Ratios, Rates lessons condensed
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Transcript Ratios, Rates lessons condensed
RATIOS – DAY 1
How can you represent a
relationship between two
quantities?
INTRODUCTION
ACTIVITY 3
ACTIVITY 4
FREE THROW COMPARISON
Shots Made
21
Shots Missed
Total Number
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
RATES
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?
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
6
8
36
Hint: I find multiplying
the easiest way to
complete the ratio table.
Think of it like finding
equivalent fractions.
water
4
sugar
1
20
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
green
12
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
100
4
16
2
3
25 x 16 = 100 x ?
400 = 100 x ?
400 = 100 x 4
3
4.5
2 x 4.5 = 3 x ?
9=3x3
PRACTICE WITH PROPORTIONS
17
34
24
21
2
10
=
7
𝑥
=
𝑥
35
=
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?