Tuesday, October 8, 2013

Mathematical Practices, writing, and computer science

Here is a collection of student journal reflections connecting the Common Core Standards for Mathematical Practice and binary numbers and the Cartesian coordinate system.
The eight mathematical practices:
1)  Make sense of problems and persevere in solving them.
2)  Reason abstractly and quantitatively.
3) Construct viable arguments and critique the reasoning of others.
4)  Model with mathematics.
5)  Use appropriate tools strategically.
6)  Attend to precision.
7)  Look for and make use of structure.
8)  Look for and express regularity in repeated reasoning.

3rd grader:
"In binary numbers, I use math practice number 6 when doing code.  Binary numbers are the digits 0 and 1.  Code for binary numbers is doubling one number starting with one and writing them in 0 or 1.  You see, trying binary numbers with cards make it easier.  We did it in class once.  First, our teacher made us cards that say 1,2,4,8, and 16.  Cards that are showing are 1.  Cards that are not are 0. Then our teacher, Mrs. Mak, said a number and we had to put the cards face-down if they did not equal to the number Mrs. Mak said.  For example, is all the cards were showing and we had to make the number 12, then we would flip over 16, 2, and 1 so that only numbers that are showing are 8 and 4 because if you add them together, you get 12.  So in binary, it would be 01100 You have to attend to precision when doing binary numbers."

4th grader:
"When we were learning about binary numbers, we were using math practice #7 "Look for and make use of structure."  We made use of structure when we made the binary patterns.  For example, one structure was the binary pattern which equaled 5.  Our cards were in this order (16, 8, 4, 2,1).  We turned over the 4 and the 1, so the pattern was 00101.  That is the math practice I used."

"When we learned the Cartesian coordinate system and played "Connect Four," we used math practice #7 which is "look for and make use of structure."  When we got four in a row, the structure might be horizontal, vertical or diagonal.  If it is vertical, the X-axis will be the same and the Y axis will increase.  For example, if the four-in-a-row coordinates are (3,1), (3,2), (3,3), and (3,4), the Y-axis increases, but the X-axis doesn't change.  If the four-in-a-row is horizontal, the X-axis will increase or decrease, but the Y-axis won't change.  Let's say the coordinates are (-5,-4), (-4,-4), (-3,-4), and (-2,-4).  The X-axis changes and the Y-axis doesn't."

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