Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Similar presentations


Presentation on theme: "Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Quarter 3 Instructional Strategies Grade 7."— Presentation transcript:

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

2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Chapter 5 Ratios, Proportions, and Similarity Grade 7

3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Writing Ratios 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 girls boys Step 3 Simplify 20 girls 16 boys 4 5 girls 4 4 boys 5 girls 4 boys == 5.1 Ratios 5 girls : 4 boys 5 girls to 4 boys

4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Comparing Unit Rates Derricks car travels 360 miles and uses 15 gallons of gas. Louises car travels 340 miles and uses 10 gallons of gas. Whose car gets better gas mileage (in miles per gallon)? miles gallons Identify the two ratios being compared and the units of each ratio Step 1 Step 2 Write each ratio Step 3 Divide each ratio (make each ratio into a unit rate) and compare! 360 mi 15 gal = 24 miles per gallon 5.2 Rates and unit rates miles gallons 340 mi 10 gal = 34 miles per gallon Louises car gets 10 miles per gallon more than Derricks!

5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Solving Proportions Solve: Step 1: Cross multiply Step 2: Solve for x 3 x =12 5 3x = 60 3 x = Proportions

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

7 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 Pages Minutes x How many pages does Jared have left to print? = 180

8 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 = x = 4 3 x = 12 It will take 12 minutes to print the rest of the paper! x

9 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-up a proportion 5.3 Proportions Square feet Cans of paint Square feet Cans of paint Wall 1 + Wall =1075 = =

10 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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? p = Solving Real-life Problems Using Proportions (Continued)

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

12 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Dimensional Analysis Convert 480 minutes into hours Step 1Write 480 minutes as a fraction Step 2 Find the conversion factor How many minutes in 1 hour? Step 3Multiply 480 min. and the conversion factor Step 4Simplify 1 hour = 60 minutes 8 hours 8 hours 5.4 Dimensional Analysis

13 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Chapter 6 Percents Grade 7

14 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Lets Find Percents 70% of 90 Percent means out of a hundred of means multiply Per Out of or Divide Cent Fraction, Decimals, Percents 70% 90

15 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent is defined as how many parts out of100. Percent is defined as how many parts out of Fraction, Decimals, Percents %

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

17 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Proportions for Percent Problems Part (is) Whole (of) 100 Percent The variable can be placed in the Part, Whole, or Percent.

18 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Proportions for Percent Problems Part Whole 100 Percent Louis got 40 out of 50 correct on his test. What is his percent correct? x 50x = x = x = 80 Louis got 80% right. 6-3 Finding Percents

19 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? 18 x x = x = x = 20 The survey had 20 questions. 6-4 finding a number when % is known Part Whole 100 Percent

20 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Proportions for Percent Problems Five hundred students applied to Jordans IB magnet. How many will get accepted if Jordan IB only accepts 40% ? x x = x = x = students 200 students will be accepted into Jordans IB magnet. 6-4 finding a number when % is known Part Whole 100 Percent

21 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.

22 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Equations for Percent Problems Currently there are 1,100 seniors (12 th 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 1100 p = 495 Substitute Solve 1100 p = 0.45 Change to % p = 45% 45% 45% of the seniors at Wilson completed college admission requirements

23 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 w Substitute Solve 0.75 w = 20 Change % to decimal w 0.75 = questions were on Giselles test. 1575%=

24 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 = q 420 = q 420 students were accepted into Millikans Quest Program. Substitute Solve Change % to decimal %= q

25 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent of Increase At Julios 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 = 2.Use The percent of increase is 30%. 6-5 Applying % increase and decrease Original Amount of Change Change to percent Change to decimal 0 150

26 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent of Increase (equation) At Kats 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 = Use an equation and solve Original Percent = Amount of price change 250 p = p = 0.6 Change to percent p = 60% The percent of increase is 60%.

27 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent of Decrease Kats 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 = Use an equation and solve Original Percent = Amount of price change 1000 p = p = 0.4 Change to percent Change to percent p = 40% The percent of decrease is 40%.

