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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
MAP2D
Quarter 3Instructional Strategies
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
MAP2D
Chapter 5Ratios, Proportions, and
Similarity
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Writing RatiosWrite the ratio of girls to boys in
simplest formA class has 20 girls to 16 boys.
Identify the two quantities being comparedStep 1
Step 2 Write as a ratio
girls
boys
Step 3 Simplify20 girls
16 boys
4∙5 girls
4∙4 boys
5 girls4 boys= =
5.1 Ratios
5 girls:4 boys 5 girls to 4 boys
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Comparing Unit RatesDerrick’s car travels 360 miles and uses 15 gallons of
gas. Louise’s car travels 340 miles and uses 10 gallons of gas. Whose car gets better gas mileage (in miles per
gallon)?
milesgallons
Identify the two ratios being compared and the units of each ratioStep 1
Step 2 Write each ratio
Step 3 Divide each ratio (make each ratio into a unit rate) and compare!
360 mi15 gal
= 24 miles per gallon
5.2 Rates and unit rates
milesgallons
340 mi10 gal
= 34 miles per gallon
Louise’s car gets 10 miles per gallon more than Derrick’s!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
35
12=
xSolving Proportions
Solve:
Step 1: Cross multiply
Step 2: Solve for x
3 x =12 5
3x = 603x = 603 3
x = 205.3 Proportions
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Solving Real-life Problems Using Proportions
Step 1: Write a ratiousing words
Step 3: Cross multiply
12 25 = 15 x 300 = 15x
300 = 15x 15 15
x = 20 pages
Step 4: Solve for x
Pagesminutes
1215
x 25
=
Jason can read 12 pages of a book in15 minutes. How many pages can he read
in 25 minutes?
Step 2: Set-upa proportion
5.3 Proportions
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Step 1: Write a ratio using words
Solving Real-life Problems Using Proportions
Jared is printing a 240 page research paper for his college class. The printer prints the first 60 pages in 4 minutes. How long will it
take to print the rest of the paper?
Step 2: Set-up a proportion
PagesMinutes
604
180x
How many pages does Jaredhave left to print?240 ― 60 = 180
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Solving Real-Life Problems Using Proportions (cont.)
Step 3: Cross multiply and solve for x
Jared is printing a 240 page research paper for his college class. The printer prints the
first 60 pages in 4 minutes. How long will it take
to print the rest of the paper?
60x = 4•18060 60
x = 4 • 3x = 12
It will take 12 minutes to print the rest of the
paper!
604
180x
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
75 sq. ft.3 cans
1075 sq. ft.p cans
Solving Real-life Problems Using Proportions
Austin needs to paint two walls. One wall is 450 square feet and the other is 625 square
feet. If 3 cans of paint covers 75 square feet, how many cans will Austin need?
Step 1: Write as proportion using words
Step 2: Set-upa proportion
5.3 Proportions
Square feetCans of paint
Square feetCans of paint
Wall 1 + Wall 2450 + 625
=1075
=
=
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
43p
75751075375 p
Step 3: Cross multiply and solve
Austin needs 43 cans of paint.
Austin needs to paint two walls. One wall is 450 square feet and the other is 625 square
feet. If 3 cans of paint covers 75 square feet, how many cans will Austin need?
753
1075p
=
Solving Real-life Problems Using Proportions (Continued)
254325
p
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Dimensional AnalysisConvert 5.5 ft to inchesStep 1 Write 5.5 ft as
a fraction
Step 2 Find the conversion factor
How many How many inches in 1 ft?inches in 1 ft?
How many How many inches in 1 ft?inches in 1 ft?
Step 3 Multiply 5.5 ft and the conversion
factorStep 4 Simplify
1
ft5.5
1 ft = 12 1 ft = 12 inin
1 ft = 12 1 ft = 12 inin
ft1in12
1
ft5.5
ft1in12
66 in66 in5.4 Dimensional Analysis
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
1min. 480
min. 60hour1
Dimensional AnalysisConvert 480 minutes into hours
Step 1 Write 480 minutes as a fraction
Step 2 Find the conversion factor
How many How many minutes in 1 minutes in 1
hour?hour?
