Today you will
- Compare quantities with numbers and without numbers.
- Define and use rates to solve problems.
- Compare and order part-to-part and part-to-whole ratios and rates shown with words, pictures, and numbers.
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Essential question
You know how to write a ratio as a comparison of two quantities.
How can you compare two ratios to make decisions in real-world situations?
Qualitative Comparisons
In this activity you will compare two quantities without measuring or counting quantities. When you reason like this, it is called qualitative reasoning.
Language help
Think-Pair-Share in threes. There are a lot of words in these situations. Work in groups of three. Each person takes one part of Question 1 (1a, 1b, or 1c), talks it through, and then teaches it to the other two. Use Listen to hear any scenario read aloud.
- teaspoon
- A very small spoon for measuring. Lemon mix is measured in teaspoons here.
- fluid ounce
- A small amount of liquid. Two fluid ounces is about a small shot glass.
- tablespoon
- A bigger measuring spoon. It is written with a capital T.
- lap
- One trip all the way around a race track.
- pitcher
- A large container with a handle for pouring drinks.
Comparing Comparisons
A rate is a comparison by division between two quantities that have different units. The 6th-grade students are making hot chocolate to sell at the Winter Carnival. Each homeroom (HR) suggested a different recipe.
Language help
Some people may not know the unit tablespoon. It is a measuring spoon, shown next to a cup above. The Word helper in the thinking tools (below) explains the other math words too.
Ordering Part-to-Part and Part-to-Whole Rates
Suppose your class is in charge of providing punch at the upcoming open house. The Parent-Teacher Association bought lemon-lime soda and pineapple juice to combine for the punch, but they did not tell your class how much of each to use. Your classmates submitted suggestions for how to make the tastiest punch.
Sort the Punch Rate Cards from the least lemon-lime concentration to the most lemon-lime concentration. When you think more than one card describes the same ratio of lemon-lime soda and pineapple juice, group those cards together.
The shading, or lack of shading, of each cup shows the type of concentration. Not every ratio is shown in every form.
A soccer team has been awarded a penalty shot at the end of a tie game. If they make the penalty shot, they will win the league championship. The coach is considering three players to take the penalty. Jasmine has taken 4 penalty shots this season and has made 3 of them. Luna has taken 6 penalty shots and made 4. Kayla has taken 3 penalty shots and made 2.
Essential question
How can you compare two ratios to make decisions in real-world situations?
Your first thoughts from the start of the lesson:
(You have not written anything yet.)
I can use reasoning to compare two ratios by measuring or counting quantities or without measuring or counting quantities.
The big ideas
- Two quantities can still be compared in the absence of numeric values.
- Ratios and rates are compared by reasoning about the amount of each quantity.
- Ratios written in different forms are compared and ordered.
- Ratios are useful when making decisions.
Start over
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