Transcript Lesson 1 PPT

Today’s Lesson:
What:
rates and proportions
Why:
To introduce essential vocabulary
and begin to solve proportions.
Vocabulary:
comparison
Ratio – __________________________
of
two numbers (15 students to 1 teacher).
Rate – comparing two numbers with
𝟑 𝒇𝒕
different _____________
(
).
units
𝟏 𝒚𝒅
Unit Rate – rate that is out of ________
one
𝟖𝟎 𝒃𝒆𝒂𝒕𝒔
(
).
𝟏 𝒎𝒊𝒏.
Proportion – two ratios that are
equivalent
_____________________
to one another
𝟏
𝟑
( = ).
𝟐
𝟔
Three Ways to Write a Ratio:
1) By using a colon (3 boys : 2 girls) ;
𝟑 𝒃𝒐𝒚𝒔
𝟐 𝒈𝒊𝒓𝒍𝒔
2)
using a fraction (
3)
using words (three boys to every 2
girls) .
); and
Write the following ratios in all 3 ways:
1) The ratio of months that end in the letter
“r” to the total number of months in a
year (be sure to reduce):
4 : 12 or 1 : 3 ;
𝟒
𝟏𝟐
or
𝟏
𝟑
;
one to three
2) The ratio of vowels to consonants in
the word “C-A-L-E-N-D-A-R”:
3 :5 ;
𝟑
𝟓
;
three to five
3) The ratio of boys to girls in Ms. Dyson’s
class:
What do you notice about the following
ratios??
1)
2)
9
12
and
Answer:
3
4
3)
4
5
and
8
10
10
15
and
2
3
Each set of ratios are equivalent.
Also, their cross-products are the same.
So, in order for two ratios to form a
proportion, they must be ________________.
equal
Therefore, their cross-products are also
equal. That means, we can cross-multiply
to find out whether or not two ratios are
proportional!!
Do the following ratios form proportions?
Cross-multiply to find out . . .
1)
2)
8
5
and
4
5
5
3
no
and
16
20
yes
3)
4)
11
15
and
no
3
4
10
15
and
yes
4
6
How can we solve a proportion??
2nd Example from video: Video
Hawaii Map Example:
𝟗 𝒎𝒊
𝟓 𝒄𝒎
=
n 𝒎𝒊
20 𝒄𝒎
180 = 5n
5
5
36 = n
n = 36 mi
Soooo, these are the steps:
Step One: Cross Multiply
Step Two: Divide by the coefficient
(# with “x”)
9
𝑥
Example:
=
12
8
72 = 12x
12
12
x = 6
On your own:
1)
𝟏𝟓
𝒙
=
𝟔
𝟒
x = 10
2)
𝟑
𝟒
=
𝒙
𝟏𝟎
x = 7.5
Real-life Proportions . . .
1) If 4 tickets to a concert cost $62, how
much would it cost for 10 people to go to
the concert?
x = $155
Real-life Proportions . . .
2) A certain car drove 110 miles on 5
gallons of gas. How far should it be able
to go on 11 gallons?
x = 242 miles
Real-life Proportions . . .
3) The ratio of boys to girls at Simpson
Middle School is 4 : 5. If Simpson has
420 boys, how many total students are at
Simpson?
x = 525 girls
Since there are 420 boys and 525 girls,
there are 945 TOTAL STUDENTS!
Unit Rates:
4) If $12.80 will buy 4 jars of pickles,
then how much is one jar?
x = $3.20
Unit Rates:
5) If Jill can type 150 words in 5 min.,
then how many words can she type in
1 min.?
x = 30 words per minute
homework
IXL: J.6 & J.9
END OF LESSON
The next slides are student copies of the notes and
handouts for this lesson. These were handed out in
class and filled-in as the lesson progressed.
NAME:
Math-7 NOTES
DATE: ______/_______/_______
What:
rates and proportions
Why:
To introduce essential vocabulary and begin to solve proportions.
Vocabulary:
Ratio – _________________________________ of two numbers (15
students to 1 teacher).
