Lesson 5: Area of Composite Shape

Lesson 5: Area of Composite Shape

Subject: Math Unit: Area

Time needed: 60 minutes

Grade: 6th

Date: 2nd

semester

Materials ,

Lap tops or computer with Geogebra

Create a scaled version of the

Texts Needed,

if possible

playground on Geogebra.

or advanced

Tangrams

preparation:

Calculators

CCSS

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.

CCSS.Math.Practice.MP4 Model with mathematics. This standard is addressed by having the students solve a real world problem that is relevant to them. They will use all their skills learned in this unit to conclude a total area for their playground.

Target Objective (I Can): Technology Standards (S):

I can break apart a polygon into simpler parts to find its area.

1. Creativity and Innovation: Use models and simulations to explore complex systems and issues

2. Critical Thinking, Problem Solving, and Decision Making: Use multiple processes and diverse perspectives to explore alternative solutions

Key understandings: Essential Question: Prior Knowledge:

Shapes can be broken down into other shapes in order to find the area.

How can we find the area of shapes that are not a rectangle, parallelogram, trapezoid, or triangle?

Area of a rectangle can be found by the length of a side multiplied by the length of a perpendicular side. Since two triangles can be composited together to form a rectangle or parallelogram by rotating one triangle 180 , we can assume that half the area of a rectangle or parallelogram would

be the area of a triangle. The area of a triangle is the

A parallelogram area is the same as a rectangle since we can draw a perpendicular line down from

a vertex to the base making a right triangle. This right triangle can be then rotated 180 and

moved so that the congruent hypotenuse would be adjacent to the opposite side. This makes a

rectangle. Since the area of a rectangle is , the area of a parallelogram is

as well

Properties of shapes such as parallel lines, or congruent side lengths.

Common Misconceptions:

Students may not realize they can over estimate a shape and then subtract a portion to make it more exact of an answer. They may only see decomposing as adding shape areas together to estimate the total area. They may not believe that there is more than one way to decompose a figure. They may forget that the model given to them is scaled down and will report their area in terms of Geogebra measurements. Students think because they can make a rectangle from a triangle that the area is length times width as well. Same with our trapezoids

Key Vocabulary:

Area

Composite shape

Strategies/ Sequence

Engagement:

1) Explain the problem: A team of contractors is coming to your school to resurface your playground. They are wondering how much material to bring. Since your playground is not a perfect square, they don't know what to do. They need to know the area of your playground

in square feet. Your principal wants to make sure she is paying for just the right amount, with not too much left over. Can you help them out? Whichever group is the closest to the actual area of the playground wins a small prize.

Model/ Explain:

2) Yesterday's lesson we began to break apart our shapes into formulas based on the rectangle. In today's lesson, we are going to review these formulas and fill in our graphic organizer on formulas. Yesterdays homework was to find the area of a trapezoid. At the end of the lesson, I realized through the chaos that this may not have been conveyed to everyone in class and the directions were not clear. I would like to revist how we found the area of a trapezoid before we precede. In this part of the lesson, we will look at how we can double the trapezoid or spit it in half to form a parallelogram.

3) On the document camera work through the trapezoid cutting in half and moving one half to lay next to the other to form a long parallelogram and then labeling parts base 1 base 2 and height. Then ask to them to look at their formulas and make any corrections they need before proceeding. "what is the height of our trapezoid?" Have we remember that we cut it in half?" "what is the new length of the rectangle?" Is it double? Are we summing the two together?

4) Record our observations in the graphic organizer. Repeat the formulas so they understand. Review how we found the formula before we write down in the graphic organizer.

5) Once this is done, have the students put everything but a pen, graphic organizer, and calculator on the ground. Obtain a computer from the cart and log on to the computer to Mrs. Steele's website.

Guided Practice:

6) On the website, there is a link to an applet which refreshes their mind on how we found those

formulas they have written down. They will engage with the applet for a few minutes. Once

they have are a bit more comfortable with the formulas, open up the area practice applet on

the website as well.

7) This applet is one the teacher will help the students to figure out Geogebra. The students will

be guided through the program on how to measure lengths and how to measure heights.

This program is all for the benefit of students for their project with Geogebra. It is a precursor

to understanding the formulas as well as the application.

