Circles and Cylinders

BIG IDEAS:(taken from “Big Ideas by Dr. Small”):

1. Familiarity with known benchmark measurements can help you estimate and calculate other measurements.

2. The unit chosen for a measurement affects the numerical value of the measurement; if you use a bigger unit, fewer units are required.

3. The length of an object is a one-dimensional attribute. Length can be the measurement of a single measure of an object or a combined linear measure, like perimeter.

4. The area of an object is a two-dimensional attribute. Area can be a single measure of a 2-D shape on an object or a combined measure of a 3-D shape, like surface area.

STUDENT LEARNING GOALS:

GOAL #1: I can convert between different metric units.

• VIDEO: Metric Conversion (Source: Khan Academy)

• VIDEO: Converting Metric Cubic Units (Source: TuLyn Math)

• VIDEO: Converting Metric Units of Volume (Source: Tyler DeWitt)

• QUIZ: Metric Relationships (converting units) (Source: Nelson Education)

• GAME: Metric Matching (Source: Sheppard Software)

• GAME: Metric System Rockets (Source: Math Fox)

• GAME: Metric Measurement Millionaire (Source: Quia)

GOAL #2: I can determine the perimeter of 2D shapes (including the circumference of a circle).

• VIDEO: Introduction to Perimeter (Source: Khan Academy)

• VIDEO: Finding Perimeter when a Side Length is Missing (Source: Khan Academy)

• VIDEO: Determining the Formula for the Circumference of a Circle (Source: Mathematics Online)

• VIDEO: What is Pi? (Source: Mathematics Online)

• VIDEO: Radius, Diameter, Circumference and Pi (Source: Khan Academy)

• VIDEO: Parts of a Circle (Source: Khan Academy)

• VIDEO: Finding Perimeter of Composite Shapes (Source: wongybon)

• PRACTICE: Radius, Diameter and Circumference (Source: Khan Academy)

• QUIZ: Calculating Circumference (Source: Nelson Education)

• GAME: Dunk Tank (Source: PBS Learning)

GOAL #3: I can determine the area of 2D shapes (including circles).

• VIDEO: Introduction to Area and Square Units (Source: Khan Academy)

• VIDEO: Rectangle Area (Source: Khan Academy)

• VIDEO: Comparing Perimeter and Area of Rectangles (Source: Khan Academy)

• VIDEO: Finding Length and Width if the Area/Perimeter is Known (Source: Khan Academy)

• VIDEO: Determining the Formula for the Area of a Circle (Source: Mathematics Online)

• VIDEO: Area of Circles (Source: Khan Academy)

• VIDEO: Finding Radius when given Area (Source: Nam Nguyen)

• VIDEO: Area of Composite Shapes (Source: The Learning Pod)

• QUIZ: Area of Circles (Source: Nelson Education)

• PRACTICE: Area of Circles (Source: Khan Academy)

• GAME: Circle Jeopardy (Source: Jeopardy Labs)

GOAL #4: I can determine the volume and surface area of 3D shapes (including cylinders).

• VIDEO: Intro to Volume (Source: Khan Academy)

• VIDEO: Overview of Volume (Source: Math Antics)

• VIDEO: Volume of Triangular Prism and Cube (Source: Khan Academy)

• VIDEO: Finding the Volume of a Cylinder (Source: Vivid Maths)

• VIDEO: Volume and Surface Area of Cylinders (Source: Khan Academy)

• VIDEO: Finding Volume and Surface Area of Cylinders (Source: Math Mashup)

• VIDEO: Volume versus Capacity (Source: Turtlediary)

• QUIZ: Volume of a Cylinder (Source: Nelson Education)

• QUIZ: Surface Area of a Cylinder (Source: Nelson Education)

• PRACTICE: Volume of Cylinders (Source: MathGames)

PROJECT: Golf Course Design

In this project,students will be designing and building (a prototype) of a mini-putt course. They will be required to meet a number of requirements including shapes and total area. After creating a blueprint, they must calculate the perimeter and area of their course before building a prototype. This course will also be used in the Angle Relationships unit.

• Project Outline (including timelines)

• Blueprint design paper (print on 11 x 17 sized paper)

• Assessment Rubric

CURRICULUM EXPECTATIONS:

• solve problems that require conversions involving metric units of area, volume, and capacity (i.e., square centimetres and square metres; cubic centimetres and cubic metres; millilitres and cubic centimetres) (Sample problem: What is the capacity of a cylindrical beaker with a radius of 5 cm and a height of 15 cm?);

• measure the circumference, radius, and diameter of circular objecs, using concrete materials (Sample Problem: Use string to measure the circumferences of different circular objects.);

• determine, through investigation using a variety of tools (e.g., cans and string, dynamic geometry software) and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas (Sample problem: Use string to measure the circumferences and the diameters of a variety of cylindrical cans, and investigate the ratio of the circumference to the diameter.);

• solve problems involving the estimation and calculation of the circumference and the area of a circle;

• determine, through investigation using a variety of tools and strategies (e.g., generalizing from the volume relationship for right prisms, and verifying using the capacity of thin-walled cylindrical containers), the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula (i.e., Volume = area of base x height);

• determine, through investigation using concrete materials, the surface area of a cylinder (Sample problem: Use the label and the plastic lid from a cylindrical container to help determine its surface area.);

• solve problems involving the surface area and the volume of cylinders, using a variety of strategies (Sample problem: Compare the volumes of the two cylinders that can be created by taping the top and bottom, or the other two sides, of a standard sheet of paper.).