How many How many minutes in 1 minutes in 1
hour?hour?Step 3 Multiply 480 min. and the conversion factorStep 4 Simplify
1min. 480
1 hour = 60 1 hour = 60 minutesminutes
1 hour = 60 1 hour = 60 minutesminutes
min. 60hour1
8 hours8 hours5.4 Dimensional Analysis
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
MAP2D
Chapter 6PercentsGrade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Let’s Find Percents
70% of 90Percent means out of a hundred
“of” means multiply
Per Out of or Divide
Cent 100
6-1 Fraction, Decimals, Percents
70% • 90
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
25.0
25.0
41
Percent is defined as how many parts out of100.
Percent is defined as how many parts out of100.
6-1 Fraction, Decimals, Percents
4 10
02
82
0
0
5
2 00
%25 10025
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
75
50
75X .10 7.50
50X .10 5.00
75 X .20 15.00
7.5 X 2 15.0
5 X 2 10
50 X .20 10.00
Notice that to find 10% of a number move the decimal one spot to the left
Notice that 20% of a number is 2 times 10% of a number.
6-2 Estimating with Percents
10% 20%number
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Proportions for Percent Problems
Part (is)
Whole (of)100Percent
The variable can be placed in the Part, Whole, or Percent.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Proportions for Percent Problems
PartWhole100
Percent
Louis got 40 out of 50 correct on his test. What is his percent
correct?
4050100
x
50x = 40 100
50x = 400050 50
x = 80Louis got 80% Louis got 80%
right.right.6-3 Finding Percents
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Proportions for Percent Problems
Susan answered 90% of the questions from an online survey. If she has answered 18 questions, how many questions were on the survey?
18x100
90
90x = 18 100
90x = 180090 90
x = 20The survey had 20
questions.6-4 finding a number when % is known
PartWhole100
Percent
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Proportions for Percent ProblemsFive hundred students applied to
Jordan’s IB magnet. How many will get accepted if Jordan IB only
accepts 40% ?
x500100
40
100x = 40 500100x =
20000100 100x = 200
200200 students students will be accepted into Jordan’s IB magnet.
6-4 finding a number when % is known
PartWhole100
Percent
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Equations for Percent Problems
Whole • Percent = Part
Change to a Decimal!
Change to a Decimal!
The variable can be placed in the Part, Whole, or Percent.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Equations for Percent ProblemsCurrently there are 1,100 seniors (12th grade
students) enrolled at Wilson High School. The number of seniors completing all college
admission requirements is 495. What percent of the seniors completed college requirements?
Whole • Percent = Part1100 • p = 495
Substitute
Solve1100 1100p = 0.45
Change to Change to %%p = 45%45%45% of the seniors at Wilson completed
college admission requirements
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Equations for Percent ProblemsGiselle answered 15 problems correct on her test. If her percent correct was 75%.
How many questions were on her test?
Whole • Percent = Part
w Substitute
Solve0.75 0.75
w = 20
Change Change %% to to decimaldecimalw • 0.75 =
15
20 questions were on Giselle’s test.
1575%
=•
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Equations for Percent ProblemsSix hundred students applied to Millikan's
Quest Program. How many will get accepted if Quest only accepts 70% ?
Whole • Percent = Part
600 • 0.70 = q 420 = q
420 students were accepted into 420 students were accepted into Millikan’s Quest Program.Millikan’s Quest Program.
Substitute
Solve
Change Change %% to to decimaldecimal
600 • 70% = q
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Percent of Increase
0.15505015
At Julio’s Computers they buy computers
for $500 and sell them for $650.
What is the percent of increase?
1. Find the amount of change between the old price and new price
650 — 500 =
2. Use
500150
3.0
%30
The percent of increase is
30%.
The percent of increase is
30%. 6-5 Applying % increase and decrease
OriginalAmount of Change
Change to percentChange to percent
Change to decimal
3.0
0
150
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Percent of Increase (equation)
At Kat’s Computers they buy
computers for $250 and sell
them for $400. What is the percent of increase?
