Wednesday, May 4, 2016

Day 151: Vol & SA of Cube, Cube Root, MARS Pre-test, More Solving Inequalities

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.
Students estimated which consecutive integers a cube root is between. It's similar to approximating square roots (radicals) because here you think of the two perfect cubes the radicand of a cube root is between. Then you simplify. Some students wondered if the number line method would work here and I told them they should investigate that.

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!!
In accelerated students finished solving a mixture of inequalities. Some of the parabolas had inequality signs that's directions needed to be changed. Then they started investigating Transforming Functions by using a constant k, like f(x)+k.

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