Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 1
Math
Unit 5
10th Grade
Lesson 1 of 15
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Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.
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
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
Suggestions for teachers to help them teach this lesson
Anchor Problem #2 will require the teacher to do a significant amount of modeling to derive the distance formula from the Pythagorean Theorem.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
What is the length of each of the line segments shown below?
Amy knows that the distance between two points is derived from the Pythagorean Theorem. Show how Amy gets from the Pythagorean Theorem to the “distance formula.”
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Find the perimeter and area (in units) of the following rectangle.
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 2
Topic A: Distance on the Coordinate Plane
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.5 G.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.10 G.SRT.B.4
Algebraically verify diagonal relationships in quadrilaterals and parallelograms.
G.CO.C.11 G.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.7 N.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.3 G.CO.A.2
Calculate and justify the area and perimeter of polygons on the coordinate plane given a system of inequalities.
A.REI.D.12 G.GPE.B.4 G.GPE.B.7
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