Ratios, Rates lessons condensed

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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

=

35
=

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

Answer
your essential
question. How you can you
complete ratio tables or
proportions when there
isn’t a known pattern?

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