Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 6
Math
Unit 5
10th Grade
Lesson 6 of 15
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Identify and create parallelograms, rectangles, rhombuses, and squares on the coordinate plane.
The core standards covered in this lesson
G.GPE.B.4 — Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
The foundational standards covered in this lesson
6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
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.
8.G.B.8 — Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
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
25-30 minutes
Is the shape below a parallelogram? A rectangle? A rhombus? A square?
Module 8: Connecting Algebra and Geometry from Secondary Mathematics One: An Integrated Approach made available by Mathematics Vision Project under the CC BY 4.0 license. © 2016 Mathematics Vision Project. Accessed March 12, 2017, 5:09 p.m..
A quadrilateral with vertices $${(-6,2),\space(-3,6),\space(9,-3),}$$ and $${(6,-7)}$$ is drawn.
Is this a Rectangle?, accessed on March 12, 2017, 5:11 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Ashanti is surveying for a new parking lot shaped like a parallelogram. She knows that three of the vertices of parallelogram $${ABCD}$$ are $${A(0,0)}$$, $${B(5,2)}$$, and $${C(6,5)}$$. Find the coordinates of point $$D$$. Justify mathematically that the figure you have drawn is a parallelogram.
G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2 is made available on JMAP by Steve Sibol and Steve Watson. Copyright © 2017 JMAP, Inc. - All rights reserved. Accessed June 1, 2018, 4:38 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The following rectangle has one side that is contained in the line $${y=2x+3}$$.
a) What are three possible equations that will contain the other three sides of the rectangles? b) What are the vertices of the rectangle you have defined?
Classifying Equations of Parallel and Perpendicular Lines from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed March 12, 2017, 5:05 p.m..
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.
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Algebraically verify midsegment, median, and parallel line relationships in triangles.
Topic A: Distance on the Coordinate Plane
Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.
Standards
G.GPE.B.7
Partition horizontal and vertical line segments into equal proportions on a number line.
G.GPE.B.6
Divide a line segment on a coordinate plane proportionally and identify the point that divides the segment proportionally.
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Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments
Algebraically and using the Pythagorean Theorem, determine the slope criteria for perpendicular lines.
G.GPE.B.5G.SRT.C.8
Describe and apply the slope criteria for parallel lines.
G.GPE.B.5
G.GPE.B.4
G.CO.C.10G.SRT.B.4
Algebraically verify diagonal relationships in quadrilaterals and parallelograms.
G.CO.C.11G.GPE.B.4
Topic C: Area and Perimeter On and Off the Coordinate Plane
Calculate and justify the area and perimeter of polygons and composite shapes off the coordinate plane.
Calculate and justify the area and perimeter of parallelograms and triangles on the coordinate plane.
Calculate and justify composite and irregular areas on the coordinate plane.
G.GPE.B.7N.Q.A.3
Describe how the area changes when a figure is scaled.
Solve area applications by creating and solving quadratic equations.
A.CED.A.1
Describe a polygon on the coordinate plane using a system of inequalities.
A.CED.A.3G.CO.A.2
Calculate and justify the area and perimeter of polygons on the coordinate plane given a system of inequalities.
A.REI.D.12G.GPE.B.4G.GPE.B.7
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