Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 10
Math
Unit 5
10th Grade
Lesson 10 of 15
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Lesson Notes
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Calculate and justify the area and perimeter of parallelograms and triangles on the coordinate plane.
The core standards covered in this lesson
G.GPE.B.7 — Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
The foundational standards covered in this lesson
7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
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
Find the area and perimeter of the following figure:
Find the perimeter and area of the following figure:
Given $${A(2,3)}$$,
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
On graph paper, draw a line segment with endpoints $${ A(0,2)}$$ and $${B(0,6)}$$.
Equal Area Triangles on the Same Base I, accessed on May 31, 2018, 2:39 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.
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.
Next
Calculate and justify composite and irregular areas on the coordinate plane.
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
Identify and create parallelograms, rectangles, rhombuses, and squares on the coordinate plane.
G.GPE.B.4
Algebraically verify midsegment, median, and parallel line relationships in triangles.
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.
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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