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6 th Grade Math Focus 1: Ratios, Rates & Proportions

6 th Grade Math Focus 1: Ratios, Rates & Proportions. Standards: 6.RP.1, 6.RP3a, 6.Rp.3d Resource: Connected Math Program2 Common Core Investigation 1. Common Core Investigation 1: Ratios and Rates Mathematical Learning Goals.

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6 th Grade Math Focus 1: Ratios, Rates & Proportions

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  1. 6th Grade MathFocus 1: Ratios, Rates & Proportions Standards: 6.RP.1, 6.RP3a, 6.Rp.3d Resource: Connected Math Program2 Common Core Investigation 1

  2. Common Core Investigation 1: Ratios and RatesMathematical Learning Goals • Understand the concept of a unit rate associated with a ratio a : b with b≠ 0, and use rate language in the context of a ratio relationship. • Make and tables of equivalent ratios, find missing values in the tables, and plot pairs of values on the coordinate plane. • Solve unit rate problems • Use ratio reasoning to convert measurement units

  3. Investigation 1.2: Learning Target • Students will solve ratio problems that require them to use the correct ratio and then to decide whether to multiply or divide. • Students will be introduced to rates, including unit rates. • Students will use ratios to convert between customary and metric units of measurement.

  4. Key Vocabulary Term- RATIO • A ratio is a comparison to two quantities. • Fractions, decimals, and percents are ways to represent ratios. • You can use the word “to,” a colon, or a fraction to write a ratio.

  5. Examples of RATIOS • For Kai, the ratio of posters to minutes is 8 to 40. • For Kai, the ratio of posters to minutes is 8 : 40. • For Kai, the ratio of posters to minutes is . • Student Practice- Write answers in your math workbook. • What do you think “the ratio of posters to minutes is 8 to 40” mean? • What is the ratio of minutes to posters? Explain.

  6. Key Vocabulary Term- RATE • A rate is a ratio that compares quantities measured in different units.

  7. Examples of RATES • Rate of production: 4 posters in 80 minutes • Rate of speed: 10 miles in 2 hours

  8. Key Vocabulary Term- UNIT RATE • A unit rate is a rate for which one of the numbers being compared is 1 unit.

  9. Examples of UNIT RATES • Rate of production: 20 minutes per poster • Rate of pay: $15 for 1 hour

  10. Problem 1.1Write answers in your math workbook.

  11. Explore 1.1Have you thought about? • Selena, Jason, Kai, Enrique, and Andre will find using ratios very helpful in solving problems while they volunteer at the local animal shelter. • How can you find the number of posters per minute for each student?

  12. Class Discussion & Sharing • Share how you and/or your group solved the following situations/questions. • How many posters per minute can each of the students make? • Which student makes the most posters per minute? The least? • If Selena makes 8 posters in 80 minutes, how does this change your answers to Parts A and B? • Matt joins the group, and it takes him 6 minutes to make each poster. How many posters can he make in 30 minutes?

  13. 6th Grade Math Homework • Exercises • #1-3, 19, 24-29 • Copy your answers in your math workbook

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