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Standards: 7.RP.1, 7.RP2a, 7.RP.2d Resource: Connected Math Program 2 Common Core Investigation 1 Common Core Investigation 1: Graphing Proportions Mathematical Learning Goals Compute unit rates associated with ratios of fractions, including quantities measured in like or different units Decide whether two quantities are in a proportional relationship Explain what any point (x,y), including (0,0) and (1,r) where r is a unit rate, on a graph of a proportional relationship means in terms of the situation Problem 1.2: Learning Target Students will extend their understanding of ratios and develop understanding of proportionality to solve problems by: Converting rates to unit rates Key Vocabulary Terms • RATE A rate is a ratio that compares quantities in different units such as miles to hours. An example of a rate is 140 𝑚𝑖𝑙𝑒𝑠 3.5 ℎ𝑜𝑢𝑟𝑠 • UNIT RATE A unit rate is a rate for which one of the numbers being compared is 1 unit. An example: 140 𝑚𝑖𝑙𝑒𝑠 3.5 ℎ𝑜𝑢𝑟𝑠 is 140 miles ÷ 3.5 hours, or 40 miles per 1 hour is 40 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑜𝑢𝑟 The rate of miles to hours becomes miles PER hour, which is written mi/h. The word “per” can be replaced with “for one.” Getting Ready for Problem 1.2 Referring to the Key Vocabulary Terms examples, answer the following: What two units are being compared in 140 miles in 3.5 hours? How could you use this rate to find the distance that could be traveled in 7 hours? Would it be helpful to find out how many miles are traveled in 1 hour? Why? How can you find the unit rate for the rate 140 𝑚𝑖𝑙𝑒𝑠 3.5 ℎ𝑜𝑢𝑟𝑠 ? Problem 1.2: Road Trip & Basketballs Problem 1.2 Have you thought about? How can converting rates to unit rates make comparing those rates easier? Class Discussion & Sharing Key Vocabulary Term • PROPORTIONAL RELATIONSHIP Two quantities are in a proportional relationship if a change in one quantities corresponds to a change by the same factor in the other quantity. The ratios between the quantities do not change when the quantities themselves change. Problem 1.2: Learning Target Review & Recap Students will extend their understanding of ratios and develop understanding of proportionality to solve problems by: Converting rates to unit rates Pre-Algebra Homework Exercises #3, 5, 7, 9 Work & answers in your math workbook