Geometry

Lesson 1

Math

Unit 7

6th Grade

Lesson 1 of 17

Objective


Find the area of parallelograms.

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

  • 3.MD.C.7.D
  • 4.MD.A.3

Criteria for Success


  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


  • 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)
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Anchor Problems


Problem 1

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

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References

GeoGebra Area of Parallelogram

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

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

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Problem 3

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

a.   

b.   

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic A > Lesson 1Shape 1 from Exercise 1

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

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Target Task


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
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Lesson 2

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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