In this lesson, students will learn how to apply percent change with word problems. Students will start with an example that walks them through applying percent change. Then, students will be exposed to finding the multiplier by adding or subtracting with `100%` to help apply percent change. Students will go through several examples using the method of their choice and then reflect on the methods. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students will be able to apply percent change with word problems.
To introduce students to applying percent change with word problems, students should try to solve the problem given.
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The problem is broken up so that students will find the amount of tax, then add that to the cost of the pants. After reviewing what students did to find the answers to the questions, help students recognize that the total cost of the pants is their cost before tax (`100%` of original) plus the cost of their tax (`7%` of original). Because they would add the resulting values, let students know they would also add the percentages here to make `107%` because the cost after tax is `107%` of the original cost.
Take students through this next example. Explain that since we’re not asked to find how many additional pages were in the second book, we can solve for the final amount using multipliers. First ask students to identify the original amount, which is `210` pages. Ask students, “since the most recent book is `20%` longer than that, will the amount increase or decrease by `20%`”? When students determine there is an increase you can show that we need to add `100% + 20%` to demonstrate that the new amount will be `120%` of the original amount.
You may want to write on the board: original `\cdot` multiplier `=` final
Tell students to convert `120%` to a decimal. Now they’ll found the multiplier! All they need to do is multiply `210` by `1.2` to find that the most recent book Russell read was `252` pages.
At this point, it will be beneficial to give students a point of reference for finding the multipliers when applying percent change with word problems. Because students have not yet seen an example with a percent decrease, it can be helpful to have a short discussion on why they should add or subtract from `100%` depending on context.
If needed, use the previous examples to help explain percent increase. With percent decrease, consider making up an example like, “John had `$100`. He spent `20%` of the money he had. How much money did he have left?”
Allow students a few minutes to try the next example on their own. Encourage students to use the multiplier method. Although students just saw that percent change can be an increase or decrease, students may automatically add `100% + 5%` without recognizing that they will need to subtract. Allow students to find their answer and check with a partner so that initial misconceptions, such as adding instead of subtracting, may be addressed by students working together.
It is important that students are able to explain why they will need to subtract from `100%` in this case. Explain that if the reservoir decreased by `5%`, it would have `95%` of its original capacity.
Although the process will still be the same to apply the percent change with the word problem, some students may be confused by “`500` million people” because they will be unsure if they should use “`500`” or “`500,000,000`”. If needed, let students know that they can use either number; however it is acceptable to use “`500`” as long as they include the word “million” after their answer.
When reviewing with students, be sure to ask them which method they used. Although students will ideally be using the multiplier method, some students may still opt to find the percent of the original, and then add it to the original.
Asking students to reflect on the different methods. Which method works best for them? Why? What do they struggle with, if anything, with the other method? This can help students build their metacognition and recognize what works (and doesn’t work) for them as a learner.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for applying percent change word problems. Check out the online practice and assign to your students for classwork and/or homework!
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