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Here you will find all the resources you need to understand and teach a lesson on how to find the area of a triangle. Enjoy!

-Michelle M., Colorado Mountain College Teacher Candidate

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CCSS.Math.Content.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.

http://www.corestandards.org/Math/Content/6/G/A/1/

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This is the necessary teacher background information required to teach this unit.

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written by Michelle M.

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Illuminations Discovering the Area Formula For Triangles

Students use graph paper to estimate the area of multiple triangles and use their data to create a formula.

https://illuminations.nctm.org/lesson.aspx?id=1874

Engage NY Grade 6 Module 5 Topic A Lesson 3

Students show the area formula for a triangular region by decomposing a triangle into right triangles

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document camera

scissors

glue

colors

area of a triangle notes sheets

20 cm. x 20 cm. squares, unmarked

area of triangle activity worksheets

4 congruent rectangles with varying triangles drawn on

area of triangle work paper worksheets

5 different real world triangle problems

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Identifying Height of the Triangle

Students may misidentify the length of one side of the triangle as the height of the triangle. Teachers can emphasize that height is a straight vertical measurement. Using a real world example, like having your height measured at the doctor, can be effective.

Avoiding Extraneous Information

Many area of a triangle problems have more measurements than needed. It can be difficult for students to pick out which ones are needed to work the problem, especially if the triangle is at an unusual angle. A strong conceptual understanding of the concept that the area of a triangle is half that of its corresponding rectangle will support students in choosing which measurements to use.

Using the Wrong Formula

Students may incorrectly apply what they already know (and probably recently learned) about the area of a rectangle to the triangle. They may multiple the base and height without realizing that the area of the triangle is half. They may also multiply the length of all sides, because this is similar to how one would figure the rectangle. It is important students to have an understanding of why the formula for area of a triangle works in order for them to be consistently successful in implementing it.

*Photo below sourced from http://www.mrbartonmaths.com/blog/misconceptions-area-triangle-maths-diagnostic-question-week-21/

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Higher-level Questions

How would you determine when to use this formula in the real world?

How would you use the area of a triangle to find the area of a regular octagon?

How does changing one of the three points of a triangle affect the area?

What can you do with the area of a triangle?

How does the area of a triangle relate to its perimeter?

Number Talk
The area is the entire square is 64 square inches.

What do we know about the area of each of the colored squares?

Estimate the area of the yellow shaded area. How do you know?

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This area of a triangle lesson lends itself to development of specific math practice standards as defined within the Common Core.

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Process

Teachers can provide varying levels of support within the problems as needed. For example, using dashed lines to represent the corresponding rectangles in diagrams. Students can continue to use mathematics supports such as writing out multiplication families as needed.

Product

Work in a flexible number of problems to work time. Have students work on more interactive projects or on simple practice problems as needed.

Content

Offer a variety of difficulty levels in problems for students to choose from. Students can view different examples of problems by watching short Khan Academy videos.

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Process

Students work in groups or individually on real world problems in which they have to measure a triangle to find area. Students can work on a more complicated problem such as using what they know about the area of a triangle to figure out the area of a large star.

Product

Students can write their own “area of a triangle” word problem.

Content

Students work in small groups with graph paper to discover the formula for area of a triangle on their own. In-class activity: students work with the formula from the other direction by using given areas to find the triangle.

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Formative Assessments

Teacher feedback on in-class activities

Summative Assessment

Schoology Quiz: 5 questions

Self Assessments

Practice Problem worksheet with answer bank

Online work problems with immediate accuracy feedback:

https://www.mathgames.com/skill/7.18-area-of-triangles-and-trapezoids

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Khan Academy Area of a Triangle Lesson

Students can watch an example of finding the area of a triangle, either in class or as homework. This lesson also offers interactive work problems that breaks the lesson up into smaller steps: finding the base and height, finding the area of a right triangle, and finding the area of any triangle.Teachers can create practice problems that support the use of these smaller steps as a learning support.

https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-triangle/v/example-finding-area-of-triangle

Practice Drills Using Easy Mental Math

Students can do a fun scoot around the room, working with partners to find area of triangles using easy mental math. Keeping the calculations simple allows students more repetitions with the formula, and the scoot offers partner support.

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Teachers Pay Teachers Vocabulary Support

TPT is a website for teachers to share resources. There are a range of options for geometry support, including word walls and flash cards. Teachers can support students that understand the prerequisite knowledge in another language by posting the relevant math vocabulary for reference. Many ESL students in general benefit from visual references as much as possible. Terms to focus on for this lesson would be area, triangle, right triangle, base, height, length, width, and half.

https://www.teacherspayteachers.com

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Mini project: find a triangle in your home. Sketch or photograph it and estimate the measurements of its sides. We will find areas and trade triangles in class.

Use students’ interests to come up with real-world examples for practice problems. Eg. soccer, fashion, etc.

Find triangles in the culture of the school by taking a mini fieldtrip around school

Students create their own triangles with their bodies and find the area.

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Virtual Manipulative:
Interactive Maths Area of a Triangle Explorer

Students move a set of 3 points to play with triangles. The lengths of the sides and area are given, allowing students to explore what happens to the area as the lengths of the different sides or the height of the triangle is changed.

http://www.interactive-maths.com/area-of-a-triangle-ggb.html

Sheppard Software Triangle Splat
Review types of triangles to prepare for the triangle area lesson
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/triangles_shoot.htm

Mr. Nussbaum Zoo Designer
Practice area & perimeter concepts while creating exhibits for animals in the zoo.
http://mrnussbaum.com/zoo/