Geometry

Lesson 2

Math

Unit 7

6th Grade

Lesson 2 of 17

Objective


Find the area of right triangles.

Common Core Standards


Core Standards

  • 6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Foundational Standards

  • 4.MD.A.3

Criteria for Success


  1. Understand that a rectangle can be cut or folded in half to create two of the same triangles. 
  2. Understand that the area of a right triangle is equal to half the area of a rectangle with the same base and height or $${A={1\over2}bh}$$.
  3. Find the area of right triangles. 

Tips for Teachers


  • This is the first of three lessons on finding the area of triangles. In this lesson, students use right triangles and their relationship to rectangles to determine the formula for finding the area of a triangle. In right triangles, since the legs are always perpendicular to one another, the base and height are the same as the measurements of those sides of the triangle. In Lessons 3 and 4, students will explore other triangles where the height is not equal to one of the sides.
  • Students re-engage in standards from their Expressions unit, specifically 6.EE.2, as they work on the formula for the area of triangles and evaluate the expression $$\frac{1}{2}bh$$.
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Anchor Problems


Problem 1

Explore ways to find the area of the triangle below.

a.   What is your best estimate for the area of this triangle? Explain how you determined your estimate.

b.   What is the exact area of this triangle? Explain how you determined the exact amount.

Guiding Questions

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Problem 2

Mr. Jones told his students they each needed half a piece of paper. Calvin cut his paper horizontally and Matthew cut his paper diagonally, as shown below. 

Which student has a half-piece of paper with the larger area? Explain your answer.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic A > Lesson 2Exercise 6

Grade 6 Mathematics > Module 5 > Topic A > Lesson 2 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..

Modified by Fishtank Learning, Inc.

Problem Set

Fishtank Plus Content

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Target Task


Problem 1

A right triangle is shown below. Explain how you can find its area, and then give the value of the area in square units.

Problem 2

Owen drew a straight diagonal line through a rectangle, from one corner to the other. He ended up with two right triangles, as shown below.

Do the two triangles have the same area? Explain how you know.

Student Response

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Additional Practice


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.

  • Examples where students use equations to solve for either the height or the base when given the area of a triangle
  • Error analysis where a triangle’s area is calculated at half of a rectangle’s area, but the base and height are different
  • Error analysis where the area is not divided in half
  • Challenge: Find the area of the triangles below by decomposing and re-arranging into rectangles.
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Lesson 1

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Lesson 3

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Topic B: Polygons in the Coordinate Plane

Topic C: Volume of Rectangular Prisms

Topic D: Nets and Surface Area

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