Geometry

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Find the area of parallelograms.

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.

Foundational Standards

The foundational standards covered in this lesson

Measurement and Data

3.MD.C.7.D — Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Measurement and Data

4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Criteria for Success

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

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1. Use the additive nature of area to rearrange a parallelogram into a rectangle and determine its area.
2. Determine the general formula for finding the area of a parallelogram: area = base × height.
3. Identify the height in a parallelogram, understanding that the height is always the distance across the parallelogram that is perpendicular to the base and can be inside or outside of the parallelogram.
4. Find the area of parallelograms.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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• Throughout the unit, students will learn and re-discover several formulas for geometric figures. Consider having the students create their own reference sheet to add to and refer back to throughout the unit as needed (MP.5). This can be placed in a sheet protector or created on cardstock.
• Students found the area of rectangles in 4th grade using the formula $$A=l×w$$ or $$A=b×h$$ . In this lesson, they extend this understanding to see how the formula $$A=b×h$$ can also be applied to parallelograms.
• Students may use calculators throughout the unit as needed.
• If you'd like students to explore using the applet in Anchor Problem 1, then students or groups of students will need access to a computer.

Lesson Materials

• Optional: Calculators (1 per student)

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

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

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Problem 1

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A parallelogram is shown below.

a. What strategies could you use to find the area of the parallelogram?

b. Follow Steps 1–4 of this GeoGebra applet Area of Parallelogram to explore the area of parallelograms. Try out different parallelograms by moving the red and blue dots.

c. In general, how can you find the area of any parallelogram?

Guiding Questions

Student Response

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References

Area of Parallelogram by Lndsay Flanagan, Hurchand is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed March 16, 2018, 3:09 p.m..

Problem 2

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The heights and bases of four parallelograms are shown below. Not all of the heights are marked correctly. For each parallelogram, determine if the measurements are marked correctly. Either explain why the measurements are correct or fix the parallelograms that are marked incorrectly.

a.

b.

c.

d.

Guiding Questions

Student Response

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Problem 3

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Find the areas of the parallelograms. Include appropriate units in your answers.

a.

b.

Guiding Questions

Student Response

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References

Grade 6 Mathematics > Module 5 > Topic A > Lesson 1 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..

Problem Set

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

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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

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

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Two students find the area of the parallelogram below.

Helen identifies the measurement 15.2 as the height and 8 as the base. Francisca identifies the measurement 14 as the height and 8 as the base.

Who is correct and why? What is the area of the parallelogram?

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 are given various parallelograms in various orientations and sizes and students identify base and height
• Error analysis of incorrectly identified heights
• Given a group of parallelograms, find the shapes with the same area (include some rectangles)
• Match a rectangle with a parallelogram with the same area

• Open Up Resources Grade 6 Unit 1 Practice Problems — Lesson 4 (do not include #5)
• Open Up Resources Grade 6 Unit 1 Practice Problems — Lesson 5
• Open Up Resources Grade 6 Unit 1 Practice Problems — Lesson 6
• EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic A > Lesson 1 — Exercises, Problem Set #1-5, 9, Exit Ticket

Lesson Map

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Find the area of parallelograms.

Find the area of right triangles.

Find the area of acute triangles using height and base.

Find the area of any triangle using height and base.

Find the area of polygons using composition and decomposition.

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