A focused Grade 6 learning session for Polygons on the Coordinate Plane using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving polygons on the coordinate plane.
Polygons on the Coordinate Plane means looking at attributes such as sides, angles, equal parts, and shape categories.
Question: What type of polygon is shown?
Why it works: The shape has four sides with opposite sides parallel and all angles at \(90\) degrees. It is a rectangle but not a square since length \(\neq\) width.
Answer: Rectangle
Question: What is the length of side AB?
Answer: \(6\) units
Question: What is the name of this quadrilateral?
Answer: Trapezoid
Question: A student plots a rectangle and claims it has vertices at \((2,2)\), \((5,2)\), \((5,5)\), and \((3,5)\). What is the error?
Why it works: The vertices \((2,2)\), \((5,2)\), \((5,5)\), and \((3,5)\) do not form a rectangle. The bottom side goes from \(x=2\) to \(x=5\) (length \(3\)), but the top side goes from \(x=3\) to \(x=5\) (length \(2\)). The sides are not parallel, so it is not a rectangle.
Answer: The shape is not a rectangle because the sides are not parallel.
Polygons on the Coordinate Plane becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Attributes prove the shape name.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A rectangle has vertices at \((1,1)\), \((7,1)\), \((7,4)\), and \((1,4)\). What is its perimeter?
Answer C: \(18\) units
Length \(=7-1=6\) units; width \(=4-1=3\) units. Perimeter \(=2(6+3)=18\) units.
A triangle has vertices at \((2,1)\), \((8,1)\), and \((5,5)\). What is the length of the base?
Answer B: \(6\) units
The base goes from \((2,1)\) to \((8,1)\), which are both on the same horizontal line. The distance is \(8-2=6\) units.
What type of polygon is shown?
Answer D: Rectangle
The shape has four sides with opposite sides parallel and all angles at \(90\) degrees. It is a rectangle but not a square since length \(\neq\) width.
A quadrilateral has vertices at \((1,2)\), \((4,2)\), \((5,6)\), and \((2,6)\). What is the length of the top side?
Answer B: \(3\) units
The top side goes from \((2,6)\) to \((5,6)\), both at \(y=6\). Distance is \(5-2=3\) units.
What is the perimeter of the rectangle shown above?
Answer C: \(14\) units
Width \(=5-1=4\) units; height \(=4-1=3\) units. Perimeter \(=2(4+3)=14\) units.
A rectangle has vertices at \((3,2)\), \((8,2)\), \((8,6)\), and \((3,6)\). If a point is at \((8,2)\), which vertex is diagonally opposite?
Answer A: \((3,6)\)
Diagonal corners of a rectangle are \((3,2)\) with \((8,6)\), and \((8,2)\) with \((3,6)\). The diagonally opposite vertex to \((8,2)\) is \((3,6)\).
What is the length of side AB?
Answer D: \(6\) units
Side AB is horizontal from \((1,2)\) to \((7,2)\). Length \(=7-1=6\) units.
A polygon has vertices at \((2,3)\), \((2,7)\), and \((6,3)\). What shape is this?
Answer A: Triangle
Three vertices form a triangle, which is a three-sided polygon.
What is the length of a horizontal segment from \((2,4)\) to \((8,4)\)?
Answer D: \(6\) units
For a horizontal segment, subtract the \(x\)-coordinates: \(8-2=6\) units.
A vertical segment goes from \((5,2)\) to \((5,8)\). What is its length?
Answer D: \(6\) units
For a vertical segment, subtract the \(y\)-coordinates: \(8-2=6\) units.
What is the name of this quadrilateral?
Answer D: Trapezoid
The quadrilateral has one pair of parallel sides (top and bottom are parallel). This makes it a trapezoid.
