Solving Measurement Problems with Estimation

Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

In this lesson, we will explain what measurement problems are and show how to solve measurement problems using estimation. We will also look at using conversion facts when solving measurement problems with estimation.

Measurement Problems

Let's consider a girl named Sally and how close her house is to her friend's houses. It is 10 miles from Sally's house to Troy's house. Barb's house is double that distance from Sally's house. In other words, if we were to draw a line representing the distance from Sally's to Troy's, then two of those lines put together would represent the distance from Sally's to Barb's.


Since it is 10 miles from Sally's to Troy's, and the distance from Sally's to Barb's is double that, it must be the case that the distance from Sally's to Barb's is

  • 2 x 10 = 20 miles.

This is an example of a measurement problem. Measurement problems involve finding measurements such as distances, lengths, amounts, or sizes.

In this case, we found the exact distance from Sally's to Barb's, but what if we wanted to know the distance from Sally's to Eric's as shown in the earlier image? We aren't given any facts about how it compares to the other distances. In this case, we can use estimation to find an approximate distance from Sally's to Eric's.

Solving Measurement Problems with Estimation

Notice that the line from Sally's to Eric's looks to be about 1/2 the length of the line from Sally's to Troy's house. This tells us that the distance from Sally's to Eric's is about half of the distance from Sally's to Troy's, or 1/2 of 10.

  • (1/2) × 10 = 5

Therefore, it is about 5 miles from Sally's to Eric's. This is an example of solving a measurement problem using estimation.

To solve measurement problems using estimation, we use a given representation of units and estimate how many of that representation fits into what we're trying to measure. For instance, suppose we have a container with 2 ounces of milk in it, and we have another same-sized container with lemonade in it as shown in the image.


It looks like the amount of lemonade is about 3 times that of the milk, so there are approximately

  • 3(2) = 6 ounces of lemonade.

Pretty neat, aye?

Sometimes we can use conversion facts in solving measurement problems with estimation. Let's look at an example of this.

Using Conversion Facts to Solve Measurement Problems With Estimation

It is a well-known fact that NFL football fields are 120 yards long. It is also a well-known conversion fact that there are 3 feet in 1 yard.

  • 3 feet = 1 yard

John, a football player, ran the distance shown in the image during a play, and we want to estimate how far he ran in feet.


To solve this measurement problem, we're going to use estimation to figure out the distance in yards, and then we're going to use our conversion fact to find that distance in feet.

First, we notice that the distance that John ran looks to be about one-quarter (1/4) of the distance of the football field. Therefore, the distance that John ran is about 1/4 of 120 yards.

  • (1/4) × 120 = 30

John ran about 30 yards. This is great, but we want to know the distance in feet. This is where the conversion fact comes into play. Since there are 3 feet in 1 yard, we multiply the 30 yards by 3 to figure out the number of feet.

  • 30 × 3 = 90

We see that John ran about 90 feet.

Let's consider one more! Suppose Susan wants to know how much she weighs, in pounds, but the only scale she has available is unmarked. She knows that her young daughter, Meghan, weighs 21 kilograms, and she also knows the conversion fact that 1 kilogram is equal to about 2.2 pounds.

  • 1 kilogram ≈ 2.2 pounds

She realizes she can approximate her weight by seeing how her weight marker on the scale compares to Meghan's. They both step on the unmarked scale, separately, and the weight marker for each of them is shown in the image.


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