Unit 3

Rational Numbers

Math

Description:

In this unit students study negative numbers, their relationship to positive numbers, and the meaning and uses of absolute value.  Students will learn that all numbers have an opposite.  Students will use the number line to order rational numbers and understand the absolute value of a number. Students will work with the coordinate system.  They identify the four quadrants.  Students will also solve real-world and mathematical problems using all four quadrants of a coordinate plane.

Standards:

 NS – The Number System Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a.    Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; b.    Recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. c.    Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. d.    Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.C.7 Understand ordering and absolute value of rational numbers. a.    Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b.    Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write −3∘𝐶 > −7∘𝐶 to express the fact that −3∘𝐶 is warmer than −7∘𝐶. c.    Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d.    Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 d dollars represents a debt greater than 30 dollars. 6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Enduring Understandings:

·         Numeric fluency includes both the understanding of and the ability to appropriately use numbers.

·         A quantity can be represented numerically in various ways.

·         The symbolic language of algebra is used to communicate and generalize the patterns in mathematics.

·         Coordinate geometry can be used to represent and verify geometric/ algebraic relationships.

Essential Questions:

·         What is the meaning of positive and negative numbers and zero in real-life situations?

·         How can I compare rational numbers on a number line?

·         How do you find value of an integer on the number line?

·         How can you write and graph positive and negative integers?

·         How does absolute value relate to distance on a number line?

·         How can you plot points on a coordinate plane?