1. Instructional Strategies
MAP2D
Quarter 3
Instructional Strategies
Grade 7
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2. Ratios, Proportions, and Similarity
MAP2D
Chapter 5
Ratios, Proportions, and Similarity
Grade 7
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3. = = Writing Ratios Step 1 Step 2 Step 3 1 girls 20 girls 4∙5 girls
Write the ratio of girls to boys in simplest form
A class has 20 girls to 16 boys.
Identify the two quantities being compared
Step 1
Step 2
Write as a ratio
Step 3
Simplify
girls
20 girls
4∙5 girls
5 girls 1 = =
boys
16 boys
4∙4 boys
4 boys
5 girls:4 boys
5 girls to 4 boys
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.1 Ratios

4. Comparing Unit Rates Step 1 Step 2 Step 3 Derrick Louise
Derrick’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)?
Identify the two ratios being compared and the units of each ratio
Step 1
Step 2
Write each ratio
Divide each ratio (make each ratio into a unit rate) and compare!
Step 3
miles
Derrick
360 mi
= 24 miles per gallon
gallons
15 gal
Louise
miles
340 mi
= 34 miles per gallon
gallons
10 gal
Louise’s car gets 10 miles per gallon more than Derrick’s!
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5.2 Rates and unit rates

5. Solving Proportions 1 Solve: Step 1: Cross multiply 3 x =12 5 3x = 60
Step 2: Solve for x
3x = 60 1
x = 20
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5.3 Proportions

6. Solving Real-life Problems Using Proportions
Jason can read 12 pages of a book in
15 minutes. How many pages can he read
in 25 minutes?
Step 1: Write a ratio
using words
Pages
minutes 12 15 x 25 =
Step 2: Set-up
a proportion
= 15 x
300 = 15x
300 = 15x
Step 3: Cross multiply
Step 4: Solve for x
x = 20 pages
5.3 Proportions
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7. 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?
Pages
Step 1: Write a ratio using words
Minutes
Step 2: Set-up a proportion
How many pages does Jared
have left to print? 60 4
180 x
240 ― 60 =
180
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

8. Solving Real-Life Problems Using Proportions (cont.)
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? 60 4
180 x
Step 3: Cross multiply
and solve for x 3
60x = 4•180
It will take 12 minutes to print the rest of the paper! 1 1
x = 4 • 3
x = 12
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

9. 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
Square feet
Square feet =
Cans of paint
Cans of paint
Wall 1 + Wall 2
=1075
Step 2: Set-up
a proportion
75 sq. ft.
3 cans
1075 sq. ft.
p cans =
5.3 Proportions
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

10. Austin needs 43 cans of paint.
Solving Real-life Problems Using Proportions (Continued)
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 3: Cross multiply and solve 1 1 25 1 75 3 =
1075 p
Austin needs 43 cans of paint.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

11. Dimensional Analysis Convert 5.5 ft to inches
Step 1 Write 5.5 ft as a fraction
Step 2 Find the conversion factor
How many inches in 1 ft?
1 ft = 12 in
Step 3 Multiply 5.5 ft and the conversion factor
Step 4 Simplify
66 in
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
5.4 Dimensional Analysis

12. How many minutes in 1 hour?
Dimensional Analysis
Convert 480 minutes into hours
Step 1 Write 480 minutes as a fraction
Step 2 Find the conversion factor
How many minutes in 1 hour?
1 hour = 60 minutes
Step 3 Multiply 480 min. and the conversion factor
8 hours
Step 4 Simplify
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5.4 Dimensional Analysis

13. Chapter 6 Percents Grade 7 MAP2D
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14. 6-1 Fraction, Decimals, Percents
Let’s Find Percents
Per  Out of or Divide
Cent  100
Percent means out of a hundred
70% of 90
“of” means multiply
70% • 90
6-1 Fraction, Decimals, Percents
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15. = = % 25 25 100 Fractions to Decimals to Percents! Fraction DECIMAL2 5
Fraction 4 1 8 1
DECIMAL 2 2 25 = = % 25
100
DECIMAL
Percent
Percent is defined as how many parts out of100.
6-1 Fraction, Decimals, Percents
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16. Let's Find 10% and 20% of a Number !75
X .10
7.50 75
X .20
15.00
7.5
X 2
15.0 75 OR 50
X .10
5.00 50
X .20
10.00 5
X 2 10 50 OR
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
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17. Proportions for Percent Problems
Part (is)
100
Whole (of)
The variable can be placed in the
Part, Whole, or Percent.
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18. Proportions for Percent Problems
Louis got 40 out of 50 correct on his test. What is his percent correct?
Part
Whole
100
Percent
50x = 40  100
50x = 4000 x 40 50
100 50
x = 80
Louis got 80% right.
6-3 Finding Percents
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19. 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?
Part
Whole
100
Percent
90x = 18  100
90x = 1800 90 18 90
100 x
x = 20
The survey had 20 questions.
6-4 finding a number when % is known
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20. Proportions for Percent Problems
Five hundred students applied to Jordan’s IB magnet. How many will get accepted if Jordan IB only accepts 40% ?
Part
Whole
100
Percent
100x = 40  500
100x = 20000 1 40 x
100
100
100
500
x = 200
200 students will be accepted into Jordan’s IB magnet.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-4 finding a number when % is known

