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Unit 3: The Building Blocks of Geometry

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1 Unit 3: The Building Blocks of Geometry
Suggested Activities Unit 3: The Building Blocks of Geometry

2 Problem Solving in Geometry
Area, Surface Area, Volume, and Perimeter Problem Solving in Geometry

3 Station 1 The “Transparent Blue Prism” Problem
How many faces are there? Find the area of each face. Use a ruler to estimate its dimensions to the nearest tenth of an inch. What’s the total surface area of the object? What percentage of the prism’s surface area is composed of the left and right faces?

4 Station 2 Find the area of one shaded corner. You may need to refer to recent formulas for circles, rectangles/squares, or parallelograms. 12 meters

5 Station 3 170.6 inches 65.3 inches inches 120 inches Find the area of the figure below. Try dissecting it into more familiar shapes. Hint: You may need to use the Pythagorean Theorem. 40.5 in 97.7 in 41.2 in 61.3 in

6 Station 4 Using a ruler, estimate the area of this irregular figure. Be sure to provide the correct label. What units did you use? Why is your estimate not a precise computation? What other methods could you use to estimate the area of the figure?

7 Station 5 Sherie & Kayla want to enclose their pool area with a fence. They have a rectangular inground pool that measures 30 feet long by 18 feet wide. If the stone walkway needs to be 4 feet wide, how much fencing do they need? What is the area of the stone walkway? What percentage of the pool area is composed of the walkway?

8 Exit Ticket Assume all three chicken nuggets are of the
same dimensions. Estimate the surface area of a single chicken nugget using the method of your choice. Using your estimation, calculate the combined surface area of the three chicken nuggets including the missing bite! 1.4” 0.87” 0.3”

9 A Geometry Lesson Polygon Patterns

10 Schema Activator A series of four images follow. You will be given seconds to study the image before it disappears. Your task is to draw the image from memory on the paper your teacher has supplied you! Your teacher may choose to return to the image once or twice more before moving on to the next one. Look quickly!

11 Image I


13 Image II


15 Image III


17 Image IV


19 Schema Activator Quick Images
For each image, what did you notice the first time you saw the shape? What features were in your first pictures? What did you miss when you first saw each shape? How did you revise your pictures?

20 Something to Consider In his book How to Solve It, George Polya passes on a famous piece of mathematical wisdom, “Geometry is the science of correct reasoning on incorrect figures.” It’s a nice phrase, but the fact is that picturing – both on paper and in your mind – is an important part of geometric reasoning. People can learn the mathematics of making accurate drawings, drawings from which you can reason. People can also learn to pay more attention to the geometry they see and to visualize with their minds.

21 Mission 1 Familiarize yourself with the pattern blocks.
Which shapes do you recognize? Can you name them? Other Introductory Extensions in the Classroom: Pair up students and have one student design their own figure. The other student takes directives from the designer and attempts to re-create the figure/pattern using only verbal instructions that do not refer to colors! Students should practice proper vocabulary use.

22 Mission 2 Figure out the measures of each of the angles in all six of the pattern blocks. Here are the rules: Don't use what you might know about the sum of the angles in polygons. Imagine that you know only what a fourth grader knows. You can use the fact that 360 degrees make a circle. You may use the measures of angles you already figured out as comparison. Try to figure out the angles for each shape multiple ways. Be prepared to share.

23 Area, Circumference, Radii and Diameter
Review of Circles Area, Circumference, Radii and Diameter

24 What do you remember about circles?
Write the formula for the area of a circle. Write the formula for the circumference of a circle (in two different ways): Given diameter Given radius Calculate the area of the circle. Calculate the circumference of the circle. 5cm 10cm Schema Activator

25 A circle has a circumference of 57. 64 ft. What is it’s area
A circle has a circumference of ft. What is it’s area? Show all work. A circle has an area of 82 in2. What is the circle’s radius? A circle has an area of 140 in2. What is the circle’s diameter? What is the area of this semi-circle? 24 m More Examples

26 Schema Activator…from 37,000 feet.
Estimate the sum of the area of the two green-shaded regions of the circles, given that the diameter of each circle is 1,200 feet.

27 Schema Activator: Traffic Cones
To prevent the cones from falling over when crazy drivers (aka Ashley, Carlton, and Devon) hit them with their cars, the cones are filled with sand to make them heavier. If the height of the cone is 16” and the radius is 4”, how much sand will be needed to fill the cone? Round to the nearest tenth. A hole is found in the cone and sand is leaking at a rate of 37 cubic inches/minute. How long will it take before the cone is empty? Round to the nearest tenth.

28 Introduction to Proof Essential Questions: What is proof?
What is it used for? How can it be used to prove triangles are congruent?

29 Schema Activator Create a two-column proof (fold your paper in half.)
Refer to the example from last class. Prove: If Mike “The Situation” Sorrentino gets a flat tire, then he will be late getting to Seaside Heights for the filming of the show.

30 One Example…© Kiara Thomas
This is why it happened. This is what happened next.

31 Schema Activator: Proof Warm-Up
Fold a piece of lined paper in half. Prove: If there is a blizzard tonight, then there will be no school tomorrow.

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