1. MJ MATH 1 : 02 RATIOS AND RATE REASONING : 02.09 Module Two Test Review

2. MJ Math 1 : 02 Ratios and Rate Reasoning Objectives: You will use ratio language to describe the relationship between two quantities. You will write a ratio to describe the relationship between two quantities. You will describe a rate and unit rate in words and understand its meaning in a situation. You will calculate and write rates from contexts. You will make tables of equivalent ratios. You will use tables to find missing values and compare ratios. You will solve unit rate problems by reasoning about ratios and rates. You will define a percentage as a ratio of a number to 100, calculate a percent of a number as a rate per 100, and solve a variety of problems involving percentages. You will define the standard units of measure for given quantities. You will use different methods of ratio reasoning to convert units and solve problems that involve the conversion of units. You will determine the appropriate conversion factor when converting units. You will convert units between metric and customary systems.

3. Lesson 02.01 Understanding a Ratio Understanding a Ratio Ratio: a comparison between two amounts, sometimes using division Scaling ratios: Compare 6 boys and 4 girls 1. Read it 6 to 4 2. Write it 6/4 or 3. 6:4  Let‘s scale 6:4  1 st you could write it like a fraction. 6 4  2 nd divide the fraction by the same number on top and bottom to make it smaller (simplifying)  6 3 or 3:2  4 2 Ratio Terms: the numbers that show the comparison (ex: 6 and 4) ÷ 2

4. Lesson 02.01 Understanding a Ratio Understanding a Ratio Types of RatiosExamples:  Part to part  8 to 6  Comparing two parts of different things  Part to whole  6 to 14  Comparing part of one thing to the total amount of things  Part to part  You are comparing how many soccer balls you have vs. how many tennis balls. 8 soccer balls to 6 tennis balls or 8:6  Part to whole  You are comparing how many tennis balls you have compared to the TOTAL amount of balls or 6:14. You could also compare soccer balls to total for 8:14.

5. Lesson 02.01-Let’s Practice Understanding a Ratio Understanding a Ratio Types of RatiosScaling Ratios:  Your Turn!  Part to part  Q. Rewrite 12 to 8 two different ways.  1.  2.  Part to whole  Q. Rewrite 3 to 9 two different ways.  1.  2.  Your Turn!  Part to part  Q. Scale 12 to 8  1.  Part to whole  Q. Scale 3 to 9  1.

6. Lesson 02.01-Let’s Practice Understanding a Ratio Understanding a Ratio Types of RatiosScaling Ratios:  Check your work!  Part to part  Rewrite 12 to 8 two different ways.  1. 12/8 fraction  2. 12:8 use colon  Part to whole  Rewrite 3 to 9 two different ways.  1. 3/9 fraction  2. 3:9 use colon  Check your work!  Part to part  Scale 12 to 8  1. 12 3  8 2  Part to whole  Scale 3 to 9  1. 3 1  9 3 ÷ 4 ÷ 3

7. Lesson 02.02 The Unit Rate The Unit Rate Writing rates RATE:a ratio where two measurements are related to each other 1) Kiki can buy 18 ounces of cereal for $3.29.  Steps:  Step 1: Write your ratio as a fraction- $3.29  18 oz.  Step 2: Compare units-ounces vs. dollars. This means that Kiki pays $3.29 for 18 ounces of cereal. 2) Mae throws a football 70 feet in 4 seconds.  Steps:  Step 1: Write your ratio as a fraction- 70 feet  4 seconds  Step 2: Compare units-feet vs. seconds. This means that Mae throws 70 feet in 4 seconds. $$$ on top

8. Lesson 02.02 The Unit Rate The Unit Rate Unit rate and 2 nd unit rateHow to find the unit rates:  First Unit rates are easily calculated. Once a rate has been created, divide both of the terms of the rate by the second term.  Second unit rate(reciprocal)-  Flip the numbers and compare :  18oz 5.5 oz.  $3.29 $1  Examples:  Kiki can buy 18 ounces of cereal for $3.29.  Step 1: Write your ratio as a fraction- $3.29  18 oz.  $3.29 18  Kiki pays $0.18 per ounce or $0.18  1 oz. Divide the numerator by the denominator.

