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Cool Math In Real Life - Ratios, Ratio Language, Reduction to Unit Rate

Posted by Kate Chesnutt

Mar 23, 2015 7:30:00 AM

At LearnBop we know that sometimes taking math concepts from the page to the real world is hard. Students often ask, “When will I ever use this in ‘real life?’”

At LearnBop, we want to help students stay interested and engaged in math. That's why we started this weekly series that outlines how problems or patterns emerge “in real life.” In our second edition we will go over CCSS.Math.Content.6.RP.A.1 and  CCSS.Math.Content.6.RP.A.2, covering ratios, ratio language, and ratio relationships (reduction to unit rates).

Common Core Math Standard—CCSSM 6.RP.A.1 & CCSSM 6.RP.A.2

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.


Ratios let us to compare one thing to another. For example, compairing 5 fingers to 1 hand (5:1). These comparisons allow us to make judgements and choose more wisely. Would you rather have an offer where you buy 3 get 1 free (3:1) or buy 4 get 2 free (4:2)? This seems simple when we reduce it to a unit cost to compare. The offer where you buy 4 and get 2 free reduces to (2:1), clearly a better deal. When ratios are simplified, they become easier to compare and to scale.

Just as you cannot compare something to nothing, ratios must be a comparison to something, which cannot be 0. (You wouldn't say, "I bought 5 bananas and got 0 free" because you would just say you bought 5 bananas. Unless you are frustrated by the lack of banana promotions, which is a whole different story :) ).

You will hear ratio and ratio language used to describe many of life's experiences and decisions, which may or may not involve bananas.

Where Do You See Ratios?

Some places we see ratios used are in measurements, sports, and business. In real life you see ratios used everyday. Look at the headlines of any newspaper. Some of the headlines seem straight foward. "One in Seven 2-Year Olds in Boston Drinks Coffee" or "One in Four Deaths in America is Due to Heart Disease."

Other times, you will read things like, "Congress reaches deal on 1600-page, $1.1 trillion spending bill" from the Washington Times. These kinds of numbers can seem too large to think about, too complex to handle. But through rations we can say that this bill proposes spending on a scale of about $700 million per page. By reducing the ratio, we can begin to understand the scale.


Consider the words of the late Steve Jobs: "Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple." Using ratios and unit rates, you can simplify the complex.

Ratios in Measurements

If you want to be a builder, a baker, or do anything that requires measurement, you will need to understand ratios and their importance.

Builders and Contractors


As a contractor or builder, it would be imperative to know how many pounds of weight each beam could support and to make sure that buildings are made to code. Codes or regulations include ratios like: thickness to height ratios; occumpancy to area; and height to length (the slope) of ramps. Contractors also need to understand ratios so that they can order the correct number of parts or estimate additional costs. If every additional wall requires 3 sheets of plywood and 84 nails (3 sheets: 84 nails reduces to 1 sheet: 28 nails), you could extrapolate the quantities and costs of the project. 

Baking and Cooking


Have you ever dreamed of baking or being the next Gordon Ramsay or Rachel Ray? The truth is that making delicious food not only requires a great palate, but also using the right ratio of sweet to savory, water to flour, or oil to vinegar. Many a masterchef has tanked because they did not use the right ratios in their dishes. Masterchef Junior's Nathan used the right ratio of pastry to filling in his banana macaron to win the banana challenge. (See how the cost of bananas matters now?)

 

Ratios in Sports


This month is March Madness. Whether you are a baseketball fan or not, you probably know that last year (2014) Warren Buffett and Quicken Loans offered $1 Billion to whoever had a perfect bracket. The odds of winning were 1:9.2 Quintillion. You have a much better chance of winning the Powerball lottery.


We use ratios and odds in sports to describe anything from basketball freethrows (freethrows made/freethows taken) to yards per play in football. Understanding these numbers allows coaches to figure out who to put in the game and their odds of winning or achieving a certain objective. The movie Moneyball, starring Brad Pitt, is a great example of how coaches use these ratios. The movie profiles Billy Beane's use of various ratios to help recruit for the Oakland A's on a lean budget. 

Ratios in Business

If you want to operate in business, you will need to be able to not only understand ratios, but also reduce them to a unit rate. The Sharks on ABC's show Shark Tank often ask what is the, "average acquisition cost per customer", "average cost per unit", and "average selling cost." These numbers are per unit rates. This simplification allows "the sharks" to clearly see the complex numbers in front of them and understand if a company is a wise investment. Additionally in business, you will see ratios in time units such as units produced per day or profit per quarter. The sharks finish by offering a price (P) for an amount of equity in the business - this too is a ratio!

Watch this video about the Tree TPee, where Kevin O'Leary points out the ratio of water used per tree at the 2:45 mark. He notes watering the trees used 25,000 gallons per tree without the Tree TPee, but with the Tree TPee it only uses about 800 gallons per tree. Mark Cuban chimes in, "How much does it cost to make one?" This is asking for a per unit rate, which is a ratio! It costs $2.95 per TPee.

 
 

Topics: Implementing the Common Core, Resources, Teaching & Learning, Algebra & Algebra Readiness

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