Welcome to Day 3 of Part 1Computation
Unit Rates
Percents
Data Analysis
TODAY’S TOPICS
Ratios &
Proportions
Let’s check your basic
knowledge of percents.
On your Genius Card, write 3 facts
about percents.
Find the fallacy in each percent
statement.Write the error on your
Genius Card.
What’s wrong
with this?
The hippy dippy weatherman said
that he can correctly predict the weather 100% of the time.
Hmm…
On a recent TAKS item, 5% chose A, 22% chose B, 3% chose C, and 72%
chose D.
Great shots!
The Never-Miss basketball team
made 30% of their field goals.
Absolutely!
The coach said, “I expect to see 200% effort in this game!”
?
Bo tossed two dice to test the probability of landing on an even
number. He noticed that the dice landed on
evens 17% of the time and on odds 73% of the
time.
Makes sense to
me!
Moe and Joe ordered a $10 pizza. They tipped the delivery
boy $5.
Okay…
When the movie began, 30 people
were in the theater. Within 5 minutes, 50% more people
entered making the total number 60.
Go, Pixie!
These are the results of a recent MISD election:
Mixie: 32%Pixie: 35%Dixie: 33%
Pixie was declared the winner for receiving a majority of the votes.
How did you do?
Next, we will try to apply our vast knowledge of
percents.
But first, a thought…
Percents are actually a fraction with 100
as the denominator.
So…
𝑛100
=𝑛%
So if we set up equivalent fractions……we could solve a
percent problem!
PART
WHOLE 100
n
=
A no-fail way to solve a percent application is to set up a percent proportion.
𝑝𝑎𝑟𝑡h𝑤 𝑜𝑙𝑒
=𝑛100
The part we are
considering
The entire amount we are
considering
The percent
This is always 100!
Equivalent fractions!
(AKA: proportion)
PART
WHOLE 100
n
=
35 is what percent of 700?
35700
=𝑛100
35
700
?
100
The part we are
considering
The entire amount we are
considering
The percent
This is always 100!
Solve the proportion.
PART
WHOLE 100
n
=
What number is 15% of 80?
𝑛80
=15100
?
80
15
100
The part we are
considering
The entire amount we are
considering
The percent
This is always 100!
Solve the proportion.
PART
WHOLE 100
n
=
48 is 24% of what number?
48𝑛
=24100
48
?
24
100
The part we are
considering
The entire amount we are
considering
The percent
This is always 100!
Solve the proportion.
Now, you are ready to apply your even
more vast knowledge of
percents.
Ziggy answered 15 out of 25 questions
correctly. What percent did Ziggy answer correctly?
There are 42 birds in the park. This is
56% of all the animals in the park. How many animals
are in the park?
62% of the coins landed on tails. If 50
coins were tossed, how many landed on
tails?
Now we will throw in a few
“tricks”…
Ready?
55% of the Ned’s coins are shiny. If Ned has 80 coins,
how many are not shiny?
TRICK!
Ted added a 18% tip to the price of his meal, which was
$7.50. How much did Ted pay in all?
EINSTEIN BREAK!Rest your brains!
It is time for
YOU to try some
percent problems!
On the desks, you see 16 different
problems. You must complete 12 of
them. You may cross out four items on your record sheet.
Unit Rates
Percents
Data Analysis
WHERE ARE WE?
Ratios &
Proportions
Unit rates & ratios will be EASY after
percents!
Ready?
A ratio is a numerical comparison of like
quantities.
Example: If the ratio of dogs to cats is 5:7, how many dogs are there if there are 84
cats?
A rate is a numerical comparison of unlike
quantities.
Example: We traveled 685 miles to Florida. If we drove 50 miles an hour,
how many hours did it take to make it to
Florida?Round to nearest whole number.
A unit rate is a numerical
comparison of like quantities with a denominator of 1
unit.
Example: Cereal A costs $4.49 for 12 ounces. Cereal B costs $3.14 for 8
ounces. Which is the better buy?
There are ratios all around us…
We will explore a few.
Now you will try some ratio problems.
Are you ready?
Brittney led the Bears in scoring two-thirds of the games last season. If the Bears played 42 games, in how many
was Brittney the leading scorer?
Which of the following is the least expensive
cost per apple?10 apples for $3.9912 apples for $4.598 apples for $3.15
Four snowcones cost $7.20. Ziggy wants
to buy five snowcones. How
much will 5 snowcones cost?
