Area of Triangles

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Objective

SWBAT: • Identify and create perpendicular and parallel lines. • Identify the height and base of a triangle. • Find the area of a triangle.

Big Idea

Students apply what they know about area of other polygons to develop a formula for finding the area of a triangle.

Do Now

5 minutes

See my Do Now video in my Strategy Folder for more details on how I begin my class.  I chose #1 because many students struggled with it on a recent quiz.  I took the most common incorrect answer and presented it as student work.  I present the work as correct, because obviously 16+4 = 20. I have a student explain why that is incorrect and how to find the correct answer.

I chose #2 to get students thinking about perimeter and area.  A side length that is a fraction can scare some students.  I look for a student who added and multiplied fractions to find the perimeter and area and I have them quickly explain what they did.  I look for a student who felt more comfortable changing 1 ½ to 1.5 and have them quickly explain their work.

Problem

12 minutes

Review of Lines

5 minutes

In order for students to be able to identify the base and height of a triangle, they must be able to identify perpendicular lines.  I use a few minutes to review parallel, perpendicular lines.  Parallel lines will come into play later when we classify quadrilaterals.

Parts of a Triangle

5 minutes

Here I emphasize that in right triangles, the base and height are also sides.  With obtuse and acute triangles, the height is not a side length because the base and height must intersect at a 90 degree angle.  A common misconception for #3 is that the height is 15cm.  For #3 I declare, “I think the base is 22 cm and the height is 15 cm.” I call on student to share if they agree/disagree.

Area Formula for a Triangle

5 minutes

We copy the two versions of the formula.  Most of my students prefer to multiply the base and height and then divide by 2 (rather than multiply by ½). 

A common mistake that students make is that they multiply the base and height and then forget to divide by 2 (or multiply by ½).  When a student makes this mistake I revisit the formula and ask, “Why do we have to divide by 2?”  We have to divide by 2 because if we didn’t we would be find the area of a rectangle that has those dimensions.  The triangle that we have takes up ½ of the space of the rectangle.  The song is another way for students to remember the formula.

Practice

10 minutes

I ask whether students think that any of the triangles have the same area (C &D, F&H).  Many students struggle to be able to see that although the triangles look differently, if they have the same base and height then the area will be equal.  This is okay!  I want students to come across these relationships as they work.

I have students calculate the area of A, C, and G first and use clickers to share their answers.  You can also use whiteboards for students to show you their work.  Some students will struggle with G, because of the way it is located the height is outside of the triangle.

Depending how students do with A, C, and G I may address incorrect answers as a whole class, with a small group, or individually. Students continue to work and check key when they are finished.  See my video Posting A Key in my Strategy Folder.

If students complete page 7-8, they will go on to the other problems in the packet.  The challenge on p. 10 pushes students to draw a rectangle around the triangle and then figure out the area of the triangles that surround the gray triangle.  Students can then compare the area of the surrounding triangles to the area of the rectangle to find the area of the gray triangle.

Closure and Ticket to Go

5 minutes

I have a student review our objectives for the lesson. Then I ask students how they found the area of triangle H on p. 7. Next I ask which triangle on the page has the same area as triangle H (triangle F). How can they have the same area when they look differently? I want students to articulate that since both triangles have the same base and height, they will have the same area.

Students will complete ticket to go 6.2.