21. Equations for Percent Problems
Whole • Percent = Part
Change to a
Decimal!
The variable can be placed in the
Part, Whole, or Percent.
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22. Equations for Percent Problems
Currently 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 = Part
 Substitute
1100 • p = 495
 Solve
1100
1100
p = 0.45
 Change to %
p = 45%
45% of the seniors at Wilson completed college admission requirements
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

23. Equations for Percent Problems
Giselle answered 15 problems correct on her test. If her percent correct was 75%. How many questions were on her test?
Whole • Percent = Part
 Substitute w •
75% = 15
 Change % to decimal
w • = 15 1
 Solve
0.75
0.75
w = 20
20 questions were on Giselle’s test.
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24. Equations for Percent Problems
Six hundred students applied to Millikan's Quest Program. How many will get accepted if Quest only accepts 70% ?
Whole • Percent = Part
 Substitute
600 •
70%
= q
 Change % to decimal
600 • = q
 Solve
420 = q
420 students were accepted into
Millikan’s Quest Program.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

25. The percent of increase is 30%.
At Julio’s Computers they buy computers for $500 and sell them for $650. What is the percent of increase?
Find the amount of change between the old price and new price
650 — 500 =
Use
150
Original
Amount of Change
Change to decimal
The percent of increase is 30%.
Change to percent
6-5 Applying % increase and decrease
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26. Percent of Increase (equation)
Find the amount of change between the old price and new price
400 – 250 = 150
Use an equation and solve
At Kat’s Computers they buy computers for $250 and sell them for $400. What is the percent of increase?
Original • Percent = Amount of
price change
250 • p = 150
The percent of increase is 60%.
p = 0.6
Change to percent
p = 60%
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

27. The percent of decrease is 40%.
Kat’s Computers is having a sale. They are advertising a $1000 computer for $600. What is the percent of decrease?
Find the amount of change between old price and new price
1000―600 = 400
Use an equation and solve
Original • Percent = Amount of
price change
1000 • p = 400
p = 0.4
The percent of decrease is 40%.
Change to percent
p = 40%
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28. 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
Part
Whole
100
Percent
The discount is $45
$150 original price
discount
$105 sale price
Step 2: Subtract the
discount from the
original price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-5 Applying % increase and decrease

29. Discounts (equation) 360 • 40% = ? 360 • 0.40 = 144
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
360 • 40% = ?
Whole • Percent = Part
360 • 0.40 = 144
The discount is $144
$360 original price
― 144 discount
$216 sale price
Step 2: Subtract the
discount from the
original price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-5 Applying % increase and decrease

30. Sales Tax (proportion)
Steve bought a jacket that was priced
at $80. Find the sales tax and
price including tax if the sales tax is 6%.
Step 1: Calculate the sales tax
Part
Whole
100
Percent
The sales tax is $4.80
Step 2: Add the
sales tax to the
price
$ price
sales tax
$ price after tax
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-6 Sales Tax, Commission, and Profit

31. 6-5 Applying % increase and decrease
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
80 • 9% = ?
Whole • Percent = Part
80 • 0.09 = 7.2
The sales tax is $7.20
$80.00 original price
sales tax
$ Total price
Step 2: Add the
Sales tax to the
original price
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-5 Applying % increase and decrease

32. 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?
Price • Percent off = discount
Step 1:
Find the discount
220 • 15% = ?
220 • 0.15 = $33
Step 2:
Find the sales price
Original – discount = sales price
$220-$33 = $187
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33. Total Price (cont.) The total price of the Wii is $203.83
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?
Sales price = $187
Step 3
Find the sales tax
Sale price • tax rate = Sales tax
187 • 9% = ?
187 • 0.09 = 16.83
Step 4
Find the total price
Sales price + tax = Total price =
The total price of the Wii is $203.83
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

34. Commission
Phillip makes 8% commission at AA Appliance store. His sales last month were $15,000. What was his commission last month?
Part
Whole
100
Percent
Phillip made $1200 in commission!
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
6-6 Sales Tax, Commission, and Profit

35. Profit
Marilee'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?
Whole • Percent = Part
s • 20% = 60,000
s • 0.20 = 60,000
0.20
0.20
s = 300,000
Marilee’s total sales were $300,000.
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36. Simple Interest Interest = Principal  rate  time I = P  r  t
Interest: the amount of money paid to you on savings, or paid by you on money borrowed
Principal: the initial amount of money
rate: the percent charged or paid (must be changed to a decimal or fraction)
time: measured in years
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6-7 Applying Simple and Compound Interest

