Common Core Standards: Math
3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Unless they naturally love working with numbers (hey, some of us do!), your students probably don't exactly relish the idea of learning abstract mathematical concepts that don't apply to their daily lives. Lucky for them, proportions are the exact opposite of that.
It's true! Proportions are all kinds of useful in tons of different real-life situations. We're talking sales tax, gratuity, simple-interest loans, discounts at Bed, Bath & Beyond—basically anything that involves a percent increase or decrease. And here's why: percents are really just proportions in disguise.
The classic example here is tipping. At some point in their lives, your students will probably have to figure out what to tip a waiter at a restaurant. Those guys and gals work hard, and they deserve a little sumthin'-sumthin' on top of the bill.
For example, our waiter at The Bruschetta Barn does a pretty decent job, and we want to tip him 18% of the $25.07 bill. First off, we'd turn that percentage into a ratio: . Since our ratio represents the part to the whole, we can set it equal to another ratio with the total bill in the denominator and our unknown tip amount up top in the numerator:
Then we just solve for x in whatever way we'd like—and boom! Tip acquired!
It's a good idea to run your students through tons of different examples here till they get the hang of it, but all of them pretty much boil down to this: turn your percentage into a ratio, then set up a proportion to find the missing value in a second ratio. Tip calculators are for babies.
LinksRatio and Proportional Relationships Worksheet 3
Ratio and Proportional Relationships Worksheet 3 – Solutions
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