8) Begin with the rectangle

(pink). Ask the students for the formula for area and have

them repeat it loudly. Show them how to measure length and width by clicking on the

measure tool and then clicking on a line segment.

9) Have them practice independently on the

rectangle. To speed things up, they may use

a calculator.

10) Discuss how in the formula of parallelogram how we need the height, not the length of one

side. Review why we need the height (to form the side of our rectangle). Discuss the term

perpendicular and how it means 90 between the two lines like the corners of a rectangle.

11) Show them how to make a perpendicular line from one corner to the base. Once they have

the line, they need to put a point where the two lines intersect. (discuss how the lines

become bolded when they are selected). Since this is a line that will go on forever, students

need to click one point to the other point to measure the distance.

Explore:

12) When they become comfortable with the perpendicular line. Have them practice with the triangles. Discuss how you can use any of the heights to find the area. Show them how each one will still turn and create a parallelogram or rectangle.

13) Walk through the trapezoid with them. Remind them of our formula where we have to find two bases and a height.

14) Depending on time, students will either have time to break up their figure, or to work on more trapezoid, parallelogram, and triangle practice from 10-2 worksheet. This will conclude part 1 of the lesson.

15) Part 2 of the lesson will have the students working on breaking the shape into familiar shapes that we do know.

16) "How can we find the area of this figure?" "Are there shapes that we know that can be used to find this area?" "This figure is a scaled down version of our playground. What does it mean to be a scaled down version?" The teacher will model how to decompose a figure into smaller shapes using tangrams on the document camera. They will model this twice to make sure the students understand the concept. Tangrams are great way to show how to decompose a shape since they only use triangles, trapezoids, rectangles, parallelograms. "So we could take a ruler and measure the lengths that we need on the triangle, trapezoids, parallelograms, and rectangles to find the area of this scaled down playground." Model how you would measure one or two of the shapes to refresh their memory on area of shapes from previous lessons. We will be doing the same thing on a life like model of your playground.

17) The students will log on to their computers and open up the GEOGEBRA application. While they are logging on, Go over the directions of the worksheet with the students. Have them repeat back to you what they need to do.

18) The teacher will need to explain or hand out a sheet on how to use Geogebra if this is an unfamiliar application. (this was done in part 1 of the assignment) Discuss the key features of the program that will be used today: point, line segment, perpendicular line, and the measuring tool.

19) "You may work with a partner on this project. You and your partner need to decide on the best way to break up the playground. Remember, we can over estimate or under estimate by a little if the shape breaks up to a convenient shape. Try to avoid excess over or under estimation. This will result in too much or too little amount of material bought." Show an example on the board of what this means.

20) The students will turn in their work when completed to be assessed on their skills with area. More time may be given to properly assess all learners.

21) Note that this image is older image and there is 2 octagon gaga pits which would need to be resurfaced as well. This is noted in the image below as the white octagons. These can be considered circular if the students have learned about circles already.

Independent practice:

They will be engaged in independent partner time when dividing the shape up into their own creative strategy.

Extension:

Have students actually measure out the playground and figure a way to solve it using the big playground rather than a scaled version.

Assessments and Check for understandings:

Students will be assessed on the skills of computing area of irregular shapes. They will be assessed on the ability to break down a shape into shapes they know how to find area of and will be assessed on their ability to apply the knowledge from previous chapters. This is a summative assessment of the Area concepts covered in this lesson.

21st Century Themes and Skills:

Solve Problems Solve different kinds of non-familiar problems in both conventional and innovative ways

Apply Technology Effectively Use technology as a tool to research, organize, evaluate, and communicate information

Differentiation:

Students who need extra practice with the tangrams may have time to manipulate and measure the tangrams. They can make all their predictions based on the tangrams. They may not have the visual spatial recognition to decompose a shape into other shapes until they have split apart tangrams. This time should be encouraged for those that need the extra practice. Even though this may result in over or under estimations, encourage the students who are hung up on the formulas to break the shape into only 3 components. Use the sides and the angles to help decompose the shapes. The shape may need to have one part broken down so they can see the other shapes easier.

Resources:

Bursley School, Georgetown, MI (2013). Googlemaps. Retrieved from

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Example of how to break down Bursley Playground into familiar shapes

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