?

How far does the train go in 100 minutes?

Pick one of the questions that was displayed, but don’t tell anyone which question you picked. Find the answer to the question.

Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible?

Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible?

What size should they use for the scaled copy of the Mona Lisa on the notebook cover?

What is the scale factor from the real painting to its copy on the notebook cover?

Discuss your thinking with your partner. Did you use the same scale factor? If not, is one more reasonable than the other?

5 \div \frac{1}{3}

2 \div \frac{1}{3}

\frac{1}{2} \div \frac{1}{3}

2\frac{1}{2} \div \frac{1}{3}

How far does the train go in 100 minutes?

Pick one of the questions that was displayed, but don’t tell anyone which question you picked. Find the answer to the question.

Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible?

Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible?

What size should they use for the scaled copy of the Mona Lisa on the notebook cover?

What is the scale factor from the real painting to its copy on the notebook cover?

Discuss your thinking with your partner. Did you use the same scale factor? If not, is one more reasonable than the other?