Rate – comparing two numbers with different __________ (
Unit Rate – rate that is out of ___________ (
80 𝑏𝑒𝑎𝑡𝑠
1 𝑚𝑖𝑛.
3 𝑓𝑡
1 𝑦𝑑
).
).
Proportion – two ratios that are _____________________ to
1
3
one another ( = ).
2
6
Three Ways to Write a Ratio:
1) By using a _____________ ( _____________________________ );
2) using a ________________ (
3 𝑏𝑜𝑦𝑠
2 𝑔𝑖𝑟𝑙𝑠
) ; and
3) using ___________ (_________________________________________________ ) .
Write the following ratios in all 3 ways:
1)
The ratio of months that end in the letter “r” to the total number of
months in a year (be sure to reduce):
2)
The ratio of vowels to consonants in the word
“C-A-L-E-N-D-A-R”:
3)
The ratio of boys to girls in Ms. Dyson’s class:
What do you notice about the following ratios??
1)
2)
9
12
and
3
4
3)
4
5
and
8
10
10
15
and
2
3
Answer:
So, in order for two ratios to form a proportion, they must be
___________________. Therefore, their cross-products are also
equal. That means, we can cross-multiply to find out whether or
not two ratios are proportional!!
Do the following ratios form proportions? Cross-multiply to find
out . . .
1)
2)
8
5
and
5
3
3)
4
5
and
16
20
4)
11
15
and
Video (2ndexample from video):
Hawaii Map Example:
𝟗 𝒎𝒊
𝟓 𝒄𝒎
=
𝒎𝒊
𝒄𝒎
3
4
10
15
and
4
6
Soooo, these are the steps:
Step One: Cross Multiply
Step Two: Divide by the coefficient (# with “x”)
9
12
Example:
𝑥
8
=
72 = 12x
12
12
x = 6
On your own:
1)
𝟏𝟓
𝒙
=
𝟔
𝟒
2)
𝟑
𝟒
=
𝒙
𝟏𝟎
Real-life Proportions . . .
1) If 4 tickets to a concert cost $62, how much would it cost for 10 people to go
to the concert?
2) A certain car drove 110 miles on 5 gallons of gas. How far should it be able to
go on 11 gallons?
3) The ratio of boys to girls at Simpson Middle School is 4 : 5. If Simpson has
420 boys, how many total students are at Simpson?
Unit Rates:
4)
If $12.80 will buy 4 jars of pickles, then how much is one jar?
5) If Jill can type 150 words in 5 min., then how many words can she type in 1 min.?
IXL: 7th Grade, J. 6 and J.9
(scratch work required for J.9)
NAME:___________________________________________________________________________
DATE: ______/_______/_______
For each word problem, you must set up a proportion (label the correct units), and show steps required to
solve. You may stop once you achieve a MINIMUM smart score of 70% (can keep going if desired), or once
you have spent 15 minutes or more. No scratch work will result in a loss of points!
Example:
Answer (showing my work):
Type answer
in box.
𝟏𝟖 𝒍𝒊𝒕𝒆𝒓𝒔
𝟗 𝒅𝒂𝒚𝒔
𝟗𝒙
𝟗
𝒙
= 𝟏𝟎 𝒅𝒂𝒚𝒔
=
𝟏𝟖𝟎
𝟗
x = 20 liters
Proportion:
Proportion:
=
Proportion:
Proportion:
Proportion:
=
Proportion:
Proportion:
=
Proportion:
=
=
Proportion:
=
=
=
Proportion:
Proportion:
=
=
Proportion:
=
=
Proportion:
Proportion:
=
Proportion:
Proportion:
Proportion:
=
Proportion:
Proportion:
=
Proportion:
=
Proportion:
=
=
Proportion:
=
=
=
Proportion:
Proportion:
=
=
Proportion:
Proportion:
=
=
Proportion:
=
=
NAME:___________________________________________________________________________
DATE: ______/_______/_______
Do the following ratios form proportions. Answer “yes” or “no” (cross-multiply):
Solve the following proportions:
For each of the below situations, set up a proportion to solve:
1.
2.
3.
4.
5.
6.