Module 1. Ratios and Proportional Relationships Lessons 11 14
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1 Math 7 Module Lessons.notebook September, 05 Module Ratios and Proportional Relationships Lessons Lesson # September, 05 You need: pencil, calculator and binder. Do Now: Find your group and complete do now independently. A computer programmer charges customers per line of code written. Fill in the blanks with the amount of change between consecutive numbers. Lines of Code Cost ($),000,000 3,000,000 Label the diagram below with the terms change in lines, change in dollars, and constant rate of change. = $, lines = $0 line (unit rate) The is $0 per line of programming code. Find the unit rate to determine the constant rate of change.
2 Math 7 Module Lessons.notebook September, 05 Module Ratios and Proportional Relationships Lessons Lesson # September, 05 You need: pencil, calculator and binder. Do now: Finish your quiz Lines of Code Cost ($),000,000 3,000,000 = $, lines = $0 line (unit rate) The is $0 per line of programming code. Find the unit rate to determine the constant rate of change.
3 Math 7 Module Lessons.notebook September, 05. A computer programmer charges customers per line of code written. Fill in the blanks with the amount of change between consecutive numbers. Lines of Code Cost ($),000,000 3,000,000 Label the diagram below with the terms change in lines, change in dollars, and constant rate of change. = $, lines $0 = (unit rate) line The is $0 per line of programming code. Find the unit rate to determine the constant rate of change. 3
4 Math 7 Module Lessons.notebook September, 05 Group Roles. Group reader. Group checker 3. Group reporter. Group time/task keeper
5 Math 7 Module Lessons.notebook September, 05 Notes: Slope Hero Comics prints on recycled paper. The table shows the total number of pounds of recycled paper that has been used each day during the month. Total Recycled (lbs) 3 36 Day of Month Graph the ordered pairs on the coordinate plane. Hero Comics Total Pounds Recycled Day of the Month. Explain why the graph is linear?. 3. Use two points to find the constant rate of change. Point : change in pounds pounds Point : change in days days So, the constant rate of change is or pounds per day. Slope is the rate of change between any two points on a line. slope = change in y change in x = or 5
6 Math 7 Module Lessons.notebook September, 05 6
7 Math 7 Module Lessons.notebook September, 05 The slope tells how steep the line is. The vertical change is sometimes called 'rise' while the horizontal change is called 'run'. rise You can say that slope = run. Count the number of units that make up the rise of the line in the graph. Write this number for the numerator of the fraction. Count the number of units that make up the run of the line. Write this number for the denominator of the fraction. slope = rise run = rise. run Example : The table shows the relationship between the number of seconds y it takes to hear thunder after a lightning strike and the miles x you are from the lightening. Graph the data and find the slope. Explain what the slope represents. Miles (x) Seconds (y) seconds miles slope = rise run = So, for every seconds between a lightening flash and the sound of thunder, there is mile between you and the lightening strike. 7
8 Math 7 Module Lessons.notebook September, 05 Try It! CW: #. Graph the data about plant height for a science fair project. Then find the slope of the line. Explain what the slope represents. Week Height (cm) Plant height (cm) Time (weeks). The table shows the number of small packs of fruit snacks y per box x. Graph the data. Then find the slope of the line. Explain what the slope represents. Boxes (x) Fruit Snacks (y)
9 Math 7 Module Lessons.notebook September, 05 Homework #6 HW: # 3. The table shows the number of pages Adriano read in x hours. Graph the data. Then find the slope of the line. Explain what the slope represents. 9
10 Math 7 Module Lessons.notebook September, 05. Graph the data. Find the numerical value of the slope and interpret it in words. 0
11 Math 7 Module Lessons.notebook September, 05
12 Math 7 Module Lessons.notebook September, 05 Lesson # September, 05 You need: pencil, calculator and binder. Do Now: Determine if each situation is proprtional. Explain your reasoning.. Taxi cab passengers are charged $.50. They are then charged $.00 for every mile traveled.. A restaurant charges $5 for one sandwich, $9.90 for two sandwiches, and $.5 for three sandwiches. 3. Tickets Purchased 3 Cost ($) Cups of Flour Cups of Sugar Correct HW #6
13 Math 7 Module Lessons.notebook September, 05 test and project 3
