Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 12
Math
Unit 5
10th Grade
Lesson 12 of 15
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Describe how the area changes when a figure is scaled.
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.EE.A.2 — Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
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
a. Triangle $${ABC}$$ is dilated by a factor of $$3$$ about point $$A$$. How does the area of triangle $${ABC}$$ compare to the area of triangle $$A'B'C'$$?
b. The parallelogram shown below is dilated by a factor of $${{1\over2}}$$. How do the areas of the original and the scaled parallelograms compare?
Geometry > Module 3 > Topic A > Lesson 3 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..
The dimensions of rectangle $$A$$ are $$3$$ units and $$4$$ units, and the area of rectangle $$B$$ is $${75\space \mathrm{units}^2}$$. What are the dimensions of rectangle $$B$$?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
In the following figure, $${\overline{AE}}$$ and $${\overline{BD}}$$ are segments.
a) Show that $${{{{\triangle ABC}}}}$$ and $${{{{\triangle CDE}}}}$$ are similar. b) What is the scale factor of similarity transformation that takes $${{{{\triangle ABC}}}}$$ to $${{{{\triangle CDE}}}}$$? c) What is the value of the ratio of the area of $${{{{\triangle ABC}}}}$$ to the area of $${{{{\triangle CDE}}}}$$? Explain how you know. d) If the area of $${{{{\triangle ABC}}}}$$ is $${30\space \mathrm{cm^2}}$$, what is the area of $${{{{\triangle CDE}}}}$$?
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 11
Lesson 13
Topic A: Distance on the Coordinate Plane
Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.
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
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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