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.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Every rational number, whether it is 3, -2.5 or -7/4, has its own spot on the number line. In sixth grade the number line is extended to the left of zero, and the coordinate grid from fifth grade grows into all four quadrants. Students place integers, fractions and decimals on horizontal and vertical number lines and plot ordered pairs such as (-3, 2) and (4, -1.5).
Two ideas run through the three parts of this standard. First, opposites: 5 and -5 are the same distance from 0 on opposite sides, the opposite of the opposite of a number is the number itself, so -(-3) = 3, and 0 is its own opposite. Second, signs in ordered pairs tell you the quadrant. A point with a negative x-coordinate and a positive y-coordinate lies in Quadrant II. When two points differ only in sign, like (2, 5) and (2, -5), one is the reflection of the other across an axis, here the x-axis.
Students may put -1/2 between -1 and -2 because the 'number' is 1 and 2. Remind them -1/2 is half way from 0 to -1.
Plotting (-3, 2) at (2, -3) is common. 'Across the hall, then up the stairs' is a helpful reminder that x comes first.
Two negative signs look extra negative. Read -(-3) as 'the opposite of negative three' and find it on the number line: it is 3.
(2, 5) and (2, -5) have the same x and opposite y, so they are mirrored across the x-axis, not the y-axis.
Point A is at (-4, 3). Name its quadrant, then give the point you get by reflecting A across the x-axis and the point you get by reflecting A across the y-axis.
Answer: A is in Quadrant II. Across the x-axis: (-4, -3). Across the y-axis: (4, 3).
Paper number lines that students fold at 0 show opposites matching up. For the coordinate plane, a large floor grid lets students stand on points and physically reflect across an axis.
Expect assessment items that ask students to plot or identify points, name a quadrant, give the opposite of a number, or find the reflection of a point. Fractions and decimals on vertical number lines are common distractors.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 9
The opposite of a number is the same distance from 0 on the other side. The opposite of -9 is 9.
Answer: B) Quadrant IV
x is positive and y is negative, so the point is to the right and below the origin: Quadrant IV.
Answer: -6
The opposite of -6 is 6, and the opposite of that is -6. Three negative signs leave a negative.
Answer: D) (3, 7)
A reflection across the y-axis changes the sign of x and keeps y: (3, 7).
Answer: C) -1.5
-1.5 is halfway between -1 and -2. -0.5 is between -1 and 0, and -2.5 is beyond -2.
Answer: 2
Both coordinates change sign, so the point is reflected across the x-axis and then the y-axis: 2 reflections.
A full lesson with slides, activities and an exit ticket on rational numbers on number lines and coordinate planes, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 6.NS.C.6 with an answer key, ready in about a minute.
Make a worksheet βTurn rational numbers on number lines and coordinate planes into a quiz students answer online that marks itself, with a class summary for you.
Build a test βPart a covers opposites, including -(-3) = 3. Part b covers signs in ordered pairs, quadrants and reflections. Part c covers placing rational numbers on number lines and points on the coordinate plane.
Yes. Any number that can be written as a fraction of integers is rational, including negative fractions, decimals like -0.75 and integers.