The estimation today was the flight distance from Vancouver, Canada to Ontario Canada. 2,200 miles represented a cross country flight so less than that and north was around 300 miles less.
To begin class I wanted to review the volume and surface area of a cube with side length 3 feet as well as go in depth about correct units.
Some students told me the volume was 3 * 3 * 3 = 27. Some students correctly said it was 27 cubic feet or feet to the 3rd power. I asked students why and they said it was because it was volume. I stressed that you were multiplying feet by itself 3 times. I wrote "cubic feet" in quotations on the board.
For surface area students said to do 3 times 3 and then multiply that by 6. Many students said do 3 times 3 to get one "side." Then multiply by 6 sides. I asked students what word was inside surface. They said "face." Some classes piped in "surf" and "ace." Face is what we call the flat 2 dimensional side of a 3 dimensional figure. I stressed that 3 feet multiplied by 3 feet is 9 square feet. That is the area of one face. Then that is multiplied by 6, the number of faces. I asked students, "what is the highest number you can roll on a number cube? (die)" They replied, "6!" This reinforced that the numbers 1 through 6 number the faces of a cube.
I borrowed a diagram from my colleague Ms. Wong where she shows 1 centimeter long line. It's a 1 one dimensional measurement. I a 1 cm by 1 cm square is 1 cm^2 or 1 square centimeter, a two dimensional measurement. Finally, a cube with side length 1 cm is 1 cubic centimeter. The exponent tells you what dimension you are in.
In 5th period I added on that centimeters on a circle would be circumference, area would be 2 dimensional, and a sphere's volume would be 3 dimensional.
Then students reminded themselves how to press MATH on the TI calculator to get down to the 4th menu option, the cube root. Yesterday I showed them how to find the button on the iPhone's calculator in landscape mode.
Some students are struggling to show the last step when getting the Pythagorean theorem to c squared = 100. I've stressed that every math operation has an inverse operation. What's the inverse operation of squaring c? Square rooting. (Some students assumed "unsquaring") I want them to show that operation on both sides before stating their answer.
|Students will be assessed on using the correct units and solving the volume and surface area of a cube. To the right is the 3 types of measurements.|
Then in the last 10 minutes I gave students the task "Patterns in Prague" that investigated area of complex figures as well as finding the perimeter of irrational side lengths.
|This student nailed it as well as rounding the square root of 50 to 7 centimeters.|
|This student even went as far as approximating the square root of 50 as 7 and 1/15!!|