Ratios, Rates, and Unit Rates across the Universe
description
Transcript of Ratios, Rates, and Unit Rates across the Universe
![Page 1: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/1.jpg)
Ratios, Rates, and Unit Rates across the Universe
What is the difference between a ratio and a rate?
706.2.7 use ratios and proportions to solve problems
![Page 2: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/2.jpg)
Ratios
Definition: A comparison of two numbers:
Parts to whole: Or
Parts to Parts:
Finding Missing Part of Ratio:
See how many times it takes to go from one fraction to the other.
Do the same thing to the top or bottom.
Comparing Ratios You can use fraction rules to compare
Or You can turn the ratios into decimals
Written As:Fraction, with :, and to
Examples:
8/35, 8:35, 8 to 35
Equivalent Ratios = Equivalent FractionsYou can multiply the top and bottom by the same # or reduce to get an
Equivalent ratio
![Page 3: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/3.jpg)
RATIOS
A ratio makes a comparison. There are 3 green aliens and 4 purple aliens. The ratio of green aliens to
purple aliens is
3 to 4.
![Page 4: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/4.jpg)
RATIOS
A ratio makes a comparison. The ratio of green aliens to total aliens is 3 to 7. The ratio of total aliens to purple
aliens is 7 to 4.
![Page 5: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/5.jpg)
RATIOS
A ratio makes a comparison. Ratios
can be written in three different
ways.
3 to 4
3:4
3
4
![Page 6: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/6.jpg)
Ratios
• Ratios can be written as a comparison of parts to parts or a comparison of parts to whole.
• Ex: 3 boys to 5 girls (not a true fraction)
• Ex: 3 boys to 8 students (true fraction)
![Page 7: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/7.jpg)
Ratios
Definition: A comparison of two numbers:
Parts to whole: Or
Parts to Parts:
Written As:
Fraction, with :, and to(Out of : part to whole only)
Examples:
8/35, 8:35, 8 to 35
![Page 8: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/8.jpg)
White Board Practice
Wins to LossesWins=17, Losses=14
Write the ratio three different ways:17:14 17 to 14 17/14
Now write a ratio three different ways for the wins to total games played.
17:31 17 to 31 17/31
![Page 9: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/9.jpg)
Definition: A comparison of two numbers:
Parts to whole: Or
Parts to Parts:
![Page 10: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/10.jpg)
Assessment Prompt
• What is a ratio?
• What are different ways to write a ratio?
![Page 12: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/12.jpg)
Ratios
Definition: A comparison of two numbers:
Parts to whole: Or
Parts to Parts:
Written As:Fraction, with :, and to
Examples:
8/35, 8:35, 8 to 35
Equivalent Ratios = Equivalent FractionsYou can multiply the top and bottom by the same # or reduce to get an
Equivalent ratio
![Page 13: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/13.jpg)
White Board PracticeWrite the ratio in simplest form and in an
equivalent form.For every 6 boys there are 10 girls.
3:5 12 to 20 60 to 100
Why would a fraction not be a good choice for this ratio?
![Page 14: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/14.jpg)
![Page 15: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/15.jpg)
Ratios
Definition: A comparison of two numbers:
Parts to whole: Or
Parts to Parts:
Finding Missing Part of Ratio:
See how many times it takes to go from one common part of a fraction to the other. Do the same thing to the top or bottom.
Comparing Ratios You can use fraction rules to compare
Or You can turn the ratios into decimals
Written As:Fraction, with :, and to
Examples:
8/35, 8:35, 8 to 35
Equivalent Ratios = Equivalent FractionsYou can multiply the top and bottom by the same # or reduce to get an
Equivalent ratio
![Page 16: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/16.jpg)
![Page 17: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/17.jpg)
Assessment Prompt
• How do you find the missing part of a ratio? 3/5 x/20
![Page 18: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/18.jpg)
Real World Uses• Population: Ethnicity, gender, etc.
• Sports statistics: ERA, Batting Avg, Free Throw Percent.
• Probability: Odds of occurrences
• Comparison Shopping: items per package
![Page 19: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/19.jpg)
![Page 20: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/20.jpg)
White Board Practice
Who has the greater ratio of Rock CD’s to total CD’s?
Luis RaeRock = 9 Rock = 14Total = 11 Total = 18
Simply turn your fractions into decimals (divide) to see who has the greater amount.
Luis has the greater amount .81
![Page 21: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/21.jpg)
White Board Practice
Who has the greater ratio of Rock CD’s to total CD’s?
Luis RaeRock = 9 Rock = 14Total = 11 Total = 18
You could also use cross products to see which is larger: 18 * 9 = 162 = Luis
11 * 14 = 154 = Rae, Luis has more.
![Page 22: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/22.jpg)
Assessment Prompt
• Text a friend and tell them what a ratio is and how we compare them?
![Page 23: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/23.jpg)
Rates
Unit Cost:Money goes on top because you are
Trying to find the cost per 1 unityou will turn the denominator into a
1 through division
Comparing Rates Compare rates like you would a fraction
Definition: A ratio that compares two different
Units of measurement30 pages : 20 minutes
Unit Rate:How many per 13 corndogs : $1
62 miles per hour
You can also find unit cost by dividing the cost by the number of items. $5 : 15 mini butterfingers = 5 ÷ 15 = $0.33 per 1 mini butterfinger
![Page 24: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/24.jpg)
RATES
A rate is a ratio that compares quantities that
are measured in different units.
