I SPY… with my little eye Teachers, please read the notes section of each slide for important information! You may have to scroll to see everything in the notes. I SPY WITH MY LITTLE EYE… This PowerPoint can be used as an Anticipatory Set for Irregular figures. It is designed to get the students use to looking for basic shapes within a complex figure. Lesson 5.3.4 Area of Complex Figures

Area of complex figures A complex figure is a figure that can be divided (or decomposed) into more than one of the basic shapes. Some people refer to these figures as irregular figures.

Eye Spy Let’s play the game “I Spy” to see if we can spot the basic shapes that make up some of the following complex figures! Continue

I spy with my little eye… What shapes do you see? Answers may vary. Some may say 2 circles, 1 square or 4 semi-circles, 1 square What kind of eye is it? Human

I spy with my little eye… Answers may vary. Some may say 2 triangles, 1 rectangle, or 1 triangle, 1 trapezoid What kind of eye is it? Cat eye

I spy with my little eye… Answers may vary. Some may say 1 big rectangle, 1 little rectangle (garage), 1 square (house) What kind of eyes are these? Husky eyes

I spy with my little eye… Possible response 1 triangle, 1 circle. What kind of eyes are these? Snowy Owl eyes

I spy with my little eye… Possible response 2 triangles, 1 rectangle What kind of eyes are these? Spider Monkey

I spy with my little eye… Possible response 1 square, 1 circle What kind of eyes are these? Red-Eye Tree frog

I spy with my little eye… Point out rectangle and semi-circle. Some students may know that the big semi-circle is the 3 point shot line. What kind of eye is this? Tiger eye

I spy with my little eye… Possible response Some may be a square inside of a square. Others may notice the triangles that surround the inside square. What kind of eye is this? Human (model obviously)

I spy with my little eye… Possible response: 2 triangles, 1 rectangle and hopefully students will notice the whole shape is a trapezoid! What kind of eye is this? Aye-Aye Aye-Ayes can be found only on the island of Madagascar. These rare animals are related to chimpanzees, apes, and humans!

I spy with my little eye… Can you a spot a trapezoid? Is there a rectangle? What about a triangle? Is there a circle? Sometimes there is more than one way to look at a shape. Some may see two rectangles, a triangle, and a semi-circle. Others may see a trapezoid, rectangle, and a semi-circle. What kind of eye is this? Bald Eagle

I spy with my little eye… Possible response 4 rectangles some may see 5 rectangles Some students may divide some of the large rectangles into smaller rectangles. What famous star has these green eyes? Hint if needed: She plays a Vampire  Kristen Stewart “Bella” from Twilight What famous star has these green eyes? Kristen Stewart - Bella from “Twilight”

Today’s Lesson Section 1: Opening Activity Today will be all about using your eyes to decompose shapes. We will take really weird looking shapes and break them down into simpler shapes that we know. We will also be working towards finding the area of these weird shapes. Section 1: Opening Activity Section 2: What are Complex Figures? Section 3: Decomposing Complex Figures Section 4: Finding the Area of Complex Figures

Let’s Get Started Section 1: Opening Activity Section 2: What are Complex Figures? Section 3: Decomposing Complex Figures Section 4: Finding the Area of Complex Figures

Opening Activity The trapezoid below is decomposed (cut) into three different shapes, a rectangle and two triangles. Part A Find the area of each of the three shapes separately. Triangle 1 Triangle 2 Rectangle ½ • b • h ½ • 5 • 12 = 30 ft² ½ • b • h ½ • 5 • 12 = 30 ft² b • h 12 • 12 = 144 ft² What is the area of the three pieces if you add them together? Objective 6.G.1 states that students should be able to find the area of triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. This activity will show the students that a trapezoid can be decomposed into rectangles and triangles. We can find the area of each individual shape, add them up and it gives us the same answer as using the area formula of a trapezoid. The activity will also lead us into more complex shapes as the lesson progresses. Give the students 7-8 minutes to complete activity, then hit enter to display and review each answer. Students should begin to realize that there are different ways to looking at a figure. 30 + 30 + 144 = 204 ft² Part B Use the formula A = ½ • (b1 + b2) • h to find the area of the trapezoid. ½ • (b1 + b2) • h ½ • (22 +12) • 12 = 204 ft² Did you get the same answer as you did in Part A? Yes

Moving On Section 1: Opening Activity Section 2: What are Complex Figures? Section 3: Decomposing Complex Figures Section 4: Finding the Area of Complex Figures

What are Complex Figures? A Complex figure is a figure that can be divided into more than one of the basic shapes. Some people call them irregular figures. Turn and talk to your neighbor about the different shapes you see in each figure. Answers will vary. But students may see rectangles, triangles, and trapezoids.

Moving On Section 1: Opening Activity Section 2: What are Complex Figures? Section 3: Decomposing Complex Figures Section 4: Finding the Area of Complex Figures

Decomposing Complex Figures Sometimes you need to decompose figures to help find missing information on a figure. You will also use this skill in the next section to help find the area of complex figures. Let’s take a look at these examples. Example 1 Example 2 You-Try this one! In order to find the area of complex figures you need to know how to decompose the shape and possibly find missing side lengths.

Example 3 Give this one a shot! Sometimes there is more than one way to decompose a complex figure! The Intermediate School is producing a play that needs a special stage built. A diagram is shown below.   On the first diagram, divide the stage into three rectangles using two horizontal lines. On the second diagram, divide the stage into three rectangles using two vertical lines. On the third diagram, divide the stage into three rectangles using one horizontal line and one vertical line. In order to find the area of complex figures you need to know how to decompose the shape and possible find missing side lengths.

Almost Done! Section 1: Opening Activity Section 2: What are Complex Figures? Section 3: Decomposing Complex Figures Section 4: Finding the Area of Complex Figures

Area of Complex Figures There is not an easy formula to find the area of complex figures. Now is the time when you really need to understand how to compose and decompose a figure. There are two types of complex figures. Shapes that Connect Shapes Inside of Shapes How you calculate the area depends upon what type of complex figure you have and the shapes that can be decomposed.

To find the area of shapes that connect follow these steps. Find the total area of the shape below. This should be done whole group. See student notes answer keys for solutions.

To find the area of shapes inside of shapes follow these steps. Find the area of the shaded region of the shape below. This should be done whole group. See student notes answer keys for solutions.

Apply What You Have Learned About Decomposing and Composing Which formulas could be used to find the area of this shape? Select all that apply. Closure (½ ● b ● h) + (b ● h) + (½ ● b ● h) ½ ● (b1 + b2) ● h (½ ● b ● h) + (½ ● (b1 + b2) ● h) (½ ● b ● h) + (b ● h) Answer: All of them can be used to find the area of the figure. It depends on how you look at the figure. A. triangle, square, triangle trapezoid triangle, trapezoid You can put the two end triangles together to form one triangle, then add the square

I spy with my little eye… How can this complex figure be decomposed? 2 rectangles, 1 triangle or 1 rectangle, 1 triangle, 1 trapezoid Are these connecting shapes or a shape inside of a shape? Connecting shapes Explain how you would find the area of the complex figure? Closure Find the area of each basic shape using formulas, then add the areas together to get the total! Answers may vary. They may see 2 rectangles, 1 triangle others may see 1 rectangle, 1 triangle, 1 trapezoid What kind of eyes? Baby eyes