How can you represent a relationship between two quantities? Ratios – Day 1 How can you represent a relationship between two quantities?

Introduction

Activity 3

Activity 4

Free Throw Comparison Shots Made Shots Missed Total Number 21 35 Complete the chart and then complete the following statements. - There were ______ shots made to ________ total number of shots. There were ______ shots missed to _______ total number of shots. There were ______ shots made to _______ shots missed.

You just wrote several ratios! Ratio – Comparison of two quantities. They can be part – to - part, part – to – whole, or whole – to – part. Ratios can be written three ways and must be in simplest form. Example Ratio of orange to blue Ratio of orange to all crayons Ratio of all crayons to blue

Ratios with Money Write the following rations. Quarters to pennies - Dimes to quarters -Dimes to total number of coins Quarters to total number of coins

Extension Activity In the continental United States, the ratio of states that border the ocean to those that do not border an ocean is 7 : 9. How many of the states border an ocean?

Summary of Ratios - Put at the end of yesterday’s notes

How can you use rates to describe changes in real-life problems?

Complete Activities 1 and 2

Activity 2

Key Terms Rate – a ratio of two quantities using different units Unit Rate - compares a quantity to one unit of another quantity Common unit rates are miles per gallon, miles per hour, words per minute, $ per pound Equivalent rates – rates that are the same

Unit Rates – rate for one unit To find a unit rate, divide the first quantity by the second quantity. a units : b units = a b

Find the unit rate $24 saved in 4 weeks 270 miles in 6 hours 880 calories in 8 servings $12.50 for 5 ounces

Equivalent Rates How can you determine if two rates are equivalent? See if the unit rates are the same. 24 laps in 6 minutes 72 laps in 18 minutes

Which bag of dog food is the better buy? A 20 pound bag for $17.20 or a 30 pound bag for $25.20. Work in groups for a few minutes to see if you can determine which bag is the better deal.

Independent Practice

Summary of Rates in your notes Remember to answer the essential question. How can you use rates to describe changes in real-life problems?

How can you find two ratios that describe the same relationship? Ratio tables How can you find two ratios that describe the same relationship?

Equivalent Ratios and Ratio Tables Equivalent Ratios – Two ratios that describe the same relationship. Equivalent ratios can be found by adding and subtracting quantities in equivalent ratios multiplying or dividing each quantity in the ratio by the same number.

3 8 6 36 Hint: I find multiplying the easiest way to complete the ratio table. Think of it like finding equivalent fractions.

water 4 20 sugar 1

Practice with Ratio tables

Ratio tables

19 and 20 answers Basketball 7 28 Soccer 6 24 Pop 5 40 Rock 4 32

Using a ratio table You mix 3 pints of yellow paint for every 4 pints of blue paint to make green paint. You use 12 pints of blue paint. How much green paint do you make? yellow 3 blue 4 12 green

Summary – Put at the end of your notes How can you find two ratios that describe the same relationship?

Using Ratio Tables to Solve Proportions How can you complete ratio tables when there isn’t a pattern?

Activity Work in groups to see if you can complete the two ratio tables.

How do you solve Proportions? Ratio tables are actually proportions, two equivalent ratios. Try solving by cross multiplying. 25 x 16 = 100 x ? 400 = 100 x ? 400 = 100 x 4 25   100 16 4 2   3 4.5 3 2 x 4.5 = 3 x ? 9 = 3 x 3

Practice with Proportions 17 34 = 7 𝑥 24 21 = 𝑥 35 2 10 = 𝑥 35

Word Problem with Proportions 6 girls How many girls are in the group that has 12 boys? 8 girls

Practice With Proportions 8 9 = 40 𝑚 Answer your essential question. How you can you complete ratio tables or proportions when there isn’t a known pattern?