9. Lesson 02.02 The Unit Rate The Unit Rate Comparing Unit Pricing and Unit Sizes How to find the unit rate:  Fertilizer is 6.75lbs for $9.00 vs. 14.8lbs for $18.50  Which is the better deal?  Bag 1 vs. Bag 2  Bag 1= $1.33 per pound  Bag 2= $1.25 per pound  Step 1  Bag 1- 6.75lbs for $9.00  Step 1: Write your ratio as a fraction- $9.00  6.75lbs  $9.00 6.75 $1.33  1 lb.  Bag 2- 14.8lbs for $18.50  $18.50 14.8lbs $1.25  1 lb.

10. Lesson 02.02-LET’S PRACTICE The Unit Rate The Unit Rate Find the unit rate:Comparing Unit Pricing  Your Turn!  Q. Bag 1-Chicken wings are is 20.75lbs for $40.25  What is the unit rate?  A.  Q. Bag 2-Chicken wings are is 20.75 lbs for $50.25  What is the unit rate?  A.  Your Turn!  Which is the better deal?  Bag 1 vs. Bag 2  A. Compare the unit rate for bag 1 cost vs. bag 2 cost.  (hint:Which is cheaper?)

11. Lesson 02.02-LET’S PRACTICE The Unit Rate The Unit Rate Find the unit rate:Comparing Unit Pricing  Check your work  Q. Bag 1-Chicken wings are is 20.75lbs for $40.25  What is the unit rate?  A. $40.25 $1.94  20.75 lbs. 1lb  Q. Bag 2-Chicken wings are is 25.30 lbs for $50.25  What is the unit rate?  A. $50.25 $1.99  25.30lbs 1l b.  Check your work  Which is the better deal?  Bag 1 vs. Bag 2  A. Bag 1= $1.94/1lb  Bag 2=$1.99/1lb The better deal is Bag 1= $1.94/1lb because it is 4cents cheaper per pound.

12. Lesson 02.03 Equivalent Ratios Equivalent Ratios ratios that have the same simplest form and express the same relationship between two quantities Horizontal Chart  The instructions recommend that for every 2 fluid ounces of syrup, she must mix in 8 fluid ounces of water to taste the best  Adding or multiplying Syrup2 (+2)4 (+2)6(+2)8(+2)10 fl oz of syrup Water8(+8)16 (+8) 24(+8)32(+8)40 fl oz of water

13. Lesson 02.03 Equivalent Ratios Equivalent Ratios ratios that have the same simplest form and express the same relationship between two quantities  The instructions recommend that for every 2 fluid ounces of syrup, she must mix in 8 fluid ounces of water to taste the best  Adding or multiplying Vertical Chart SyrupWater 2 (add 2)8 (add 8) 416 624 832 1040 SyrupWater 2 (* 2) 8 (*2) 416 624 832 1040

14. Lesson 02.03 Equivalent Ratios Equivalent Ratios  The instructions recommend that for every 2 fluid ounces of syrup, she must mix in 8 fluid ounces of water to taste the best 2fl oz. of syrup 2 = 1 oz. syrup 8oz of water 2 4oz water Finding unit rates and using tables SyrupWater 1 (+1) 4(+4) 28 312 416 520 AddAdd SyrupWater 1 (*4)= 4 28 312 416 520

15. Lesson 02.03-LET’S PRACTICE Equivalent Ratios Equivalent Ratios Your turn!  The instructions recommend that for every 2 tablespoons of chocolate, Zoe must mix in 12 fluid ounces of milk to make hot chocolate.  Q. How many tablespoons would you need for 5floz. of milk? Your turn! Q. How many ounces of milk would you need for 7 tablespoons chocolate? Unit rates and using multiplication horizontally ChocolateMilk ChocolateMilk Hint: Find the unit rate first!

