Find Percent Change Word Problems Lesson Plan

Warm Up

The first problem students will work on should help them recall what they already know about finding the percent of a number. From there, students will take that value to find the cost of the shirt after tax.

Because of how the questions are framed, students should be able to calculate the amount of tax, and then add it to the cost of the shirt to find the total cost. Help students recognize that tax is an example of a percent increase.

Connecting to percent change

Before moving on, ask students if they would be able to calculate the percent of tax if they had only been given the amount of tax charged, cost of the shirt before tax, and cost of the shirt after tax. Students might point out that they only need to use `2` numbers to figure the percent. Encourage students to try their calculations with the numbers to see if they can find the `8%` tax with the warm up example. Students should recognize that `8%` can be written as a fraction of the amount of tax over the cost before tax.

Percent increase or decrease

For this first example, it can be helpful to have students consider if there was a percent increase or decrease. Even though it does not directly affect their calculations, it can help students identify the original value. Encourage students to explain how they know there was a decrease. From there, students should at least be able to calculate the change in Ricardo’s collection.

If students are only able to come up with the difference between the values but are not sure how to find the percent, remind them of the warm up problem. In the warm up, the tax represented the percent change from the original amount; however, it could also be represented by a fraction of the difference divided by the original amount. Helping students understand how to write percent change as a fraction can help them better understand what values to use.

Formula for reference

At this point, it can be helpful to give students a formula to reference. Students need to understand that percent change is always the ratio of the difference to the original. It can be helpful to remind students that difference is always positive.

Some students might find `\frac{\text{new}}{\text{original}}`, convert to percent and then subtract the answer from `100%`. This method works fine as long students remember to subtract the answer from `\frac{\text{new}}{\text{original}}` from `100%`.

Population and rounding

For this example, students should write the fraction that represents the percent change, then calculate the percent change. This problem results in a non-terminating decimal, so it will be helpful to talk about what place value you want students to round to, and possibly provide them with a quick review of how to round correctly. A common error students make it to round the decimal value before converting to percent.

Common misconceptions

As students are working, you may notice some common misconceptions:

• Writing the difference over the new value: Remind students that it is always difference over original, since we’re looking for the change from the original amount. 
• Finding `\frac{\text{new}}{\text{original}}`: Some students might also find new/original and convert to a percent but not subtract their answer from `100%`. I have seen this typically happen when there is a percent decrease. For example if `\frac{\text{new}}{\text{original}} = 20/25=0.8`, students might answer that there is an `80%` decrease.   
• Only converting fraction to a decimal: Some students may forget to convert the decimal to a percent for their final answer.
• Rounding errors: Students may make rounding errors.