Lesson 3 | Geometry | 6th Grade Mathematics

Objective

Find the area of acute triangles using height and base.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Geometry

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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Find the area of acute triangles by dividing them into two right triangles, finding the areas of the right triangles, and adding the areas.
Understand that the line segment that represents the height of a triangle is always perpendicular to the line segment representing the base.
Determine that the formula $${A={1\over2}bh}$$ can be used with non-right triangles.
Identify and draw the line segment that represents the height of a triangle given a base.
Find the area of acute triangles using base and height.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This is the second of three lessons on finding the area of triangles. In this lesson, students decompose acute triangles into right triangles to find area and determine that the formula to find the area of right triangles will also work for acute triangles (MP.7).
Students continue to re-engage in 6.EE.2, evaluating the area of triangles using the formula.
Students will need to know the meaning of the word perpendicular in order to accurately understand how the base and height of a triangle are related. If needed, review this term.

Lesson Materials

Optional: Index cards (1 per student)

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Two triangles are shown below with some measurements.

a. Find the area of Triangle A.

b. Can you find the area of Triangle B with the measurements given? Why or why not?

c. Triangle B is redrawn below. A new line has been drawn to divide Triangle B into two right triangles. Find the area of Triangle B in two different ways.

Guiding Questions

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Problem 2

In each triangle below, draw a line to represent the height of the triangle. Use an index card if helpful.

Guiding Questions

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References

Open Up Resources Grade 6 Unit 1 Lesson 10 — Lesson 10.2

Grade 6 Unit 1 Lesson 10 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 20, 2018, 4:18 p.m..

Modified by Fishtank Learning, Inc.

Open Up Resources Grade 6 Unit 1 Lesson 10 — Summary

Problem 3

Which triangle has the greater area?

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Identify a base and a corresponding height in the triangle below. Use them to find the area of the triangle.

References

Open Up Resources Grade 6 Unit 1 Lesson 9 — 9.4: Two More Triangles

Grade 6 Unit 1 Lesson 9 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 16, 2018, 3:44 p.m..

Modified by Fishtank Learning, Inc.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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 identify the height in acute triangles given different bases
Error analysis of triangles with incorrectly drawn heights

EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic A > Lesson 3 — Exercises and Problem Set

Lesson 2

Lesson 4

Lesson Map

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Find the area of parallelograms.

6.G.A.1

Find the area of right triangles.

6.G.A.1

Find the area of acute triangles using height and base.

6.G.A.1

Find the area of any triangle using height and base.

6.G.A.1

Find the area of polygons using composition and decomposition.

6.G.A.1

Solve real-world and mathematical problems involving area of polygons.

6.G.A.1

Topic B: Polygons in the Coordinate Plane

Draw polygons in the coordinate plane and find area and perimeter (Part 1).

6.G.A.3

Draw polygons in the coordinate plane and find area and perimeter (Part 2).

6.G.A.3

Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.

6.G.A.1 6.G.A.3

Topic C: Volume of Rectangular Prisms

Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.

6.G.A.2

Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.

6.G.A.2

Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.

6.G.A.2

Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.

6.G.A.2

Topic D: Nets and Surface Area

Describe features of and identify nets that match prisms and pyramids.

6.G.A.4

Create nets and use them to find surface area of three-dimensional figures.

6.G.A.4

Find the surface area of three-dimensional figures with and without nets.

6.G.A.4

Find surface area and volume in real-world problems.

6.G.A.2 6.G.A.4

Geometry

Objective

Common Core Standards

Core Standards

Geometry

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Target Task

References

Student Response

Additional Practice

Lesson Map

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