# How to Introduce and Teach Unit Rate: Practical Tips

So, your child is stuck on their homework. They have to find “unit rate.” And you’re looking at their homework paper and thinking, “What is unit rate?”

Or at least, that’s what my husband said when he asked what I was writing about. “Unit rate, huh. What’s that?”

I was a little surprised that my math savvy husband didn’t know about this crucial math skill he probably uses nearly every day. Once I told him what it was he said, “Oh. I use that all the time.”

So, don’t feel bad if you don’t know the term. It really is something people use frequently, but if you aren’t familiar, you probably will be after reading this post.

And if you’re a teacher or homeschooling parent, I have some suggestions on how to teach unit rate to your students.

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## What is a Rate?

According to Math at Hand (a super useful reference book every home should have):

a rate is a special ratio that involves quantities that aren’t measured the same way, like miles and hours.”

Example, if you rode your bike 40 miles in 2 hours, the rate would be 40 miles/2 hours. Or if you’re me-passed out on the side of the road from exhaustion.

Think about all of the ways to measure things and you can see we have a lot of options for rate: weight/time, volume/mass, distance/time, etc.

As useful as rate is, there’s a specific kind of rate that’s even more useful. It’s called unit rate.

A unit rate has a denominator of 1. You remember denominators, yes? The bottom of a fraction (in this case, ratio).

In our bicycling problem, the unit rate would be 20 miles/hour (read, 20 miles per hour).

## How are Unit Rates Useful

There are 2 reasons you might want to find unit rate. To compare two or more events/items and as a jumping off point to solve other, more challenging problems.

### Using Unit Rate to Compare:

Let’s say you want a bag of chips. After all, who doesn’t?

You’ve chosen the brand. But should you buy the big bag or the smaller one? You decide to save yourself some money and buy the smaller bag. But did you really save yourself money?

Assuming a large bag of chips would last longer than the smaller (not always a safe assumption in my house), the smaller bag probably costs more. But how to know for sure?

The problem is, each bag weighs and costs a different amount. In order to compare them, we need either price or weight to be the same. Let’s use weight.

Let’s find the unit price, the price for 1 unit. To find the unit price, divide the price by the weight.

Let’s pretend an 8 oz bag costs \$2.50 and a 16 oz bag costs \$4.00.

\$2.50/8 oz = \$0.31/1 oz

\$4/16 oz = \$0.25/1 oz

You would save 6 cents an oz if you buy the bigger bag for a total of 50 cents saved.

Shopper beware, buying in bulk is not always cheaper. In fact, I used real numbers to make this example and the first brand I looked at, the bigger bag was more expensive than the smaller.

### Using Unit Rates As a Starting Point:

Another reason to use unit rate is as a place to build off of.

For example: If I have \$20 spending money a month, how long will it take until I can afford that \$100 dress I want?

\$20/month is my starting point. Each month I add another \$20 until, after 5 months, I am at \$100.

## Ideas For Introducing Unit Rate to Students

The examples I gave are near and dear to my heart. With 5 children on one income, saving money on groceries is an important life skill I use regularly. Planning spending money is fun and something else I do frequently.

So the question is, what makes your students interested? The perfect topic would interest them, be easy to collect data on, and offer many opportunities to ask questions. If you’re not sure where to start, I have found students are often interested in themselves and what they can do.

I once took my 8th graders outside to the track to time how long it took them to complete a mile. There might have been some incentives for this lesson, like it was spring and I really wanted to be outside!

Once back in the classroom, they answered questions like:

• How fast do they run one lap?
• How many miles could they run in 1 hour?
• How long would it take them to run to a town nearby, how about a town further off, or to the next state…etc.

I would avoid comparing students. But you could compare students to animals like cheetahs or turtles. (Biggest, Strongest, Fastest by Steve Jenkins would be a great book to read along with this lesson).

Some other things students can measure about themselves: number of jumping jacks/minute, words written or typed/minute, words read/minute.

I would encourage you to find something students can be a part of. But sometimes that’s not feasible.

If that’s the case, pick something they can see (how fast does the ball roll down the track) or something they’ve seen so many times they can easily imagine it (bike riding). A very easy unit rate problem to demonstrate would be cost/item. All you would need is a bag of candy to get them both the visual and the interest.

## Suggested Order to Teach Unit Rate

Once they can see unit rate (cost of one candy, jumping jacks in one minute), solve simple problems starting with unit rate. If one candy costs 5 cents, how much is 10 candies, 20, 100, x? Introduce a wide variety of measurements, sometimes length, sometimes weight, sometimes time, but always the same concept.

Next, have students find unit rate. It’s a little harder to find unit rate because division is harder than multiplication. That’s why this step is second. An example problem would be: 12 sodas cost \$3, how much does one cost? Again, introduce them to a wide variety of measurements.

Once those two steps are easy, introduce multi-step problems. Multi-step problems could use either of the above skills and are not always as obvious what you are supposed to do.

Example: 12 pack of soda costs \$3, how much do you save buying the 12 pack instead of the \$0.75 soda from the vending machine?

## Just How Useful is Unit Rate?

Whether you are a teacher, a homeschooling student or a parent helping their kid with homework, unit rate is something we all use. I hope this post has taught you something you didn’t know and given you fun ideas for how to teach unit rate.

And if you’re interested, there’s a fun and engaging lesson on unit rate included in the Math Geek Mama Membership site: Passing Snowballs. Click here to learn more about membership.

And please share in the comments how you have used or taught unit rate, either in the classroom or in real life!

Danielle is a homeschooling mamma of 5.  She is committed to making life with young children easier and sharing her passion for math.  If you would like to learn more about teaching math to multiple age groups visit Blessedly Busy or follow her on:  Facebook, Instagram, Pinterest  or Twitter.

## One Comment

1. Nicole says:

My children use unit rate frequently in the real world. We calculated how much gas it would cost to drive to Texas or New Orleans from our house in California and compared that to the cost of a plane ticket or train ticket. We decide which boxed snacks to buy after figuring out the cost of each item individually. We buy rice, margarine, chips and other items that we use frequently by figuring out which size packages are the cheapest by volume. When they fundraise, we know we don’t want to sell anything for over a dollar so we see which candies can be bought for fifty cents or less so that every item sold is at least a fifty cent profit. When we sell loose candies for spare change, we compare the profit and time required from a spare change drive to those of a dollar per snack drive and they decide which drive to do next after considering which takes the maximum time as well as which brings the greatest profit. When they want a special treat that doesn’t cost too much, we figure out how long/how many games they can play at the arcade for the same price of going to the theater and they decide which is more worth their time. When we buy toilet paper, we literally compute the cost per square of our preferred brands to decide which to buy that trip. When we want to envision how big some prehistoric animal is, we calculate how many of our living room wall or double garages long it is, or how many beds in a row, or how many kitchen tiles, or how many counter depths, since these are things they know the size of and can visualize readily. When we want to compare an animal’s life span to ours to see how old it is in its own “critter years,” we decide the typical lifespan of the animal and conpare it to an 80 year old human lifespan then compute. There are lots of ways to throw math into every day living and musing