Erick Lee
@theericklee.bsky.social
787 followers 462 following 411 posts
High School Math Teacher | Desmos Fellow | Nova Scotia Math Teachers Assn President. #ITeachMath. I occasionally blog about math at pbbmath.weebly.com
High School Math Teacher | Desmos Fellow | Nova Scotia Math Teachers Assn President. #ITeachMath. I occasionally blog about math at pbbmath.weebly.com
![An online calculus practice question from mathmatize.com.
The problem statement reads: "The region enclosed by y = (x^2)/4 and y = 5 - x^2 is rotated about the x-axis. Fill in the blanks to correctly compute the volume of the resulting solid:"
Below the text is an incomplete integral formula:
Volume = Integral from [dashed blank] to [blank] of [blank] dx
At the bottom, a multiple-choice interface for "Blank 1" shows a row of selectable numerical buttons: -4, -2, -1, -1/2, 0, 1, 1/2, 2, and 4. A purple button below reads "CHECK ANSWER" with "3 attempts remain" written underneath.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fpm7mbu3gmxtohbxgnm52izt/bafkreigxksfrvmexssvx6tybilqtjylwx5xipcpk3acejiauc4d2uxe3x4)
![A calculus problem statement and four parts labeled A through D.
The problem text reads: "Consider the region bounded by the graphs of f(x) = -x^2 + 4x + 3 and g(x) = x + 3."
The individual parts are:
A. Sketch the two functions on the same coordinate plane and shade the region trapped between them.
B. Find the x-coordinates of the points of intersection, x = a and x = b.
C. Find the maximum vertical distance between the two functions on the interval [a, b].
D. Find the exact area of the trapped region.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fpm7mbu3gmxtohbxgnm52izt/bafkreigqmqwogspwfdpqnykhaqczbahdwzuynbtk4fvitltwfsginbcu7i)
![A photograph of a Wipebook grid whiteboard containing a handwritten math solution to the calculus problem.
At the top left, the functions are written: f(x) = -x^2 + 4x + 3 and g(x) = x + 3. Below them is a rough sketch of a coordinate plane showing a downward-opening parabola intersecting an upward-sloping line. The area between them is shaded, with intersection points labeled at (0, 3) and (3, 6).
The board is divided into two columns of algebraic work:
Left column (Finding intersection and max distance):
The equations are set equal to find the points of intersection (POI): -x^2 + 4x + 3 = x + 3, simplifying to -x^2 + 3x = 0, then x(x - 3) = 0. The points of intersection are boxed as x = 0, x = 3.
Below this, the vertical distance function is defined as M = -x^2 + 4x + 3 - x - 3, which simplifies to -x^2 + 3x.
The derivative is taken to find the maximum distance: M' = -2x + 3 = 0, giving x = 3/2.
Plunging x = 3/2 back into the distance equation yields M = -9/4 + 9/2 = 9/4, which is circled and labeled "max distance".
Right column (Finding the area):
The area is calculated using a definite integral from 0 to 3 of (-x^2 + 3x) dx.
The antiderivative is written as [-x^3/3 + 3/2 x^2] evaluated from 0 to 3.
Plugging in the bounds results in -9 + 27/2 - 0, which simplifies to -18/2 + 27/2.
The final answer is boxed as 9/2 and labeled "Area".](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fpm7mbu3gmxtohbxgnm52izt/bafkreifbo2rtik2cfnd75dksjz5xsk6ztvwx2asll6sxd47k65gtqgfpam)
!["Each group will receive two playing cards. Answer both questions given your cards. (Jack=11, Queen=12, King=13, and Ace=14)"
Below are two math problems in red rounded boxes:
Box 1: "A ladder of length [Higher Card] ft is leaning against a vertical wall. The base of the ladder is being pulled away from the wall at a rate of 2 ft/s. How fast is the top of the ladder sliding down the wall when the base of the ladder is [Lower Card] feet away from the wall?"
Box 2: "A water tank in the shape of an inverted cone has a height of [Higher Card] meters and a top radius of 5 m. Water is being pumped into the tank at a rate of 3 m³/min. How fast is the water level rising when the water is exactly [Lower Card] meters deep?"](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fpm7mbu3gmxtohbxgnm52izt/bafkreiayfbdekxl45lwroawbkqecv4x45ylcup6aknrqhpomxc3j6jbyoi)
![An email that begins with, Dear [Teacher’s Name]…](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fpm7mbu3gmxtohbxgnm52izt/bafkreidn6vgskcdltq54lna35gyaxa6tovzqnbtyr3apsy2kzrokjb32wy)