16. Lesson 02.03-LET’S PRACTICE Equivalent Ratios Equivalent Ratios Check your work!  The instructions recommend that for every 2 tablespoon of chocolate, Zoe must mix in 12 fluid ounces of milk to make hot chocolate.  Q. How many tablespoons would you need for 30 floz. of milk? Check your work! Q. How many ounces of milk would you need for 7 tablespoons chocolate? Unit rates and using multiplication horizontally ChocolateMilk 1(+1) 6(+6) 212 318 424 530 ChocolateMilk 1 (*6) = 6 2 12 3 18 424 530 636 742 Unit rate: 2tbs ÷2= 12floz÷2= 1Tbs c hoco. 6oz. milk

17. Lesson 02.05 Percentages Percentages Using Percentages:  Words:  26 out of 100  26 for every 100  Ratio  26:100  26 to 100 or  26  100  Percentage  26% A percentage is a part-to-whole ratio that compares a number to 100; percentages are written with the percent symbol (%). Multiplying by 100, turn a decimal into a percent: When you multiply a number by 100, you move the decimal point of the factor two places to the right. For example: 0.43 × 100 = 43 or 27.6 × 100 = 2,760 If you have a decimal, it can be written as a percent by multiplying the number by 100. For example: 0.16 × 100 = 16% or 0.035 100 = 3.5% When you divide a number by a 100, you move the decimal point of the number being divided two places to the left. For example: 54 100 = 0.54 or 8.23 ÷ 100 = 0.0823

18. Lesson 02.05 Percentages Percentages  For example: What percent is 6 out of 25?  Create a table and use equivalent ratios until the second term is 100. 6 212 224 25 250 2100 Start

19. Lesson 02.05 Percentages Percentages  What is 35% of 75? 35 35 = 0.35 35 = 0.35 100 100 …….. First Part Whole

20. Lesson 02.05-LET’S PRACTICE Percentages Percentages Your turn!  Q. What percent is 4 out of 20? Your turn!  Q. What is 35% of 75?  A. ? 4 20

21. Lesson 02.05-LET’S PRACTICE Percentages Percentages Check your work!  Q. What percent is 4 out of 20? Check your work!  Q. What is 35% of 75?  A. Step 1 : convert 35% to 0.35  Step 2: 0.35* 75  =26.25 45 = 20 5= 100 20%

22. Lesson 02.06 Measurements Measurements US Customary Units

23. Lesson 02.06 Measurements Measurements ConversionsScenarios:  Step 1: Identify the conversion from the table.  1 pint=2 cups  Step 2: Make a chart  Determine number to multiply by top number for your recipe. Q - A recipe calls for 3 pints of cream and caramel sauce to make ice cream. How many cups of cream do you need? Pints1 33 cups2 3 6 cups for recipe Conversion Factor

24. Lesson 02.06 Measurements Measurements

25. Lesson 02.06-Let’s Practice Measurements Measurements Your turn!  Q. A recipe for oatmeal calls for 6 quarts of milk. How many pints would you have? Your turn! Q. If you ran 7 ½ yards, how many feet did you run? Quarts Pints

26. Lesson 02.06-Let’s Practice Measurements Measurements Check your work!  Q. A recipe for oatmeal calls for 6 quarts of milk. How many pints would you have?   A. 12 pints Check your work! Q. If you ran 7 ½ yards, how many feet did you run? A. 16 feet Quarts1(*6) =6 Pints2(*6)= 12 pints 16 Feet

27. Lesson 02.07 Unit Conversions Unit Conversions  Step 1: Identify the conversion in your table.  How many pounds are in 10 Kilograms?  Set the units from the numerator to match the denominator of the second conversion factor to cancel out the units.  The units cancel out.  Now multiply across to find the converted unit. Converting from one unit of measurement to another unit of measurement. 1. 2. 3.

28. Lesson 02.07-Let’s Practice Unit Conversions Unit Conversions Your turn! Converting from one unit of measurement to another unit of measurement.  Q. How many liters are in 5 gallons?  5 gallons=? liters  Q. How many centimeters are in 55 inches? 55 inches=? centimeters

29. Lesson 02.07-Let’s Practice Unit Conversions Unit Conversions Check your work!! Converting from one unit of measurement to another unit of measurement.  Q. How many liters are in 5 gallons?  A. 5 gallons=? liters  Q. How many centimeters are in 55 inches? A. 1.