6.G.3 - About the Math, Learning Targets, and Increasing Rigor

Grade 5 AGL Geometry

6.G.3

Full Standard

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.

Learning Targets (I can)

Draw polygons on the coordinate plane when given coordinates of the vertices.
Apply understanding of attributes of polygons to find unknown coordinates.
Solve real-world problems with polygons on a coordinate plane.

About the Math

Students learning Grade 6 mathematics standards build on their work with area in the previous grades by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, student discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 mathematics by drawing polygons in the coordinate plane. Essential vocabulary for this standard includes: axis/axes, coordinate, coordinate plane, coordinate system, length, ordered pair, origin, polygon, side, and vertex/vertices. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
			Draw polygons on the coordinate plane when given coordinates of the vertices. Apply understanding of attributes of polygons to find unknown coordinates. Solve real-world problems with polygons on a coordinate plane.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 5	Grade 8
Real world problems graphed on coordinate system (5.G.2)	Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates (8.G.3)

TASKS

These tasks can be used with small group or whole group instruction.

On the coordinate plane draw a polygon in which all of the coordinates in the ordered pair has negative values. Now take the same polygon and double its dimensions. Write your new coordinate points.
Using a coordinate grid, Heather's house is located at (-4,-3) and Jodi's house is located at (2,-3). The distance from Kim's house to Heather's house is 1 1/2 times the distance between Heather and Jodi's house. What could be the coordinates of Kim's house? Possible answers: (-4,-12), (-4,6), (5,-3), (-13,-3)
The following coordinate points create a rectangle (-1,1) (-1,5) (-7,1) (-7,5). Draw it on the coordinate grid then create another rectangle that has the same area, but different perimeter as the first rectangle.
A parallelogram is sketched on a coordinate grid with these points: (6,-3), (3,-3) and (1,-6). What are the coordinates of the fourth vertex of this parallelogram?
Two vertices of a right triangle are (-2,2) and (-4,2), this results in a base length of 2 units. The area of the triangle is 6 square units. Find the height of the triangle and then find the possible coordinates of the final vertex of this triangle. (possible answers: (-2,8), (-4,8), (-2,-4), (-4,-4))

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.