Mrs. Brigman7th Grade Math 2014-2015 - Home



7th Grade MathUnit 3: Ratios and Proportional Relationships Lesson 1 – RatiosEQ: What are ratios and how can I represent them?Vocabulary:Ratio ________________________________________________________________________________________________________________________________________________________________________________________________________________________________3 Ways to Write Ratios WordsNumbersAlgebraEquivalent Ratios ________________________________________________________________________________________________________________________________________________________________________ExamplesExample 1: Writing a Ratio 1. You can make comparisons about games played by the Cubs. a. Wins to losseswins = , losses = Answer: _______b. Wins to games playedwins = , games = Answer: _________YOUR TURN:Use the table above to write the ratio for the Padres.1. Wins to losses2. Wins to games played3. Losses to winsExample 2: Writing Ratios in Simplest Form2. Amusement Parks ?A ride on a roller coaster lasts 2 minutes. Suppose you wait in line for 1 ? hours to ride the roller coaster. Follow the steps below to find the ratio of time spent in line to time spent on the ride.-Write hours as minutes so that the units are the same.-Write the ratio of time spent in line to time spent on the ride.Example 3: Comparing Ratios Music ?Luis and Amber compared their CD collections. To determine who has a greater ratio of rock CDs to pop CDs, write the ratios.Write ratios as fractions (rock/pop).Write fractions as decimals and compare.Luis:Amber: YOUR TURN:Use the table above.Does Luis or Amber have a greater ratio of pop CDs to hip-hop CDs? Does Luis or Amber have a greater ratio of hip-hop CDs to rock CDs?Lesson 2 – RatesEQ: How can I find a unit rate?VocabularyRate________________________________________________________________________________________________________________Unit Rate (write the examples of the three equivalent unit rates)________________________________________________________________________________________________________________Example 1: Finding a Unit RateKudzu ?During peak growing season, the kudzu vine can grow 6 inches in 12 hours. What is the growth rate of kudzu in inches per hour?YOUR TURN:Find the Unit Rate.$54 in 6 hours68 miles in 4 days2 cups in 8 servingsExample 2: Finding An Average Speed Speed Skating ?A skater took 2 minutes 30 seconds to complete a 1500 meter race. What was the skater’s average speed?Example 3: Comparing Unit RatesPasta ?A store sells the same pasta the following two ways: 10 pounds of bulk pasta for $15.00 and 2 pounds of packaged pasta for $3.98. To determine which is the better buy, find the unit price for both types.YOUR TURN:It takes you 1 minute 40 seconds to walk 550 feet. What is your average speed?Which of the following is the better buy: 2 AA batteries for $1.50 or 6 AA batteries for $4.80?Lesson 3: Slope and Unit RatesEQ: What is the slope and how is it related to a unit rate?VocabularySlope________________________________________________________________________________________________________________________________________________________________________Please draw all of the examples of lines with positive, negative, and zero slopes below:The slope of a vertical line is ________________________.Example 1: Finding the Slope of a LineTo find the slope of a line, find the _____________ of the rise to the run between two points on the line. Example 2: Interpreting Slope as a Unit RateSlope as a Unit Rate________________________________________________________________________________________________________________Volcanoes The graph represents the distance traveled by a lava flow over time. To find the speed of the lava flow, find the slope of the line.300418515240000YOUR TURN: Use the graph for number one .1.Plot the points (3, 4) and (6, 3). Then find the slope of the line that passes through the points.2. In Example 2: Volcanoes, suppose the line starts at the origin and passes through the point (3, 6). Find the speed of the lava flow.Example 3: Using Slope to Draw a Line Draw the line that has a slope of –3 and passes through (2, 5).YOUR TURN:Draw the line that has a slope of 1/3 and passes through (2, 5).Lesson 4: Writing and Solving ProportionsEQ: How can I use a proportion to solve real-world problems?VocabularyProportion________________________________________________________________________________________________________________________________________________________________________Example 1: Using Equivalent RatiosSports ?A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding for 60 minutes? You will use a proportion to answer this question.Example 2: Solving Proportions Using AlgebraSolve the Proportion = YOUR TURN (use equivalent ratios for 1-4 and use algebra to solve 5-8):1.15=z20 5. 414=m492.83=k18 6. 2530=x123.27c=912 7. h33=264. 