Lizzy can read 160 words per minute. At the same rate, how
long would it take Lizzy to read 240 words?
Unit Rates
Percents
Data Analysis
Let’s keep
going!Ratios
& Proportions
What does that mean?????????
Mean, Mode, Median, Range,…
All are measures of central tendency.
129
146
169
Find the mean.
129
146
169
Find the mode.
129
146
169
Find the median.
129
146
169
Find the range.
Playing with “mean” can be fun!
3328373230
Take a list of numbers like this.
Pick a number that seems to be near the
center.3328373230
Let’s pick 31.
Find the difference between 31 and each number.33
28373230
Write the difference as positive (how
much above 31) or negative (how much below 31).
3328373230
+231
-3+6+1-1
Add these numbers (the differences).
5Divide by the
number of numbers (5).
1 + 31Add the answer to 31.
The mean
is 32.
Try this list:
4547483540
And one more:
5849575556
Thinking about central tendency:
If Ned and Jed both have an 85 average,
what do we know about their grades?
Ned and Jed both have an 85 average. The
range of Ned’s scores is 23. The range of
Jed’s scores is 5. What do we know about their
grades?
Fred and Ted both have an 85 average. The
median of Fred’s scores is 90. The median of
Jed’s scores is 80. What do we know
about their grades?
EINSTEIN BREAK!Rest your brains!
Unit Rates
Percents
Data Analysis
Show what you
know! Ratios &
Proportions
Earn points by answering correctly at each level. We will begin with the easiest
problems (Level 1) and work up in levels of
difficulty to the challenging problems
(Level 2).
LEVEL 1 One Point
Percent
Izzy correctly answered 45 out of 60 problems on his
math test. What percent of the questions did he
correctly answer?
LEVEL 1One Point
Unit Rate & Ratios
Which is the better buy?15 batteries for $10.98
8 batteries for $6 12 batteries for $8.75
LEVEL 1One Point
Proportions
Joe can ride his scooter 20 miles per hour.
At this rate, how far could he ride from 8:00 am until
12:00 noon?
LEVEL 1One Point
Data Analysis
What is the mean of this
list of numbers?
2316281320
LEVEL 22 Points
Percent
Thirty-six of the scooters at the Hewitt Hobby Shop are blue. This represents 45% of all the scooters in the
store. How many scooters are in the store?
Unit Rate & Ratios
LEVEL 22 Points
The ratio of pigs to cows on McDonald’s farm is 8 to 7. If
there are 84 cows on his farm, how many pigs are on
his farm?
Proportions
LEVEL 22 Points
At HEB, 15 out of 43 watermelons are seedless.
If there are 258 watermelons, how many are
not seedless?
21192733
Data Analysis
LEVEL 22 Points
Which measure of
central tendency is
greater for this list of
numbers: mean, mode, or median?
LEVEL 33 Points
Percent
Fred and Jed bought a soccer ball. Fred paid 40%
of the total cost. If Fred paid $7.20, how much did Jed
pay?
LEVEL 33 Points
Unit Rate & Ratios
If Speedy can run 10 miles an hour, how many miles can he
run in 45 minutes?
LEVEL 33 Points
Proportions
Fred and Jed bought a soccer ball. Fred paid 40%
of the total cost. If Fred paid $7.20, how much did Jed
pay?
LEVEL 33 Points
Data Analysis
137
1723
Which statement is true?
A. Mean > MedianB. Mean = MedianC. Mean < MedianD. Mean > Range
LEVEL 44 Points
Percent
The number of members in the MMS math club
increased by 30% since April. If there are now 78
members in the math club, how many were in the club
in April?
LEVEL 44 Points
Unit Rate & Ratios
The ratio of the sides of an isosceles triangle is 2:5:2. If the perimeter of the triangle is 81 cm, what is the length
of the longest side?
LEVEL 44 Points
Proportions
If the ratio of offensive players to defensive
players is 21:32. At this rate, if there are 7 teams playing, how many total players would there be?
LEVEL 44 Points
Data Analysis
Moe wants to have a 93 average in math. His
scores are: 100, 88, 95, and 87. What is the lowest
score he could make on his next assignment to have a
93 average?
Add your points!
Stand.Sit when you see your point total:
102345678910111213141516
Write on your Genius Card three things you learned today about any of these topics: percent, ratios, unit rates, proportions,
measures of central tendency.