Curriculum / Math / 6th Grade / Unit 7: Geometry / Lesson 7
Math
Unit 7
6th Grade
Lesson 7 of 17
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Draw polygons in the coordinate plane and find area and perimeter (Part 1).
The core standards covered in this lesson
6.G.A.3 — 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.
The foundational standards covered in this lesson
6.NS.C.6 — 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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A rectangle has three vertices at points $${A(4, 5)}$$, $${B(4, -3)}$$, and $${C(-5, -3)}$$.
a. What are the coordinates of the fourth vertex, $$D$$, of the rectangle? If needed, use the coordinate plane above.
b. What is the area of the rectangle?
c. What is the perimeter of the rectangle?
Grade 6 Mathematics > Module 3 > Topic C > Lesson 19 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A rectangle has vertices located in the first and fourth quadrant of a coordinate plane. Two of the vertices are located at $${(2, 1)}$$ and $${(5, 1)}$$. If the perimeter of the rectangle is $${20}$$ units and the area of the rectangle is $${21}$$ square units, then what are the coordinates of the other two vertices?
Find the area and perimeter of the polygon in the coordinate plane below.
A set of suggested resources or problem types that teachers can turn into a problem set
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Square $${ ABCD}$$ is located in the first and fourth quadrant of the coordinate plane. Vertex $$A$$ is located at the point $${(1,4)}$$ and vertex $$C$$ is located at the point $${(6, -1)}$$. A coordinate plane is provided below if you need it.
a. Which of the coordinate points below could represent one of the other vertices of the square? Select all that apply.
a. $$(−1,1)$$
b. $$(1,−1)$$
c. $$(1,6)$$
d. $$(4,−1)$$
e. $$(4,6)$$
f. $$(6,4)$$
b. What is the perimeter of square $$ABCD$$?
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 6
Lesson 8
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Find the area of parallelograms.
6.G.A.1
Find the area of right triangles.
Find the area of acute triangles using height and base.
Find the area of any triangle using height and base.
Find the area of polygons using composition and decomposition.
Solve real-world and mathematical problems involving area of polygons.
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Topic B: Polygons in the Coordinate Plane
6.G.A.3
Draw polygons in the coordinate plane and find area and perimeter (Part 2).
Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.
6.G.A.1 6.G.A.3
Topic C: Volume of Rectangular Prisms
Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.
6.G.A.2
Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.
Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.
Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.
Topic D: Nets and Surface Area
Describe features of and identify nets that match prisms and pyramids.
6.G.A.4
Create nets and use them to find surface area of three-dimensional figures.
Find the surface area of three-dimensional figures with and without nets.
Find surface area and volume in real-world problems.
6.G.A.2 6.G.A.4
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