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## Math 228 Week Three Notes

by: Erika De Leygraaf

3

0

7

# Math 228 Week Three Notes 228

Erika De Leygraaf
UWSP
GPA 3.6

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These notes cover everything from week 3.
COURSE
The Teaching of Elementary School Math
PROF.
Sinan Kanbir
TYPE
Class Notes
PAGES
7
WORDS
CONCEPTS
Math, Teaching, notes
KARMA
25 ?

## Popular in math education

This 7 page Class Notes was uploaded by Erika De Leygraaf on Friday September 23, 2016. The Class Notes belongs to 228 at University of Wisconsin - Stevens Point taught by Sinan Kanbir in Fall 2016. Since its upload, it has received 3 views. For similar materials see The Teaching of Elementary School Math in math education at University of Wisconsin - Stevens Point.

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Date Created: 09/23/16
9/19/16  What We Discussed:  ­ Magic Squares  ­ All rows, columns, and diagonals  must equal the same value  ­ Example w/ Blank 3x3 Square  ___ ___ ___ 1­9  ___ ___ ___ 1+2+...+8+9=(9*10)/2  ___ ___ ___ (9*10)/2=45 45/3=​15    Each row, column, diagonal must equal 15.  9+​5​+1=15 8​ ​ 1=15 8​ ​​ 3=15 7+​ ​​​ 15  9+​4​​ ​=15 8​​ ​​ 15 7+​5​+3=15 6​+​ ​4​=15    5​ → can go into 4 different equations  The middle number is in 4 equations.  2​​ ​,​ ​8​ → can go into 3 different equations  The corner numbers are in 3 equations.  5+2+8=15 (needs to be a diagonal)  5+4+6=15 (needs to be a diagonal)    Fill In the Rest: easiest to fill in by row  2+7+6=15 (needs to be the top row)  9+5+1=15 (needs to be the middle row)  4+3+8=15 (needs to be the bottom row)  Check: by columns  2+9+4=15 7+5+3=15 6+1+8=15  2 7 6  9 5 1  4 3 8    ­ Example w/ Partial Filled 4x4 Square   16  3  2  13 1­16   5  10 ___  8   9 ___ ___  12  ___  15  14 ___    The first row is completely filled in.  16+3+2+13=​34  Each row, column, diagonal must equal 34.    Fill In the Rest:  16+5+9+​4​=34 By Column  3+10+​6​ 15=34   2+​1​ ​​ 14=34     13+8+12+1​​ 34 **OR**    5+10+​11​+8=34  9+​ ​​ 12=34 By Row  4​+15+14+​1​=34    Check: by diagonals  4​+​6​+​11​+13=34  16+10+​​ ​1​=34    16 3 2 13  5 10 11 8  9 6 7 12  4 15 14 1  ­ Example w/ Partial Filled 3x3 Square  (does not have a set range of numbers)   17 ___ ___   12  22 ___  ___ ___  27    One diagonal is completely filled in.  17+22+27=​66  Each row, column, diagonal must equal 66.    Fill in the Rest:  17+12+​37​=66 By Column  42​+22+​ ​=66   7​+​32​+27=66 **OR**    7​+22​ 7​=66 By Diagonal      Check by: Rows  17+​ 2​+​7​=66  12+22+​32​=66  37​+​2​+27=66    17 42 7  12 22 32  37 2 27   ­ Solution to Handshake Problem  4 students each give each other a  handshake. How many handshakes total?  n=the number of students    1&2 1&3 1&4 #1: ​3​ handshakes  2&3 2&4 #2: ​2​ additional handshakes  3&4 #3&4: ​1​ additional handshake    3+2+1 or (4­1)!=3!  Total of 6 handshakes. Solution: (n­1)!    Bigger number: n=17 (simplier solution)  1+16=17 2+15=17 3+14=17 4+13=17 5+12=17 6+11=17 7+10=17 8+9=17    8 pairs → 16/2=8 or (n­1)/2    17*8=136 or (16*17)/2 and 16!=136  Total 136 handshakes. Solution: [n*(n­1)]/2    Assignments:  ­ WebAssign Assignment #1  ­ Due: 9/21/16        9/20/16  What We Discussed:  ­ Problem Solving  ­ Explanation addresses the question  ­ Each step is correct and makes sense  ­ Explanation can be easily explained  to peers  ­ Key points are emphasized  ­ Contains supporting pictures,  diagrams, and equations when needed  ­ Place­Value­Based Problems  ­ Solution for #1  53284 → 26264 50,000 → 20,000 → ­30,000  3,000 → 6,000 → +3,000  80 → 60 → ­20  ­30,000+3,000­20=­27,020  ­ Solution for #3  49039 → 57364 40,000 → 50,000 → +10,000  9,000 → 7,000 → ­2,000  000 → 300 → +300  30 → 60 → +30  9 → 4 → ­5  10,000­2,000+300+30­5=8,325  Assignments:  ­ Place­Value­Based Worksheet  9/23/16  What We Discussed:  ­ Inductive vs Deductive Reasoning  ­ ab+ba → a=1 digit #, b=1 digit #  ­ Inductive Reasoning  ­ 15+51=66  ­ 39+93=132  ­ Multiples of 11  ­ (a+b)*11  ­ Deductive Reasoning  ­ 10*a+b+10*b+a  ­ 11a+11b  ­ 11(a+b)  ­ ab­ba → a=1 digit #, b=1 digit #  ­ Inductive Reasoning  ­ 51­15=36  ­ 93­39=54  ­ 21­12=9  ­ Multiples of 9  ­ (a­b)*9  ­ Deductive Reasoning  ­ (10*a+b)­(10*b+a)  ­ 10a+b­10b­a  ­ 9a­9b  ­ 9(a+b)

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