1. Lesson 3.1.6 – Teacher Notes Standard: 6.RP.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
Chapter 4 – Ratios to compare similar figures and non-geometric contexts
Lesson Focus:
The focus is understanding ratio language, (what numbers represent and how they are related). A bonus of the lesson is problem 3-82 as it relates to 6.RP.3 as well. (3-81 and 3-82)
I can describe a ratio relationship by comparing two quantities using ratio language.
I can write a ratio notation using a colon, the word “to”, and as a fraction.
I can analyze ratios to determine if they are equivalent.
Calculator: No
Literacy/Teaching Strategy: Red Light Green Light

2. 3-73. In this lesson, you looked for ways to convert between equivalent forms of fractions, decimals, and percents.  Using the portions web, write the other forms of the number for each of the given portions below.  Show your work so that a team member could understand your process.  Homework Help ✎
Write 4 5 as a decimal, as a percent, and with words/picture. 
Write 0.30 as a fraction, as a percent, and with words/picture.
Write 85% as a fraction, as a decimal, and with words/picture. 
Write one and twenty-three hundredths as a percent, as a decimal, and as a fraction.

3. 3-74. Maya and Logan each made up a “Guess my Decimal” game just for you. Use their clues to determine the number.
Maya gives you this clue: “The decimal I am thinking of is 3 tenths greater than 80%.  What is my decimal?”  Show your work. 
Logan continues the game with this clue: “My decimal is 3 hundredths less than 3 tenths.”  Use pictures and/or words to show your thinking.

4. 3-75. Amanda and Jimmy have jobs as dog walkers
3-75. Amanda and Jimmy have jobs as dog walkers.  Examine the graph at right and answer the following questions.  
Who has more hours of dog walking?  How do you know?
Who has earned the least amount of money?  How do you know?
Are both students earning the same amount of money per hour?  Show your work to justify your answer.

5. 3-76. Preston picked five playing cards and got a 2, 3, 6, 5, and 1.  
What two-digit and three-digit numbers could he create that would have the greatest sum?  Is there more than one possibility?  What is that sum? 
What two-digit and three-digit numbers could he create that would have the smallest sum?  Is there more than one possibility?  What is that sum?

6. 3-77. Use the Distributive Property to rewrite each product below
3-77. Use the Distributive Property to rewrite each product below. Simplify your answer.  Homework Help ✎
28 · 63
17(59)
458(15)

7. p to 3-82
In mathematics, a ratio is used to express certain relationships between two or more quantities. You were working with ratios when you expressed portions as percents and fractions. You also used ratios when you compared the portion of raisins or peanuts to the whole mix in the trail-mix problem.

8. Today you will extend what you know about fractions to investigate more general ratios. You will learn how they can be used to compare the trail-mix ingredients and much more. As you work with your team, keep the following questions in mind. How do the quantities compare? What quantities am I comparing? How can I represent the relationship? Can I represent it in another way?

9. 3-79. ON THE TRAIL AGAIN
Rowena and Polly are investigating their trail-mix problem again. Rowena took a handful of her mixture and counted her raisins and peanuts. She found she had 8 peanuts and 32 raisins in her sample. Rowena drew the following diagram to represent her sample. You can use a ratio to compare the number of peanuts or raisins in this sample to the total. If you find what percent of the sample is made up of raisins (or peanuts), you are writing a special kind of ratio. It describes how many raisins or peanuts would be present if the whole sample contained 100 raisins and peanuts combined. In fact, you can use a ratio to express the relationship between any two quantities in the mix.

10. 3-79 (cont.)
For the sample shown below, identify what each of the following ratios are comparing. For example, for “A ratio of 40 to 32,” you would write, “total to raisins,” because the ratio is comparing the total number, 40, to the number of raisins, 32.
A ratio of 8 to 40
A ratio of 8 to 32
A ratio of 32 to 8
A ratio of 32 to 40
Use what you have learned about portions to describe what portion of Rowena’s sample is peanuts and what portion is raisins. Express each answer as a fraction and as a percent.

11. 3-81. WAYS TO WRITE A RATIO
Just as you can express portions in multiple ways, you can write a ratio in any of three forms.
With the word “to,” such as: The ratio of raisins to peanuts is 4 to 1.
In fraction form, such as: The peanuts and raisins have a ratio of
With a colon (:), such as: The ratio of peanuts to raisins is 1: 4.
Sidra has a sample of trail mix containing 22 raisins and 28 peanuts. Write the ratio of peanuts to raisins in her sample using three different methods. What would you have to change to write the ratio of raisins to peanuts?

12. 3-81. (cont.)
Ratios, like fractions, can be written in simplified form. The ratio of 32 to 8 can be written equivalently as 4 to 1. Simplify your answer to part (a) in each of the three ratio forms.
Find the percent of Sidra’s trail mix that is peanuts. Can you use the ratios you found in parts (a) and (b)? Explain.
Find the percent of Sidra’s trail mix that is raisins.

13. 3-82. Ratios can be particularly useful when you want to keep the percent of an ingredient or the ratio of ingredients the same, but you want to change the total amount. For example: Rowena is not very fond of peanuts. So she is pleased that the number of peanuts is quite small compared to the number of raisins in her sample from problem She would like to keep the same ratio of peanuts to raisins when she mixes up a large batch of trail mix. Rowena and Polly decided to use ratio tables to describe all the relationships in the trail mix. The table will help them make sense of the ratios so they know how much of each ingredient to purchase.

14. 3-82. (cont.)
Analyze the tables below. Why did Rowena and Polly record different numbers? Did one of them make a mistake? Why or why not?

15. 3-82. (cont.)
With your team, recall the definition of “percent.” Whose table would help you find most easily the percent of the trail mix that is peanuts? Why?

16. PRACTICE
Remember: A ratio is a comparison of two quantities by division. It can be written in several ways: , 65 miles: 1 hour, or 65 miles to 1 hour
Molly’s favorite juice drink is made by mixing 3 cups of apple juice, 5 cups of cranberry juice, and 2 cups of ginger ale. State the following ratios in each of the three ways:
Ratio of cranberry juice to apple juice.
Ratio of ginger ale to apple juice.
Ratio of ginger ale to finished juice drink (the mixture).

17. PRACTICE (cont.)
A 38-passenger bus is carrying 20 girls, 16 boys, and 2 teachers on a field trip to the state capital. State the following ratios in each of the three different ways:
Ratio of girls to boys.
Ratio of boys to girls.
Ratio of teachers to students.
Ratio of teachers to passengers.

18. HOMEWORK