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6 th Grade Mathematics Unit 7 Rational Explorations: Numbers and their Opposites Excerpts from Georgia Department of Education Webinar February 26, 2013 melissa.stewart@hallco.org February 2013 Warm-Up On the same winter morning, the temperature is -28° F in Anchorage, Alaska and 65° F in Miami, Florida. How many degrees warmer was it in Miami than in Anchorage on that morning? This problem should be looked at by imagining or drawing an outside thermometer. Then, the distance from the negative temperature to 0 and the distance from 0 to 65 can be added together. This will result in the answer of 93 degrees. melissa.stewart@hallco.org February 2013 What’s the main idea of Unit 7? • Develop understanding of the system of rational numbers. • Develop understanding of absolute value. Concepts & Skills to Maintain from Previous Grades Changing between fractions and decimals Finding area of squares, rectangles, and triangles, and finding the perimeter of squares and rectangles. Website to help with the above: www.aaamath.com Enduring Understandings from this Unit Negative numbers are used to represent quantities that are less than zero such as temperatures, scores in games or sports, and loss of income in business. Absolute value is useful in ordering and graphing positive and negative numbers. Positive and negative numbers are often used to solve problems in everyday life. Rational numbers are points on a number line Numbers in ordered pairs indicate locations in quadrants of the coordinate plane melissa.stewart@hallco.org February 2013 Examples & Explanations 1. A flea is jumping around on the number line. a. If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far from zero is he? (4; 4 units) b. If he starts at 0 and jumps 5 units away, where might he have landed? (Either 5 or – 5) c. If the flea jumps 2 units and lands at zero, where might he have started? (Either 2 or – 2) d. The absolute value of a number is the distance it is from zero. The absolute value of the flea’s location is 4 and he is to the left of zero. Where is he on the number line? ( - 4) 2. Find and label the numbers 4/3,5/4,-2/3 and - ¾ on the number line. Then, state which of the following inequalities is true. - 2/3 > - ¾ OR – 2/3 < -3/4 Since –2/3 is to the right of – 3/4, then – 2/3 > - 3/4 melissa.stewart@hallco.org February 2013 3. The lowest temperature ever recorded on earth was 89° C in Antarctica. The average temperature on Mars is about -55° C. Which is warmer, the coldest temperature on earth or the average temperature on Mars? Write an inequality to support your answer. - 55 > - 89 So, the average temperature on Mars is warmer. The student edition for Unit 7 can be found at https://www.georgiastandards.org/Com mon-Core/Pages/Math-6-8.aspx On the left side, please look under mathematics, 6 – 8. Then, the right side has a pull-down menu to access the units. Additional parent guides will be posted to the parent resource page on http://www.hallco.org/boe/index.php (right had menu) as they become available. Math skills can be kept up-to-date through our Summer Learning Site at the link above. melissa.stewart@hallco.org February 2013