Instructional Strategies

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Instructional Strategies

Ratios, Proportions, and Similarity

= = 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

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! Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.2 Rates and unit rates

Solving Proportions 1 Solve: Step 1: Cross multiply 3 x =12 5 3x = 60

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

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

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

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

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

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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.4 Dimensional Analysis

Chapter 6 Percents Grade 7 MAP2D

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

= = % 25 25 100 Fractions to Decimals to Percents! Fraction DECIMAL
2 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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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

Proportions for Percent Problems

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

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

Equations for Percent Problems

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

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

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

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

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

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% 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 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

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

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

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

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

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

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

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

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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-7 Applying Simple and Compound Interest

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

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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-7 Applying Simple and Compound Interest

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 \$ Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-7 Applying Simple and Compound Interest

Chapter 7 Graphs and Functions Grade 7 MAP2D

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

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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 7-3 Graphing linear Functions

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

Slope  Steepness of a line

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

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

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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 7-3 Graphing linear Functions

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

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

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