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7 th Grade Pre-Algebra Focus 1: Proportional Reasoning

7 th Grade Pre-Algebra Focus 1: Proportional Reasoning. 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.

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7 th Grade Pre-Algebra Focus 1: Proportional Reasoning

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  1. 7th Grade Pre-AlgebraFocus 1: Proportional Reasoning Standards: 7.RP.1, 7.RP2a, 7.RP.2d Resource: Connected Math Program 2 Common Core Investigation 1

  2. Common Core Investigation 1: Graphing ProportionsMathematical 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

  3. 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

  4. 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 • UNIT RATE • A unit rate is a rate for which one of the numbers being compared is 1 unit. • An example: is 140 miles 3.5 hours, or 40 miles per 1 hour is The rate of miles to hours becomes miles PER hour, which is written mi/h. The word “per” can be replaced with “for one.”

  5. 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 ?

  6. Problem 1.2: Road Trip & Basketballs

  7. Problem 1.2Have you thought about? • How can converting rates to unit rates make comparing those rates easier?

  8. Class Discussion & Sharing

  9. 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.

  10. Problem 1.2: Learning TargetReview & Recap Students will extend their understanding of ratios and develop understanding of proportionality to solve problems by: • Converting rates to unit rates

  11. Pre-Algebra Homework Exercises #3, 5, 7, 9 Work & answers in your math workbook

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