Solve Proportions Lesson

Problem Solving with Proportions

Mr. Speh 05/05/2022

​7th Grade

What is your favorite genre of movie?

What was the largest category? Smallest?

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What percent of the class answered​ comedy? Horror? Action? Drama? Science Fiction?

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Do you notice any obvious proportions between our categories?

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If we polled the next class period, would you expect their results to be similar or different? Why or why not?​

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​If there was one more student in our class, what would you most expect them to answer?

​Lesson Objective

Students will be able to solve problems about given data by recognizing and using proportions in the data, including part-to-part and part-to-whole comparisons.​

​A survey of visitors at a national park was conducted to determine the preferred activity of each visitor to the patk. Each visitor chose one activity. The survey results are shown in the table.

​Based on this information, which prediction about the preferred activity for the next 200 visitors to the park is the most reasonable?

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A. The number of visitors who prefer water sports will be 5 more than the number of visitors who prefer biking trails.

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B. ​The number of visitors who prefer hiking trails will be 8 more than the number of visitors who prefer water sports.

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C. The number of visitors who prefer camping will be 15 times the number of visitors who prefer hiking trails.

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D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.​

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The table shows ​the numbers of different types of pies sold at a bakery during one day.

​Based on the results in this table, which statement about the pies sold in this bakery during one week is NOT true?

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A. It is two times as likely for a chocolate pie to be sold as for a lemon pie to be sold.

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B. ​It is equally likely for an apple or pecan pie to be sold as for a chocolate pie to be sold.

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C. It is more likely for an apple or lemon pie to be sold than for a pecan or chocolate pie to be sold.

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D. It is less likely for a pecan pie to be sold than for a lemon pie to be sold

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The table shows the number of bottles of different kinds of juice sold at a cafeteria on Monday.

If the cafeteria has 80 customers on Tuesday, which prediction for Tuesday is NOT supported by the data in the table?

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A. The number of bottles of cranberry juice sold will be 6 more than the number of bottles of pineapple juice sold.

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B. The number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold.

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C. There will be a total of 50 bottles of orange juice and cranberry juice sold.

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D. The difference between the number of bottles of apple juice sold and the number of bottles of pineapple juice sold will be 14.

Multiple Choice

Heather has a bag of 15 red, 11 orange, 9 yellow, 12 green, 6 blue and 11 purple markers. How many times would you expect Heather to pick a red marker if she picked a marker 90 times?

• about 11 times

• about 15 times

• about 21 times

• about 64 times

Multiple Choice

How many times would you expect the spinner to NOT land on Red if the spinner is spun 40 times? Justify your prediction.

• 8 times;

  1/5 × 40 is 8.

• 16 times;

  2/5 × 40 is 16.

• 24 times;

  3/5 × 40 is 24.

• 32 times;

  4/5 × 40 is 32.

Multiple Choice

Tony has a workout playlist consisting of 4 songs for stretching, 14 songs for running, and 6 songs for lifting weights. If the playlist is shuffled, how likely is it a randomly selected song will be a song for running?

• impossible

• as likely to happen as not

• likely

• certain

Multiple Choice

Sam is renting a car for vacation. The table shows the number of keys in a bag for each type of car in the parking lot. How many times would you expect Sam to randomly select keys for a convertible or a sports car if he selects a key 120 times?

• 6

• 9

• 15

• 25

Multiple Choice

Scarlett is making a card. She has a drawer with 3 red, 2 pink, 5 green, 1 white, and 4 purple pieces of paper. How likely is it that Scarlett will randomly select a pink piece of paper?

• unlikely

• as likely to happen as not

• likely

• certain

Multiple Choice

Justin is tossing a quarter to determine which team gets the ball at the beginning of a football game. The Rams get the ball if the quarter lands on heads and the Tigers get the ball if the quarter lands on tails. How likely is it that the Rams will have the ball at the beginning of the game?

• unlikely

• as likely to happen as not

• likely

• certain

Multiple Choice

Ava writes each letter of the alphabet on separate note cards and puts the cards in a hat. How many times would you expect Ava to pick a letter from her name if she picks a card 50 times, returning the card to the hat each time?

• about 2 times

• about 4 times

• about 13 times

• about 26 times

Multiple Choice

The table shows the number of different color balloons set up for a dart game at a carnival. Which statement is true?

• The probability of hitting a red balloon is as likely as hitting a yellow balloon.

• The probability of hitting a blue balloon is greater than hitting the other color balloons.

• The probability of hitting a yellow balloon is less than hitting the other color balloons.

• The probability of hitting a green balloon is as likely as hitting a purple balloon.