14 Math 7 Module Lessons.notebook September, 05 Notes: Complex Fractions Solve. Write in simplest form x =. x = 3. = Example: Dana is skating laps to train for a speed skating competition. She can skate lap in 0 seconds. A. Write a ratio in simplest form comparing Dana's time to her number of laps. Dana's Time (s) Number of Laps B. Suppose Dana skates for 0 seconds. How many laps will she skate? C. Write a ratio of Dana's time of 0 seconds to her number of laps. D. How could you simplify the ratio you wrote in Part C? Fractions like 0 are called. Complex fractions are fractions with a numerator, denominator or both that are also fractions. Complex fractions are simplified when both the numerator and denominator are integers. Examples:. Simplify. Simplify
15 Math 7 Module Lessons.notebook September, 05 Try It! CW: # Simplify =. 6 = 3. 3 =. Pep Club members are making spirit buttons. They make 90 spirit buttons in 3 hours. Find the number of buttons the Pep Club makes per hour. 5
16 Math 7 Module Lessons.notebook September, 05 Homework #7 HW: # 9 6
17 Math 7 Module Lessons.notebook September, 05 7
18 Math 7 Module Lessons.notebook September, 05 Lesson #3 September, 05 You need: pencil, calculator and binder. Correct HW #7 Do Now: Quiz #3 Try It! CW: 3 #. Find the unit rate in price per pound: You bought 3 pounds of candy and paid dollars. 5. It takes cups of sugar for batch of cupcakes. You use 6 cups of sugar. How many batches will you make? 3 8 REMEMBER! x 0 x 80 Multiplying by is the same as finding of a number. Multiplying by is the same as finding of a number. 3 x 0 This is the same thing as finding 3 of 0. 8
19 Math 7 Module Lessons.notebook Homework #8 HW: 3 # 6 September, 05. You received 3 pieces of candy on Halloween! In month you ate 3 of your candy. How much did you eat? How much do you have left?. Sally's hair is inches long. She went to the salon and asked for of her hair to be cut off. How many inches did she lose? How much does she have left? 3. *Tax is an amount you pay in addition to the cost of an item. A new jacket costs $00. The tax is 0 of the cost. How much will you pay in tax? What is the total price you will pay for the jacket?. *Discount is an amount that will be subtracted from the original cost of an item. A pair of sneakers costs $80. They are on sale (discount) for off. How much is the discount? How much will you pay for the sneakers? 5. *Markup is an amount added to the cost of an item by the seller. A store buys a sweatshirt at a price of $30. They mark up the cost by 5 and sell it in their store. How much is the markup? How much will the sweatshirt cost in this store? 6. *Commission is a portion of the money made that is given to the person who sells an item. Joe sells refrigerators. He sells one that costs $500. If he earns 0 of the cost in commission, how much does he earn? 9
20 Math 7 Module Lessons.notebook September, 05 Lesson # September 5, 05 You need: pencil, calculator and binder. Do Now: Find the Unit Rate for each. Show all work.. Bob walked mile in of an hour.. Jenn baked 3 batches of cookies in hours Gina read 3 books in weeks. Correct HW #8 0
21 Math 7 Module Lessons.notebook September, 05 Notes: Fractions in Proportional Relationships You are walking at a rate of 8 miles in hours. Complete the chart based on this information. Hours / / Miles Miles A) Graph the data on the coordinate plane. B) Is this a proportional relationship? Why? Hours C) Write an equation to represent this relationship.
22 Math 7 Module Lessons.notebook September, 05 Example After taking a cooking class, you decide to try out your new cooking skills by preparing a meal for your family. You have chosen a recipe that uses a gourmet mushroom mix as the main ingredient. Using the graph below, complete the table of values and answer the following questions. Weight (pounds) 0 Cost ($) / / 6 / 8 ) Is this relationship proportional? ) What is the unit rate for cost per pound? 3) Write an equation to model this data. ) What ordered pair represents the unit rate and what does it mean? 5) What does the ordered pair (,6) mean in the context of the problem? 6) If you could spend $0 on mushrooms, how many pounds could you buy? 7) What would be the cost of 30 pounds of mushrooms?
23 Math 7 Module Lessons.notebook September, 05 Example : Mother s 0K Race Sam s mother has entered a 0K race. Sam and his family want to show their support by watching her race, and meeting her at the finish line. Previously, his mother ran a 5K race with a time of ½ hours. Assume Sam s mother ran the same rate as the previous race in order to complete the chart. / / / 3 3
24 Math 7 Module Lessons.notebook September, 05 Homework #9 HW: #
25 Math 7 Module Lessons.notebook September, 05 5
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