In this lesson, we’ll introduce the concept of mental math with percentages to `6`th graders using number strings. Students use number strings to continuously relate one math problem to the next. This will allow students to find a variety of percentages of a number using mental math by using information from previous steps to help build reasoning for the other percents. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students will be able to use mental math to find percentages of numbers.
Start the lesson by giving students a warm-up for finding `0%, 100%, 10%,` and `30%` of `80`. Though `0%` and `100%` might seem simple, you will be surprised that students get stumped by these.
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Finding `10%`: Figure out how students think about `10%` of `80`. Some might want to multiply by `0.1` on paper. Some might want to set up a proportion like `10/10 = ?/80`. There are likely some students who would say we could just divide by `10`. Explore why they think we should divide by `10` (this is to ensure that they don’t confuse `10%` and dividing by `10`).
Finding `30%`: While some students might want to think of `30%` without relating it to anything they have found so far, you want to talk about how you can get to `30%` of a number by using `10%`.
In this part of the lesson, you will do a number string with percents where you use the percents you know to figure out those you don’t. Tell students they are not allowed to use a calculator or do any calculations on paper to do the number strings.
You could choose to write these percents one by one on the board or show them all at once.
We start out with `10%`, which we already know. Next, move on to `5%`. which is half of `10%`, so since `10%`of `80` is `8`, `5%` must be `4`. Keep using this process to fill out each box as a class. Ask students for their thoughts as you work through each percent. Say “which related percents can we use to find this one?” This will get students thinking about following the number string and using mental math to find the percentages.
For `85%`, some might want to multiply `5%` by a number - which is fine as long as they can do it mentally. There are several ways students might figure out `75%`: `25% + 50%, 100% - 25%, 3\cdot 25%, 85%-10%`.
To find `2.5%`, you could do half of `5%` or a tenth of `25%`. To find `12.5%`, you could do half of `25%` or add `10%` and `2.5%`.
Students will be amazed at how they are able to figure out all this using mental math!
Give students the Number String Partner Activity worksheet, where students will follow the same types of number strings to complete similar tables for different amounts. You can have students work with partners. This can lead to discussions about different ways to follow the number string.
After students have completed the partner activity, it’s time for some independent practice! ByteLearn gives you access to tons of mental math with percents activities. Check out the online practice and assign them to your students for classwork and/or homework!
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