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Download Math Grade 6: Unit 6 Rational Explorations
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Transcript
Math Grade 6: Unit 6 Rational Explorations Learning Targets: I can… • Explain the meaning of positive and negative numbers and use positive and negative numbers in real-world contexts. (6.NS.5) • Place integers and other rational numbers in the correct locations on a number line. (6.NS.6) • Correctly order rational numbers on a number line. (6.NS.7) • Explain the meaning of and represent absolute value. (6.NS.7) • Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. (6.NS.8) Words to Know absolute value: The distance between a number and zero on the number line. The symbol for absolute value is shown in the equation −8 = 8 integers: The set of whole numbers and their opposites {… − 3, −2, −1, 0, 1, 2, 3, … } negative numbers: the set of numbers less than zero. opposite number: two different numbers that have the same absolute value. Example: 4 and −4 are opposite numbers because both have an absolute value of 4. positive numbers: The set of numbers greater than zero. 𝑎 rational number: A number that can be written as 𝑏 where a and b are integers, but b is not equal to 0. sign: a symbol that indicates whether a number is positive or negative. Example: in −4, the (−) sign shows this number is read “negative four”. Big Ideas Every rational number has an opposite. -3 is the opposite of 3. 3 is the opposite of negative 3. Any rational number above or to the right of a number on a number line is greater. -3 > -5 because -3 is two units to the right. Likewise -5 < -3 because -5 is two units to the left. The absolute value of a rational number is its distance from zero. Because distance is positive, absolute value is always positive. I-3I = 3 and I4I = 4 Every rational number has a unique place on the number line. These positions help to order numbers from least to greatest and greatest to least. The number line to the right has been used to order the numbers listed at the top from least to greatest. Every point in the coordinate plane has a unique ordered pair with rational number coordinates. One of the ordered pairs to the right has the x-coordinate of -4 and a y-coordinate of 2. If you were asked “Which point would make the 4th corner of a rectangle?” for the three points to the right, it would be (2, -3). Revised 01-19-14 Math Grade 6: Unit 6 Rational Explorations How Can You Help Your Student? Sample Problems 1. Graph 3 and the opposite of 3 on a number line. Explain how this proves that 3 > the opposite of 3. Solution: 3 is greater than negative 3 or the opposite of three because 3 is to the right of -3 on the number line. 2. A scuba diver is 30 ft. below sea level and a submarine is 75 ft. below sea level. Jim thinks the inequality for this situation should be -30 ft. below sea level > -75 ft. below sea level. Sally thinks the inequality should be -30 ft. below sea level < -75 ft. below sea level. Who is correct? Why? Solution: Jim is correct. If we drew a vertical number line with zero representing sea level, -75 would be below -30. This means -30 > -75. 3. Given the point (2,3) in the coordinate plane where 2 is x and 3 is y, graph the point (x, -y). How would you describe the similarities and differences for these two points? Solution: Both points are two units to the right of zero. However, (2,3) is three units up from 2 and (2,-3) is three units down from 2. Multiple problems, different solution paths, and teacher commentary for the 6th grade standards in this unit. http://www.illustrativemathematics.org/6.NS.C • Before students can understand negative rational numbers, they must understand positive rational numbers and all their equivalent forms – fraction, decimal, and percent. For 1 example 8 = 0.125 = 12.5%. The Fractions, Decimals, and Percents Stack-N-Pack game is available for check out from your school’s Parent Center. There are Stack-N-Pack books for math concepts from Kindergarten through High School. Here is the link for all the books: Stack-N-Pack Mathematics Games for K-HS • Use bills or money owed as an example of negative numbers. For example, the electric bill is $67.50. That can be represented as -$67.50. • Suppose below sea level is negative and above sea level is positive. Pose problems like “If a plane is 200 ft. above sea level and a submarine is -150 ft. below sea level, how many feet apart are they? (350 ft.) • Math Goodies - Integers Introduction - Tutorial and Practice. http://www.mathgoodies.com/lessons/vol5/intro_integers.html • Starting with Set 5, a series of free online lesson sets related to this unit. http://learnzillion.com/courses/44?collection_id=617#collection_617 • Fun Brain - What’s The Point?- Game/Practice where students must correctly locate or name points on the coordinate plane. http://www.funbrain.com/cgibin/getskill.cgi?A1=choices&A2=co&A3=8&A4=0&A7=0&A8=math Literature related to this unit to read together at home and discuss: • The Fly on the Ceiling by Julie Glass - In this story, the author invents a way to keep track of his possessions by using a grid and coordinates. • Hottest, Coldest, Highest, Deepest by Steve Jenkins – The author describes various wonders of the world such as the deepest lake, hottest/coldest temperatures, deepest spot in the ocean, etc. Each natural wonder includes data, inset maps, diagrams, and comparisons. Students can use this book to explore integers in the real world. • Less Than Zero by Stuart Murphy - A penguin named Perry needs 9 clams to buy an ice scooter, but he has difficulty saving. Negative numbers are explored as Perry earns, spends, finds, loses, and borrows clams. Students can explore integers by making a line graph to show how Perry’s clams increase and decrease as the story is read. Revised 01-19-14