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.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Maps, game boards and floor plans all work like a coordinate plane, and sixth graders use all four quadrants to solve problems with them. They graph points with positive and negative coordinates and find how far apart two points are when the points line up horizontally or vertically.
The method depends on the signs. If two points share an x-coordinate, the distance between them is the difference in their y-coordinates. When both y-values have the same sign, subtract their absolute values: from (2, 7) to (2, 3) is 7 - 3 = 4 units. When the points are on opposite sides of the x-axis, add the absolute values: from (2, 5) to (2, -3) is 5 + 3 = 8 units, because you travel 5 units down to the axis and 3 more beyond it. Diagonal distances are not part of this standard; they need the Pythagorean theorem in eighth grade.
From (2, 5) to (2, -3), students compute 5 - 3 = 2. The points are on opposite sides of the x-axis, so the distance is 5 + 3 = 8.
Distance is always positive. If a subtraction gives -6, the distance is 6, which is why absolute value is used.
Counting the points from 1 to 4 gives 4 when the distance is 3 units. Count the jumps between points, not the points.
On a town map, the library is at (-6, 2) and the park is at (5, 2). Each unit is one block. How many blocks apart are they?
Answer: The library and the park are 11 blocks apart.
Grid maps of the school or a fictional town make the problems concrete. Have students sketch a number line along the shared row or column and mark the zero crossing before computing, so the add-or-subtract decision becomes visual.
On assessments, look for problems that combine plotting with distance, such as finding the perimeter of a rectangle drawn from given vertices. This leads directly into 6.G.A.3.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 10
Same x-coordinate. The y-values are on opposite sides of the x-axis, so add: 4 + 6 = 10 units.
Answer: D) 6 units
Same y-coordinate, both x-values negative, so subtract absolute values: 8 - 2 = 6 units.
Answer: 20
Width from -2 to 4 is 2 + 4 = 6. Height from 3 to -1 is 3 + 1 = 4. Perimeter = 2 × (6 + 4) = 20 units.
Answer: B) (0, 2)
Moving up adds to the y-coordinate: -5 + 7 = 2, so B is at (0, 2).
Answer: 5
Same x-coordinate. Both y-values are negative, so subtract absolute values: 7 - 2 = 5 units.
A full lesson with slides, activities and an exit ticket on distance on the coordinate plane, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.NS.C.8 with an answer key, ready in about a minute.
Make a worksheet →Turn distance on the coordinate plane into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. Students find distances only between points that share an x-coordinate or a y-coordinate. Diagonal distances use the Pythagorean theorem in grade 8.
The distance from a coordinate to an axis is its absolute value. Points on opposite sides of an axis are the sum of those distances apart; points on the same side are the difference.