Section D: Practice Problems Let’s Put It to Work: Problem Solving with Large Numbers

Section Summary

Details

In this section, we encountered problems that involve large numbers from different contexts and that could be solved with different strategies.

In the beginning, we saw at least five ways to find the product of 45 and 18: by multiplying and dividing in parts, using a series of equations, drawing diagrams, and more.

Later, we explored problems about measurements, with numbers up to four digits. We found that, often, the same problem could be solved using different operations.

For example, in the fitness challenge activity, Han took 32,550 steps in 7 days. We can find the number of steps he took each day by thinking in terms of multiplication (what number times 7 is 32,550?) or in terms of division (what is 32,550 divided by 7?).

We can also write different equations.

$7 \times n = 32, 550$

$32, 550 \div 7 = n$

To find out how many steps Han had to take to reach a goal of 120,000 steps if he had 96,897 steps, we can think in terms of addition (what number must be added to 96,897 to make 120,000?) or subtraction (what is the difference between 120,000 and 96,897?).

$96, 897 + n = 120, 000$

$120, 000 - 96, 897 = n$

Problem 1 (Lesson 21)

An author took a 4-hour airplane flight for a work trip. The plane flew 478 miles each hour. How many miles did she travel?
A photographer took a 4-hour drive for his work trip. The car traveled 57 miles each hour. How many miles did he travel?
How many miles further did the author travel than the photographer?

Problem 2 (Lesson 22)

The diagram shows the side lengths of a sports field.

Rectangle. Horizontal side, eighty 5 meters. Vertical side, 43 meters.

What is the perimeter of the field? Explain or show your reasoning.
What is the area of the field? Explain or show your reasoning.

Problem 3 (Lesson 23)

The table shows the number of students who have different numbers of pets at a school.

How many pets do all the students have together? Explain or show your reasoning.

number of pets	number of students
$1$	$218$
$2$	$167$
$3$	$287$
$4$	$138$

Problem 4 (Lesson 24)

A builder is covering the floor of a rectangular room that is 23 feet by 25 feet with tiles that are 1 foot by 1 foot. The tiles are sold in boxes of 12.

Diego says 59 boxes are needed to cover the floor, and that there will be a few leftover tiles.

Is Diego’s answer reasonable? Explain or show your reasoning.
How many boxes of tiles would you get to cover this floor? Explain or show your reasoning.

Problem 5 (Exploration)

Find a rectangular room at home or in the school.

Which unit would you choose for measuring the length and width: inches, feet, or yards? Explain your reasoning.
Measure the length and width to the nearest whole number.
Find the perimeter and area of the room.
Can you find a length and width pair for a room that would have the same perimeter but a different area?
Can you find a length and width pair for a room that would have the same area but a different perimeter?

Problem 6 (Exploration)

The area of a rectangle is 720 square centimeters. One side is 6 centimeters longer than the other. What is the perimeter of the rectangle? Explain or show your reasoning.