Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
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
Given a list of vertices like (-3, 2), (4, 2), (4, -1) and (-3, -1), sixth graders plot the points, join them in order and identify the polygon, here a rectangle. Then they use the coordinates to find side lengths, but only for sides that run horizontally or vertically, where one coordinate stays the same. The side from (-3, 2) to (4, 2) has length 3 + 4 = 7 units, because it crosses the y-axis.
This standard brings together two earlier ideas: the four-quadrant coordinate plane and distance from 6.NS.C.8, and area and perimeter. Once side lengths are known, students can find the perimeter of a rectangle on the grid or the area of a triangle whose base and height lie along grid lines. Real problems might involve fencing a plot drawn on a map grid or designing a floor plan in a drawing program. Sloped sides can appear in drawings, but students are not expected to measure them; that waits for the Pythagorean theorem.
From (-3, 2) to (4, 2) students compute 4 - 3 = 1. The side crosses the y-axis, so its length is 3 + 4 = 7.
Joining points in a different order can produce a crossed shape. The vertices should be connected in the order given.
A diagonal side cannot be measured by counting squares along the grid. Students should note that only horizontal and vertical sides are found this way.
A garden plot has corners at (-5, 3), (2, 3), (2, -4) and (-5, -4), with each unit 1 meter. How much fencing goes around it, and what is its area?
Answer: The plot needs 28 m of fencing and has an area of 49 m².
Have students sketch a quick number line along each horizontal or vertical side and mark where it crosses an axis. This makes the add-or-subtract decision visible.
Assessment items include completing a shape from three vertices, finding perimeter or area of a plotted polygon, and identifying the shape formed by given points.
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 y-values match. x goes from -6 to 3, crossing the y-axis, so the length is 6 + 3 = 9 units.
Answer: A) (1, -2)
The fourth corner must line up with (1, 4) vertically and with (6, -2) horizontally, so it is (1, -2).
Answer: 24
Width = 4 + 2 = 6 and height = 5 - 1 = 4. Area = 6 × 4 = 24 square units.
Answer: C) 20 square units
The base along the x-axis is 8 and the height along the y-axis is 5, so the area is 1/2 × 8 × 5 = 20 square units.
Answer: 22
Width = 1 + 4 = 5 and height = 7 - 1 = 6. Perimeter = 2 × (5 + 6) = 22 units.
A full lesson with slides, activities and an exit ticket on polygons on the coordinate plane, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.G.A.3 with an answer key, ready in about a minute.
Make a worksheet →Turn polygons on the coordinate plane into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Polygons can have sloped sides, but students only find lengths of sides that share an x-coordinate or a y-coordinate. Sloped lengths use the Pythagorean theorem in grade 8.
Both use coordinates and absolute value to find horizontal and vertical distances. 6.G.A.3 applies that skill to the sides of polygons, then to perimeter and area.