Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Quarter 3...

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

MAP2D

Quarter 3Instructional Strategies

Grade 7


MAP2D

Chapter 5Ratios, Proportions, and

Similarity

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


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!


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


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


Step 1: Write a ratio using words


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


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


75 sq. ft.3 cans

1075 sq. ft.p cans


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

=

=


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


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


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


MAP2D

Chapter 6PercentsGrade 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


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


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


Proportions for Percent Problems

Part (is)

Whole (of)100Percent

The variable can be placed in the Part, Whole, or Percent.



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



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


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


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.


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


Equations for Percent ProblemsGiselle answered 15 problems correct on her test. If her percent correct was 75%.

How many questions were on her test?


w Substitute

Solve0.75 0.75

w = 20

Change Change %% to to decimaldecimalw • 0.75 =

15

20 questions were on Giselle’s test.

1575%

=•


Equations for Percent ProblemsSix hundred students applied to Millikan's

Quest Program. How many will get accepted if Quest only accepts 70% ?


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


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%.


30%. 6-5 Applying % increase and decrease

OriginalAmount of Change

Change to percentChange to percent

Change to decimal

3.0

0

150


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%


60%.


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%.


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


$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



360 • 40% = ?

360 • 0.40 = 144


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


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



80 • 9% = ?

80 • 0.09 = 7.2


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


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


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


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


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


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.


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


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


MAP2D

Chapter 7Graphs and Functions

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


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)


Now we will graph the ordered pairs.

y = 2x + 3


(x, y)

(-2, -1)

(-1, 1)

(0, 3)

(1, 5)

(2, 7) Draw a line through the points.Label the line with the

equation.


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


Slope (m)

runrise

m

36

12

m

Run3

Run3

Rise6

Rise6

2m

Going up hill is positive

Pick two points on the line

m


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


What is the slope and y-intercept?


runrise

mSlope

y-interceptWhere line

crosses y-axis(0, b)(0, 2)b = 2

96

m

32

m

Rise6

Rise6

Run9

Run9


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


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


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


x

y

y = xCh 7


x

y

y = x

Ch 7


x

y

y = 5Ch 7


x

y

x = 2Ch 7


x

y

y = x 2Ch 7


x

y

y = x 2

Ch 7


x

y

y = x 3Ch 7

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Quarter 3...

Documents

Transcript of Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Quarter 3...