1. Find the amount of change between the old price and new price
400 – 250 = 1502. Use an equation and solveOriginal • Percent = Amount of price change250 • p = 150
250 250
p = 0.6Change to percentChange to percent
p = 60%
The percent of increase is
60%.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Percent of DecreaseKat’s Computers is having a sale.
They are advertising a
$1000 computer for $600. What is the percent of
decrease?
1. Find the amount of change between old price and new price
1000―600 = 4002. Use an equation and solveOriginal • Percent = Amount of price change1000 • p = 400
1000 1000p = 0.4
Change to percentChange to percent
p = 40%
The percent of decrease is
40%.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Discounts (proportions)Sheila bought a dress that is 30% off.
The original price of the dress is $150. •What is the discount?•What is the sale price?
Step 1: Calculate the discount
Step 2: Subtract the discount from theoriginal price
The discount is $45$150 original price- 45 discount$105 sale price
6-5 Applying % increase and decrease
15010030 discount
=
30150100 discount100100
PartWhole100
Percent
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
$360 original price― 144 discount $216 sale price
Discounts (equation)
Caleb bought a suit that is 40% off.
The original price of the suit is $360.
•What is the discount?•What is the sale price?Step 1: Calculate the discount
Step 2: Subtract the discount from theoriginal price
The discount is $144
6-5 Applying % increase and decrease
Whole • Percent = Part
360 • 40% = ?
360 • 0.40 = 144
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Sales Tax (proportion)Steve bought a jacket that was priced
at $80. Find the sales tax andprice including tax if the sales tax is 6%.
Step 1: Calculate the sales tax
Step 2: Add the sales tax to theprice
The sales tax is $4.80$80.00 price+ 4.80 sales tax$84.80 price after tax
801006 taxsales=
680100 taxsales100100
6-6 Sales Tax, Commission, and Profit
PartWhole100
Percent
8.4taxsales
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Sales Tax (equation)
Felicia is buying a pair of steel toe work boots for $80. Find the sales tax and price including tax
if the sales tax is 9%.
Step 1: Calculate sales tax
Step 2: Add the Sales tax to theoriginal price
The sales tax is $7.20
$80.00 original price+ 7.20 sales tax $87.20 Total price
6-5 Applying % increase and decrease
Whole • Percent = Part
80 • 9% = ?
80 • 0.09 = 7.2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Total Price (multi- step problem)Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii?
Step 1: Find the discount
Price • Percent off = discount
220 • 15% = ?
220 • 0.15 = $33
Step 2:Find the sales price
$220-$33 = $187
Original – discount = sales price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Total Price (cont.)Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii?
Step 3Find the sales tax 187 • 9%
= ?187 • 0.09 = 16.83Step 4 Find the total price
187 + 16.83 = 203.83
Sale price • tax rate = Sales tax
Sales price = $187
The total price of the Wii is $203.83
Sales price + tax = Total price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
CommissionPhillip makes 8% commission at AA
Appliance store. His sales last month were $15,000. What was his commission
last month?
000151008
,=
c
800015100 ,c100100
1200$c
Phillip made $1200 in commission!6-6 Sales Tax, Commission, and Profit
PartWhole100
Percent
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
ProfitMarilee's Travel Agency makes 20% profit on all tickets sold. Last month Marilee’s Travel Agency made $60,000 in profit, what were the total sales last month?
Marilee’s total sales were $300,000.
Whole • Percent = Part s • 20% = 60,000
s • 0.20 = 60,0000.20 0.20
s = 300,000
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Simple InterestInterest = Principal rate time
I = P r tInterest: the amount of money
paid to you on savings, or paid by you on money borrowed
rate: the percent charged or paid (must be changed to a decimal or fraction)
Principal: the initial amount of money
time: measured in years6-7 Applying Simple and Compound
Interest
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Simple InterestYou have $5000 in a savings account earning 3% interest.
