Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 13
Math
Unit 5
10th Grade
Lesson 13 of 15
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Solve area applications by creating and solving quadratic equations.
The core standards covered in this lesson
A.CED.A.1 — Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
The foundational standards covered in this lesson
A.REI.B.4 — Solve quadratic equations in one variable.
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
The length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. The perimeter of the rectangle is 44 inches. Sketch a diagram of this situation and find the unknown number.
Algebra I > Module 4 > Topic A > Lesson 7 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 length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15 square inches, find the unknown number.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
The perimeter of a rectangle is 54 cm. If the length is 2 cm more than a number and the width is 5 cm less than twice the same number, what are the dimensions of the rectangle?
A plot of land for sale has a width of $$x$$ feet and a length that is 8 feet less than its width. A farmer will only purchase the land if it measures 240 square feet. What value for $$x$$ will cause the farmer to purchase the land?
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 12
Lesson 14
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
Describe how the area changes when a figure is scaled.
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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