Opening Activity In your spiral, write the ratios below in three ways. Simplify if possible. Green circles to Red circles Stars to Total shapes

Equivalent Ratios and Ratio Tables

Table of Contents Date Lesson Page # Unit 8/26 Place Value and Rounding 3 Order of Operations 8/26 8/26 Decimal Operations 8/28 Fraction Operations Mixed Numbers and Improper Fractions 8/31 9/1 Introduction to Ratios 1 1 9/3 Equivalent Ratios and Ratio Tables

Learning Goal LG 701: Students will be able to analyze proportional relationships and use them to solve real-world and mathematical problems.

What are we doing today? Today I am working with ratio tables and equivalent ratios. So that I can scale ratios up or down to find missing values. I’ll know I’ve got it if I can solve problems like this:

Equivalent Ratios What do you think we mean by equivalent ratios? Could you give an example of equivalent ratios?

New Vocabulary Equivalent Ratios – ratios that are equal to each other. Ratio Table - A table where the columns are filled with pairs of numbers that have the same ratio

Equivalent Ratios A ratio is a comparison of two quantities by division. In the rectangles below, the ratio of shaded area to unshaded area is 1:2, 2:4, 3:6, and 4:8. All the rectangles have equivalent shaded areas. Ratios that make the same comparison are equivalent ratios.

Why can’t we add or subtract to find equivalent ratios? An Important Note… To find equivalent ratios always multiply or divide. Whatever we do to one number, we must do the exact same thing to the other. Why can’t we add or subtract to find equivalent ratios?

Equivalent Ratios Since ratios that make the same comparison are equivalent ratios, they all reduce to the same value. 2 3 1 10 15 5 = =

Equivalent or Nonequivalent Ratio? As the number of prints triples, the cost also triples. NON-EQUIVALENT As the number of prints doubles, the cost does not.

Equivalent Ratios Practice

Cool Trick – Cross Products Here is a cool way to see if your ratios are equivalent If the cross products are equal, the ratios are equivalent!

Cross Products Practice Determine if the ratios below are equivalent. ? ?

Math is Hard

(Volunteers must have the tables already copied.) Opening Activity Copy the tables below into your spirals. We’ll need two volunteers to help fill them in. (Volunteers must have the tables already copied.) Volunteer 1 Volunteer 2

Before we begin… Look back in your spirals at our last lesson. What are equivalent ratios? What are ratio tables? 2 : 3 8 : 9 : 15 3 :

Equivalent or Nonequivalent?? = = Equivalent Nonequivalent

You just created ratio tables! These are equivalent ratios! Let’s Have Some Fun Volunteer 1 Shots Made Shots Attempted 10 Volunteer 2 Shots Made Shots Attempted 10 What is the ratio of shots made to shots attempted for Volunteer 1? Volunteer 2? If each volunteer continued at the same pace, how many shots do you think they would make in 20 shots? 30 shots? You just created ratio tables! These are equivalent ratios!

Ratio Table Practice To disinfect 1 quart of stream water to make it drinkable, you need to add 2 tablets of iodine. How many tablets do you need to disinfect 4 quarts?

Ratio Table Practice In Table 1, how many cookies could you make with 4 cups of flour? In Table 1, how many cups of flour would you need to make 90 cookies?

What if you have a problem like this? There is no whole number you can multiply with 10 to get 15, so what do we do??

Scaling For the corn problem, we have to use scaling. Scale backward to 5 and then scale forward to 15

Ratio Table Practice Write and complete the tables below in your spiral. In 4 weeks, he’ll receive $28. 28 #1 It takes 15 minutes to run 2 km. #2 15

Working Backwards Every 2 minutes, he ate 11 hot dogs. Gross!!! ÷𝟔 11 https://www.youtube.com/watch?v=ICiY3-_hUF8

Ratio Table Practice Fill in the ratio table below to determine how many teaspoons of sugar there are in 18 ounces of a soft drink.

Let’s Play “I Have, Who Has…” For this game you will need a piece of notebook paper, a pencil and a card that I give you. One person will start us off by reading off “Who has…” on their card. On your paper, simplify the ratio your classmate read. If you think you have the simplified version, raise your hand. When time is called, read off “I Have…”