How much interest will you earn in 2 years?I = Prt Write the
formulaStep 1
Step 2 Substitute the values
I = 5000 0.03 2
Step 3 SimplifyI = 300Step 4 Answer the
question$300 interest
Your savings account will have earned $300 in interest in 2 years.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Compound InterestInterest paid on Principal and on interest already earned.
r: rate, the percent charged or paid (must be changed to a decimal or fraction)
P: Principal, the initial amount of money
t: time, measured in years
A: The final or future value of Principal
n: number of compounding periods in 1 year
A = P 1+ rn
nt
6-7 Applying Simple and Compound Interest
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Theresa deposited $5000 into a savings account that pays a 3% interest
compounded monthly. If she withdraws the money in 2 years, how much will she
have?
A = P 1+ rn
nt A = ?P = 5000
r = 3% = 0.03t = 2
n = 12 (12 months in 1 year)
212
12030
15000•.
+=A
( ) 212002515000 •.=A
06175715000 .•=A
785225308.=A
Theresa will have $5308.79
6-7 Applying Simple and Compound Interest
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
MAP2D
Chapter 7Graphs and Functions
Grade 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Coordinate PlaneOrdered Pair
(x, y)
Directions for plotting a point – Start
at origin
(3, 4)
(5, -2)
(-6, 6)
(-7, -5)7-1 the Coordinate Plane
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Make a Table
Substitute and
Calculate
y = 2x +3
7-3 Graphing linear Functions
x (x, y)yy = 2x + 3
-1
-2
0
1
2
y = 2(-2) + 3
y = 2(-1) + 3
y = 2(0) + 3
y = 2(1) + 3
y = 2(2) + 3
= -4 + 3= -1
= -2 + 3= 1
= 0 + 3= 3
= 2 + 3= 5
= 4 + 3= 7
1
-1
3
5
7
(-2, -1)
(-1, 1)
(0, 3)
(1, 5)
(2, 7)
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Now we will graph the ordered pairs.
y = 2x + 3
7-3 Graphing linear Functions
(x, y)
(-2, -1)
(-1, 1)
(0, 3)
(1, 5)
(2, 7) Draw a line through the points.Label the line with the
equation.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Und
efined S
lop
e
Up a
nd D
ow
n
Slope Steepness of a line
Positive Slope
Up Hill
Negative Slope
Down Hill
Zero Slope
Flat
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Slope (m)
runrise
m
36
12
m
Run3
Run3
Rise6
Rise6
2m
Going up hill is positive
Pick two points on the line
m
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Run 6Run 6
32
m
Slope (m)
runrise
m
Rise-4
Rise-4
Going Going down hilldown hill
is is negativenegative
Pick two points on the line
64m
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
What is the slope and y-intercept?
7-3 Graphing linear Functions
runrise
mSlope
y-interceptWhere line
crosses y-axis(0, b)(0, 2)b = 2
96
m
32
m
Rise6
Rise6
Run9
Run9
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
bmxy
y = mmx + bb
slopeslopey-intercepty-interceptWrite the equation given slope & y-intercept
Slope is and y-intercept is 232
232
xySubstitu
t
Substitu
t
e e
Slope-Intercept Form
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Graph Linear Equation Using y = mx + b
y = mx + b
m =
b =
(0, -2)
32
-2
y = x - 223
1. State slope as a fraction2. State y-intercept (b) as an
order pair3. Graph (0, b)4. Use slope to find 2 more
points5. Use points to draw a line
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
Graphing a constant rate of change
rate of change = sloperate of change = slopeSALE!
Movies$2 Each
Rate of change movie 1
2$
Order Pairs(1, 2)(2, 4)(3, 6)(0, 0)(8, 16)
Dolla
rs $
Number of
movies
Movies Cost
1
2
0
3
8
$2
$4
$0
$6
$16
runrise
slope
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
y = xCh 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
y = x
Ch 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
y = 5Ch 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
x = 2Ch 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
y = x 2Ch 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
y = x 2
Ch 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
y = x 3Ch 7
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
x
y
y = x 3Ch 7