Download Domain: Standards for Math Practice

Progressive Mathematics Initiative
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Mathematics Curriculum
Unit Plan # 11
Title: Area of Figures
Subject: Geometry
Length of Time: 2.5 weeks
Unit Summary:
In this unit, the area formulas for triangles, quadrilaterals, circles and sectors will be derived. Students will
learn to use these formulas to solve application problems, including those that involve the area of complex
figures and figures in the coordinate plane.
Learning Targets
PARCC
Major Clusters;
Supporting Clusters;
Additional Clusters + Additional Standard
Domain: Similarity, Right Triangles & Trigonometry
Cluster: Define trigonometric ratios and solve problems involving right triangles
Standard#:
G-SRT.8
Standard:
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
Cluster: Apply trigonometry to general triangles.
Standard#:
+ G-SRT.9
+ G-SRT.10
+ G-SRT.11
Standard:
Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line
from a vertex perpendicular to the opposite side.
Prove the Law of Sines and Cosines and use them to solve problems.
Understand and apply the Law of Sines and Law of Cosines to find unknown
measurements in right and non-right triangles.
Domain: Circles
Cluster: Find arc lengths and area of sectors of circles
Standard#:
G-C.5
Standard:
Derive using similarity the fact that the length of an arc intercepted by an angle is
proportional to the radius, and define radian measure of the angles as the constant of
proportionality; derive the formula for the area of a sector.
Domain: Expressing Geometric Properties with Equations
Cluster: Use coordinates to prove simple geometric theorems algebraically
Standard#:
G-GPE.7
Standard:
Use coordinates to compute perimeters of polygons and areas of triangles, rectangles,
e.g., using the distance formula.
Domain: Geometric Measurement and Dimension
Cluster: Explain volume formulas and use them to solve problems
Standard#:
G-GMD.1
Standard:
Give an informal argument for the formulas for the circumference of a circle, area of a
circle, volume of a cylinder, pyramid, and cone.
Domain: Modeling with Geometry
Cluster: Apply geometric concepts in modeling situations
Standard#:
Standard:
Geometry – Area of Figures
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NJCTL.org
G-MG.1
Use geometric shapes, their measures, and their properties to describe objects (e.g.
modeling a tree trunk or a human torso as a cylinder).
G-MG.2
Apply concepts of density based on area or volume in modeling situations (e.g. persons
per square mile, BTUs per cubic foot).
G-MG.3
Apply geometric methods to solve design problems (e.g. designing an object or structure
to satisfy physical constraints or minimize cost; working with typographical grid systems
based on ratios).
Domain: Standards for Math Practice
Standard#:
Standard:
MP1
Making sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
MP4
Model with mathematics.
MP5
Use appropriate tools strategically.
MP6
Attend to precision.
MP7
Look for and make use of structure.
MP8
Look for and express regularity in repeated reasoning.
Unit Essential Questions:
Unit Enduring Understandings:
 How do you find the area of any triangle?
 Area of any triangle
 Law of Sines
 How do you find any missing side lengths and/or
 Area of any Regular Polygon
angle measures in any triangle?
 Area of Sectors
 How do you calculate the area and perimeter of
 Formulas can be derived and used to
figures in the coordinate plane?
calculate the area of complex figures.
Unit Objectives:
 Students will be able to calculate the area of a rectangle when side lengths are unknown
using other formulas (e.g. Pythagorean Theorem).
 Students will be able to calculate the area of any triangle using trigonometric ratios after
drawing an auxiliary line from a vertex perpendicular to the opposite side.
 Students will be able to prove the Law of Sines formula and use it to solve problems.
 Students will be able to calculate the area of any parallelogram using trigonometric ratios
and its area formula.
 Students will be able to calculate the area of any regular polygon using trigonometric ratios
and its area formula.
 Students will be able to derive and use the area of a circle formula from the area formula for
any regular polygon.
 Students will be able to use the area of a circle formula and the relationship that exists
between the degrees of the arc and the area of its sector to derive the equation used to
calculate the area of a sector.
 Students will be able to derive the formula for the area of a trapezoid and use it to solve
problems.
 Students will be able to derive the formula for the area of a rhombus and use it to solve
problems.
 Students will be able to derive the formula for the area of a kite and use it to solve
problems.
 Students will be able to calculate the area of complex figures using the area formulas of 2-D
shapes.
 Students will be able to apply the area formulas and the distance formula to solve real-world
problems.
Evidence of Learning
Geometry – Area of Figures
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NJCTL.org
Formative Assessments:
 SMART Response questions at the end of each section throughout the unit.
 1 Labs
 3 Quizzes
Summative Assessment:
 Unit Test
Lesson Plan
Topics
Class Periods
Topic #1: Area of Rectangles
1
Topic #2: Area of Triangles
1
Topic #3: Law of Sines
1
Quiz 1: Area of Rectangles & Triangles
0.5
Topic #4: Area of Parallelograms
1
Topic #5: Area of Regular Polygons
2
Quiz 2: Area of Parallelograms & Regular
Polygons
Topic #6: Area of Circles & Sectors
Topic #7: Area of Other Quadrilaterals
Lab: Area of Other Quadrilaterals
Quiz 3: Area of Circles, Sectors & Other
Quadrilaterals
Topic #8: Area and Perimeter of Figures in the
Coordinate Plane
Unit Review & Test
Curriculum Resources
 https://njctl.org/courses/math/geometry/
Lesson Components
21st Century Skills
 Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Themes
 Critical Thinking and Problem Solving
 Communication and Collaboration
 Life and Career Skills
Geometry – Area of Figures
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0.5
1
1
0.5
0.5
1
2
NJCTL.org