Problem Solving and Data - Ratio, Proportion, ....

Problem Solving and DataAnalysis

Ratio, Proportion, Units, and Percentage

​Problem Solving and Data Analysis Questions

​The questions on the SAT math test that fall under this category assess your ability to use your math understanding and skills to solve problems set in the real world. The questions ask you to pay attention to the meaning of quantities, know and use different properties of mathematical operations and representations, and apply key principles of statistics.

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​This can include multiple choice and student-produced responses.

Multiple Choice

Read and complete this problem independently, then discuss your work with your neighbor.

On Thursday, 240 adults and children attended a show.  The ratio of adults to children was 5 to 1.  How many children attended the show?

• 40

• 48

• 192

• 200

​The length of a shadow

At a given time of day, ​it might be true that a fence post that is 4 feet high casts a shadow that is 6 feet long.

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Open Ended

At a given time of day, ​it might be true that a fence post that is 4 feet high casts a shadow that is 6 feet long.

What will the length of the shadow be for someone who is 6 feet tall?

What about a tree that is 28 feet tall?

Or a lawn gnome that is 2 feet tall?

What do all of these have in common?

Open Ended

At a given time of day, ​it might be true that a fence post that is 4 feet high casts a shadow that is 6 feet long.

What is the height of a person who casts an 8 foot shadow?

How about the height of a tree that casts a 17.5 foot shadow?

Or the height of a rocket ship that casts a 344.4 foot shadow?

What do these all have in common?

​Constant of proportionality

Multiple Choice

On an architect's drawing of the floor plan for a house, 1 inch represents 3 feet. If a room is represented on the floor plan by a rectangle that has sides of lengths 3.5 inches and 5 inches, what is the actual floor area of the room, in square feet.

• 17.5

• 51.0

• 52.5

• 157.5

​Units!

​Many questions on the SAT require you to pay attention to units.

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​Such as converting between metric and English units. (liters to gallons, or feet to centimeters)

Multiple Choice

Scientists estimate that the Pacific Plate, one of Earth's tectonic plates, has moved about 1,060 kilometers in the past 10.3 million year.  What was the average speed of the Pacific Plate during that time period, in centimeters per year?

• 1.03

• 10.3

• 103

• 1,030