28 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 the original price The discount is $45 $150 original price - 45 discount $105 sale price 6-5 Applying % increase and decrease Part Whole 100 Percent

29 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 the original price The discount is $ Applying % increase and decrease Whole Percent = Part % = ? = 144

30 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 and price including tax if the sales tax is 6%. Step 1: Calculate the sales tax Step 2: Add the sales tax to the price The sales tax is $4.80 $80.00 price sales tax $84.80 price after tax 6-6 Sales Tax, Commission, and Profit Part Whole 100 Percent

31 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 the original price The sales tax is $7.20 $80.00original price sales tax $87.20 Total price 6-5 Applying % increase and decrease Whole Percent = Part 80 9% = ? = 7.2

32 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 % = ? = $33 Step 2: Find the sales price $220-$33 = $187 Original – discount = sales price

33 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 3 Find the sales tax 187 9% = ? = Step 4 Find the total price = Sale price tax rate = Sales tax Sales price = $187 The total price of the Wii is $ Sales price + tax = Total price

34 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? Phillip made $1200 in commission! 6-6 Sales Tax, Commission, and Profit Part Whole 100 Percent

35 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Profit Marilee's Travel Agency makes 20% profit on all tickets sold. Last month Marilees Travel Agency made $60,000 in profit, what were the total sales last month? Marilees total sales were $300,000. Whole Percent = Part s 20% = 60,000 s 0.20 = 60, s = 300,000

36 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 rate: the percent charged or paid (must be changed to a decimal or fraction) Principal: the initial amount of money time: measured in years 6-7 Applying Simple and Compound Interest

37 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Simple Interest You have $5000 in a savings account earning 3% interest. How much interest will you earn in 2 years? I = PrtI = Prt Write the formula Step 1 Step 2Substitute the values I = Step 3Simplify I = 300 Step 4Answer the question $300 interest Your savings account will have earned $300 in interest in 2 years.

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

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

40 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Chapter 7 Graphs and Functions Grade 7

41 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Coordinate Plane Ordered Pair (x, y) Directions for plotting a point – Start at origin (3, 4) (5, -2) (-6, 6) (-7, -5) 7-1 the Coordinate Plane

42 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Make a Table Substitute and Calculate y = 2x Graphing linear Functions x(x, y)yy = 2x y = 2(-2) + 3 y = 2(-1) + 3 y = 2(0) + 3 y = 2(1) + 3 y = 2(2) + 3 = = -1 = = 1 = 0 + 3= 3 = 2 + 3= 5 = 4 + 3= (-2, -1) (-1, 1) (0, 3) (1, 5) (2, 7)

43 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Now we will graph the ordered pairs. y = 2x 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.

44 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Undefined Slope Up and Down Slope Steepness of a line Positive Slope Up Hill Negative Slope Down Hill Zero Slope Flat

45 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Slope (m) Run 3 Run 3 Rise 6 Rise 6 Going up hill is positive Pick two points on the line

46 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Run 6 Slope (m) Rise -4 Rise -4 Going down hill is negative is negative Pick two points on the line

47 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 What is the slope and y-intercept? 7-3 Graphing linear Functions y-intercept Where line crosses y-axis (0, b) (0, 2) b = 2 Rise 6 Rise 6 Run 9 Run 9

48 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 mb y = mx + b slopey-intercept Write the equation given slope & y-intercept Slope is and y-intercept is 2Substitute Slope-Intercept Form

49 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) y = x State slope as a fraction 2.State y-intercept (b) as an order pair 3. Graph (0, b) 4. Use slope to find 2 more points 5. Use points to draw a line

50 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Graphing a constant rate of change rate of change = slope SALE! Movies $2 Each Rate of change Order Pairs (1, 2) (2, 4) (3, 6) (0, 0) (8, 16) Dollars $ Number of movies Movies Cost $2 $4 $0 $6 $16

51 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y y = x Ch 7

52 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y y = x Ch 7

53 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y y = 5 Ch 7

54 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y x = 2 Ch 7

55 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y y = x 2 Ch 7

56 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y y = x 2 Ch 7

57 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y y = x 3 Ch 7

58 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 x y y = x 3 Ch 7


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

Similar presentations


Ads by Google