Delta Blocks & Basics Article
DEMOCRATIZING ACCESS (Kaput):: Some examples of the HOW of connecting EARLY CALCULUS with other "Big Ideas" in mathematics (STEM) curricula
You can use the directions for the story activity or the arrangements like those in the article below. Then links to the Kenneth Video and respective graphs from the video are shown.
SIDES VIEW OF BLOCK WALLS
You may want to start with six blocks.
You can create a wall with the blocks.
Blocks in the wall must be straight on top of each other.
There can be no hidden blocks in the wall (no hiding blocks behind the wall).
Some examples of block walls are shown on a table in the image below.
The SIDE VIEW of another block wall is shown (four blocks, a space, another space, then a block, then another block).
You can now move the green blocks to made the side view of YOUR OWN WALL. The green blocks must go in the squares and and build up from the table (as shown in the example).
USING BLOCK WALLS TO CONTROL AN ELEVATOR
Show below is a block wall with four blocks, a space, another space, a block and then another block.
How many blocks are shown?
[A] Now press the reset button then the start button. You can repeat pressing reset and start as many times as you want.
[B] What do you notice about the motion of the elevator? Where does it start? Where does it stop? How does it move? Same speed or different speeds? How do the blocks control the movement?
NOW ENTER YOUR WALL
Click on the blue dot next to a letter to drag the top of the wall up or down.
[C] Enter your wall (using six blocks total).
[D] Now press reset and start. For your wall, what do you notice about the motion of the elevator? Where does it start? Where does it stop? How does it move? Same speed or different speeds? How do the blocks control the movement? How is your motion different or the same as the shape that was there before (above).
[E] Challenges with six blocks:
(a) Find TWO arrangements of blocks that have the elevator go to the third floor, stop for people to get off, and then go to the sixth floor.
(b) Find TWO arrangements of blocks that have the elevator go to the third floor, stop, and then return to where the elevator started
[F] If you change the "initial" floor for the elevator, what does this do to the motion of the elevator? What is the same? What is different?
[G] If you ADD blocks, what do you notice about where the elevator starts? Stops? How it moves?
You may need to move things down to see where the elevator stops. How does the elevator move?
[H] If you take away blocks, what do you notice about where the elevator starts? Stops? How it moves?
[I] if take away blocks below the axis, what does this do to the final position of the elevator?
[J] Try expressing one of your elevator motions using numbers, addition and subtraction
MY ELEVATOR STORY
Tell a story to go with any arrangement of blocks you want to use. Your story might start:
"Tonya wanted to go to the fourth floor to buy a t-shirt ..." The movement of the elevator should match your story.
Be ready to share your story.
How-to questions:
How do I make the elevator go down? Answer: Drag blocks below the horizontal black line.
How do I make the elevator start on a different floor? Answer: Change the number for initial floor to something other than "0".
How do I undo something? Answer: Press the left-curving arrow to the left of the magnifying glass.
DISCUSSION
What math do you see in making your story?
Could we use numbers or symbols like "+" , "-" or"=" to describe the motion of the elevator?
Connections to other AREAS of mathematics (pun intended?)
Video of Kenneth (transcribed in the article)
Copy and paste the following iURL nto a new tab in your browser:
https://drive.google.com/file/d/0B9xoCNEJIYg-NVRLZnpkZ2p6WGM/view?usp=sharing&resourcekey=0-7bWLTcYIA7lzS8JwQjAWGA
Here is the first graph in the video (transcribed in the article):
Here is the second graph in the video (transcribed in the article):
Here is the third graph (created accidentally) as shown in the video (and transcribed in the article).
STEM? :: Compare the KINEMATICS graphs shown (constant acceleration) from PHYSICS to the last graph by Kenneth.