9n=9922 8. b8=728Example 3: Writing and Solving a ProportionYesterday you bought 8 bagels for $4. Today you want only 5 bagels. How much will 5 bagels cost?Example 4: Writing and Solving a ProportionEmpire State Building ?At maximum speed, the elevators in the Empire State Building can pass 80 floors in 45 seconds. Follow the steps below to find the number of floors that the elevators can pass in 9 seconds.Lesson 5: Solving Proportions Using Cross ProductsEQ: How can I use cross-products to solve missing parts in proportions?VocabularyCross Products ________________________________________________________________________________________________________________________________________________________________________Example 1: Solving a Proportion Using Cross Products29=3dExample 2: Writing and Solving a ProportionScience ?At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? Example 3: Writing and Solving a ProportionPenguins ?At an aquarium, the ratio of rockhopper penguins to African penguins is 3 to 7. If there are 50 penguins, how many are rockhoppers?First, determine the ratio of rockhoppers to total penguins. Then, set up proportion. Your Turn:In John’s class, the ratio of boys to girls is 5 to 8. If there are 39 students in his class, how many are girls?Lesson 6: Percents and ProportionsEQ: How can I use proportions to solve percent problems?Solving Percent ProblemsYou can represent “a is p percent of b” with the proportion where a is the _______ of the ________ b, and p is the percent.*Key Formula to Remember:Example 1: What percent of 3 is 1?Example 2: What percent of 40 is 16?Example 3: Water Sports ?In a survey, 525 teenagers were asked to name the water sport that they would most like to try, and 20% said “surfing.” How many teenagers said “surfing”? Example 4: What number is 76% of 25?Example 5: 42 is 30% of what number?YOUR TURN:1.What percent of 400 is 34?2.What percent of 12 is 8?3.What number is 5% of 400?4.What number is 12% of 50?5.What number is 37% of 200?6.In a classroom of 25 students, 16 students were wearing sandals. What percent of the students were wearing sandals?7.At a retirement dinner, 65% of those attending ordered chicken. If 120 people attended the dinner, how many people ordered chicken?Lesson 7: Percent of Increase and DecreaseEQ: How can I find the percent of change in a quantity?VocabularyA ____________ ___ __________ shows how much a quantity has increased or decreased in comparison with the original amount:Percent of change p = If the new amount is greater than the original amount, the percent of change is called a ____________ of _____________. If the new amount is less than the original amount, the percent of change is called a ___________ of ____________. Example 1: What is the percent of increase from 8 to 13?Example 2: What is the percent of decrease from 49 to 35?Example 3: Find the percent of change as an increase or decrease and find the percent of changeOriginal: 16New: 28Example 4: Tacos ?A taco company puts 24 taco shells in every box. Recently the company expanded the box and put 25% more shells in each box. How many shells are in every box now?YOUR TURN:For 1 and 2, Identify the percent of change as an increase or a decrease. Then, find the percent of change.1.Original: 35 New: 282.Original 60 New: 123.What is the percent of increase from 50 to 60?4.What is the percent of decrease from 90 to 54?5. A company used to sell a package containing 10 blank CD-Rs. They now sell a package with 10% fewer CD-R’s. How many CD-R’s are in the new package?Lesson 8: Discounts, Markups, Sales Tax, and TipsEQ: How can I use my knowledge of percents to solve real-world problems involving discounts, markups, sales tax, and tips?VocabularyDiscount –Sales Tax & Tip– Sale Price –Mark-up- Wholesale price – Retail price - Example 1: Finding a Sale PriceClothing ?You buy a pair of jeans that is 33% off the original price of $29. What is the sale price?Example 2: Finding a Retail PriceSkateboards ?A store that sells skateboards buys them from a manufacturer at a wholesale price of $57. The store’s markup is 150%. What is the retail price?Example 3: Finding Sales Tax and TipRestaurants ?At a restaurant, you order a meal that costs $12. You leave a 20% tip. The sales tax is 5%. What is the total cost of the meal?YOUR TURN:1. A store is selling all flip-flops at 20% off their original price. What is the sale price of a pair of flip-flops originally priced at $20?2. A store buys guitars from a manufacturer at a wholesale price of $38. The store’s markup is 85%. What is the retail price?3. At a restaurant, you order a meal that costs $8. You leave a 15% tip. The sales tax is 6%. What is the total cost of the meal?Lesson 9: Scale Drawings and ModelsEQ: What is scale and how is it related to a proportion?VocabularyScale Drawing ________________________________________________________________________________________________________________________________________________________________________Example 1: Using the Scale of a MapMaps ?Use the map of Maine to estimate the distance between the towns of China and New Sweden.Example 2: Finding a Dimension on a scale modelWhite House ?A scale model of the White House appears in Tobu World Square in Japan. The scale used is 1 : 25. The height of the main building of the White House is 85 feet. Find this height on the model.Example 3: Finding the ScaleDinosaurs ?A museum is creating a full-size Tyrannosaurus rex from a model. The model is 40 inches in length, from the nose to the tail. The resulting dinosaur will be 40 feet in length. What is the model’s scale? YOUR TURN:The model of the Eiffel Tower in Tobu World Square is 12 meters high. The scale used is 1 : 25. Estimate the actual height of the Eiffel Tower.On a map of Colorado, the distance from Rico to Lizard Head Pass on Route 145 is about 9.5 cm. From the map scale, 1 cm represents 2 km. Estimate the actual distance between the towns.The caboose on a model train is 6.75 inches long. The full-size caboose is 36 feet. What is the model’s scale? ................
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