This spaceship travels at a certain speed. Speed is an example of a rate.
Speed can be measured in many different ways. This spaceship can travel
100 miles in 5 seconds. 100 miles in 5 seconds is a rate.
![Page 25: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/25.jpg)
RATES
A rate is a ratio that compares quantities that
are measured in different units.
Rates are often written in fraction form.100 miles in 5 seconds is a rate.It can be written as…..
5
100 Miles
Seconds
![Page 26: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/26.jpg)
RATES
A rate is a ratio that compares quantities that
are measured in different units.
One key word that often identifies a rate is PER.Miles per gallon, Points per free throw,slices per pizza, Sticks of gum per pack
What other examples of rates can your group think of?
![Page 27: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/27.jpg)
Assessment Prompt
• What makes a rate different from a ratio?
• Is a rate a ratio? Is a ratio a rate?
![Page 28: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/28.jpg)
Write two equivalent ratios:
5/3 =
Identify the rate:
3 boys: 12 students
4 pencils per 1 bag
Complete the ratios:
5/7 = x / 21
Write two equivalent ratios:
12/20 =
Identify the rate:
2 purple flowers: 1 white flower
350 miles per 5 hours
Compare the ratios
3/8 __ 4/9
Write two equivalent ratios:
15/35=
Identify the rate:
4 pepperoni slices: 3 cheese slices
5 gals per 1 bucket
Complete the ratios
4/11 = 16/X
111
3
2
3
2
3
2
Tic-Tac-Think: Simplifying Radical Expressions: Choose 3 questions that will total at least 5 points
![Page 29: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/29.jpg)
End of Lesson
![Page 30: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/30.jpg)
Activator
• Review: what are ratios and rates?
• In math, how much is a unit?
![Page 31: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/31.jpg)
![Page 32: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/32.jpg)
Rates
Definition: A ratio that compares two different
Units of measurement30 pages : 20 minutes
Unit Rate:How many per 11 corndog : $0.5062 miles per hour
![Page 33: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/33.jpg)
![Page 34: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/34.jpg)
![Page 35: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/35.jpg)
Rates
Unit Cost:Money goes on top because you are
Trying to find the cost per 1 unityou will turn the denominator into a
1 through division
Comparing Rates Find the unit rate, the larger unit rate is
Bigger.
Definition: A ratio that compares two different
Units of measurement30 pages : 20 minutes
Unit Rate:How many per 13 corndogs : $1
62 miles per hour
You can also find unit cost by dividing the cost by the number of items. $5 : 15 mini butterfingers = 5 ÷ 15 = $0.33 per 1 mini butterfinger
![Page 36: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/36.jpg)
![Page 37: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/37.jpg)
White Board Practice
Convert the ratios to a rate80 miles traveled in 2 hours
40 miles : 1 Hour
24 oranges for $3.00
1 orange for $0.13
![Page 38: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/38.jpg)
Assessment Prompt
• What is the difference between a rate and a unit rate?
![Page 39: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/39.jpg)
Two ways to solve:
1. Making equivalent ratio to 1.
$15 / 3 bags = $? / 1 bag
2. Divide the numerator by the denominator:
$15 / 3 bags = $5
2. Key Points: $ should always be on top unless you are finding how much a $1 will buy.
![Page 40: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/40.jpg)
![Page 41: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/41.jpg)
Find the Unit Rate:
• $350/ 5 nights (solve using equivalent rates)
• $1.88 / 20 oz (solve using division)
• 90 miles / 3 hours (your choice)
![Page 42: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/42.jpg)
![Page 43: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/43.jpg)
Finding a rate from a unit rate
• This is real world: You know that 1 bag of dog food costs $5.68. You want to find the rate of 12 bags.
You start with a unit rate and work backwards:
![Page 44: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/44.jpg)
Finding a rate from a unit rate
• This is real world: You can travel 3.8 km per hour. How far could you travel in 4 hours? How far in 270 minutes?
You start with a unit rate and work backwards:
![Page 45: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/45.jpg)
Using unit rate to find a bargain
• You are buying chips for a party. You want to get the most bang for your buck so you want the best price per unit. You have two choices: $8.96 per 40 oz or $9.84 per 48 oz. Which bag of chips should you buy if you want the cheapest unit price?
![Page 46: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/46.jpg)
What is the denominator of a unit rate?
• Explain the error and correct:
$36 $1 4 apples .11 apples
![Page 47: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/47.jpg)
Worksheet
• Turn the camera on and do the worksheet “Is Bigger Always Better?”
![Page 48: Ratios, Rates, and Unit Rates across the Universe](https://reader035.fdocuments.in/reader035/viewer/2022062409/56814ff8550346895dbdc285/html5/thumbnails/48.jpg)
Homework
WORKBOOK: pg. 69-70 all (that is a total of 21 problems if you count # 14 as two separate problems.)