37. Simple Interest I = Prt I = 5000  0.03  2 I = 300 $300 interest
You have $5000 in a savings
account earning 3% interest.
How much interest will you earn in 2 years?
Write the formula
Step 1
I = Prt
Step 2
Substitute the values
I = 5000  0.03  2
Step 3
Simplify
I = 300
Step 4
Answer the question
$300 interest
Your savings account will have earned $300 in interest in 2 years.
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38. 6-7 Applying Simple and Compound Interest
Compound Interest Interest paid on Principal and on interest already earned.
A = P 1+ r n nt
A: The final or future value of Principal
P: Principal, the initial amount of money
r: rate, the percent charged or paid (must be changed to a decimal or fraction)
t: time, measured in years
n: number of compounding periods in 1 year
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6-7 Applying Simple and Compound Interest

39. 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 = 5000
r = 3% = 0.03
t = 2
n = 12
(12 months in 1 year)
A = P 1+ r n nt
Theresa will have $
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6-7 Applying Simple and Compound Interest

40. Chapter 7 Graphs and Functions Grade 7 MAP2D
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41. Directions for plotting a point – Start at origin
Coordinate Plane
Ordered Pair
(x, y)
Directions for plotting a point – Start at origin
(3, 4)
(5, -2)
(-6, 6)
(-7, -5)
y-axis
Quadrant II
(-,+) 10
Quadrant I
(+,+) 9 8 + + 7 - 6 - 5 4 3 2 1
x-axis 4
-10 -9 -8 -7 -6
Origin
(0,0) -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 3 -2 -3 -4 5 -2 -5 -6 6 -6 -7
Quadrant III
(-,-)
Quadrant IV
(+,-) -8 -9 -7 -5
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7
-10
7-1 the Coordinate Plane

42. y = 2x +3 Let's Graph a Linear Equation x y = 2x + 3 y (x, y)
Make a Table x
y = 2x + 3 y
(x, y) -2 -1
(-2, -1)
y = 2(-2) + 3 =
= -1
Substitute and Calculate -1 1
y = 2(-1) + 3 =
= 1
(-1, 1) 3
(0, 3)
y = 2(0) + 3
= 0 + 3
= 3 1 5
y = 2(1) + 3
= 2 + 3
= 5
(1, 5) 2 7
(2, 7)
y = 2(2) + 3
= 4 + 3
= 7
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7-3 Graphing linear Functions

43. Now we will graph the ordered pairs.1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9
y = 2x + 3
(x, y)
y = 2x +3
(-2, -1)
(-1, 1)
(0, 3)
(1, 5)
Draw a line through the points.
(2, 7)
Label the line with the equation.
7-3 Graphing linear Functions
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44. Slope  Steepness of a line
Negative Slope
Down Hill
Positive Slope
Up Hill
Undefined Slope
Up and Down
Zero Slope
Flat
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45. Going up hill is positive
Slope (m)
Pick two points on the line 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7
Run 3
Rise 6
Simplify
Going up hill is positive
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46. Slope (m) Simplify Rise -4 Run 6 Pick two points on the line
Going down hill
is negative 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7
Rise -4
Simplify
Run 6
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47. What is the slope and y-intercept?
Run 9 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7
Simplify
Rise 6
y-intercept
Where line crosses y-axis
(0, b)
(0, 2)
b = 2
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7-3 Graphing linear Functions

48. Slope is and y-intercept is 2
Slope-Intercept Form
y = mx + b
slope
y-intercept
Write the equation given slope & y-intercept
Slope is and y-intercept is 2
Substitute
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49. Graph Linear Equation Using y = mx + b
State slope as a fraction
State y-intercept (b) as an order pair
Graph (0, b)
Use slope to find 2 more points
Use points to draw a line
y = mx + b
y = x - 2 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 3 2
m =
b = -2
Whiteboards, have students try on own either on whiteboard with graph paper or on note paper
(0, -2)
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50. Graphing a constant rate of change
SALE!
Movies
$2 Each
rate of change = slope 1 3 2 4 5 6 7 8 9 10
Movies
Cost
Order Pairs
(1, 2)
(2, 4)
(3, 6)
(0, 0)
(8, 16) 1 $2
Dollars $ 2 $4 3 $6 $0 8
$16 1 3 2 4 5 6
Rate of change
Number of movies
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51. x y
y = x
Ch 7
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52. x y
y = x
Ch 7
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53. x y
y = 5
Ch 7
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54. x y
x = 2
Ch 7
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55. x y
y = x 2
Ch 7
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56. x y
y = x 2
Ch 7
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57. x y
y = x 3
Ch 7
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58. x y
y = x 3
Ch 7
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