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# Math

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by

## Jonathan Menzin

on 22 January 2014

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#### Transcript of Math

Flexible Problem Solving by
Jon Menzin

"There are many ways to solve math problems"
"How else could you solve the same problem?"
Multiplication
4583 x 3792
Multiplication
Lattice
"Math is creative and innovative expression"
Subtraction
using manipulatives
"See if you can figure out another way to solve the same problem"
Subtraction
26 + 37
20
6
30
7
50
13
Decomposing & recomposing
Tree model
26 + 37
26
30
+4
30 + 37 = 67
67
Shifting method
-4
346 - 188
346
-
188
3
4
6
1
8
8
2
16
13
=
8
5
1
= 158
188
200
+12
346 - 200 = 146
146
+12
= 158
Left-to-right partial differences
346
- 188
200
-40
-2
=158
+
+
"There is almost always more than one way to solve a mathematics problem"
Multiplication
"Students should not just be memorizing past methods; they need to engage, do, act, perform, and problem solve."
Division
Math is "a powerful way of expressing relationships and ideas in numerical, graphical, symbolic, verbal, and pictorial forms. "
Division
Fractions
4 2/5 + 3 1/6
The Generic Rectangle model
4000
500
80
3
3000
700
90
2
12,000,000
2,800,000
360,000
8,000
1,500,000
350,000
45,000
1,000
240,000
9,000
56,000
7,200
160
2,100
270
6
11,376
296,000 + 7,360
1,896,000
14,800,000 + 368,000
15,168,000
2,199,360
17,368,000 - 640
17,379,376 - 640
17,378,000 + 1,376 - 640
17,378,000 + 736
=17,378,736
4
5
8
3
3
7
9
2
4583 x 3792
6
2
7
2
1
9
1
6
7
2
5
6
2
4
1
5
3
5
4
5
1
0
8
3
6
2
8
1
2
6
3
7
8
7
3
7
1
= 17,378,736
"Math allows you to investigate problems from a variety of perspectives."
4583
x 3792
Left-to-right
Partial Products method

12000000
1500000
240000
9000
2800000
350000
56000
2100
360000
45000
7200
270
8000
1000
160
6
6
3
7
8
7
3
7
1
6256 94
Generic Rectangles
6000
256
94
63 R78
2 R68
63 R78 + 2 R68 = 65 R146
65 R146 = 66 R52
94 x 2 = 188
256 - 188 = 68
94 x 60 = 5640
6000 - 5640 = 360
94 x 3 = 282
360 - 282 = 78
Partial Quotients
"People do not need to regurgitate hundreds of standard methods. They need to reason and problem solve, flexibly applying methods in new situations."
"Long and complicated problems...encourage persistence, a critical trait for young people to develop that will stand them in good stead in life and work."
6256 94
94
6256
Math facts for 94
94 x 10 = 940
94 x 20 = 1880
94 x 40 = 3760
94 x 50 = 4700
4700
50
1556
940
10
616
94 x 5 = 470
470
5
146
94
1
52
66 R52 = 66 52/94 = 66 26/47
66 R52 = 66 52/94 = 66 26/47
63
= 63
"Did anyone solve the problem a different way?"
346 - 188
using the Shifting method
Subtraction
2 8/9 - 1/3
3 5/9 x 2/7
5 2/7
7
= 7 17/30
3
3 - 1/3 = 2 2/3
3
5/9
2/7
6/7
10/63
6/7 + 10/63
54/63 + 10/63
= 64/63
= 1 1/63
"Children need to...use, adapt, and apply standard methods, as well as to make connections between methods and to reason mathematically."
Division
6256 94
47
3128
Math facts for 94
94 x 10 = 940
94 x 20 = 1880
94 x 40 = 3760
94 x 50 = 4700
1880
40
1248
940
20
308
94 x 5 = 470
235
5
73
47
1
26
66 R26 = 66 26/47
Equivalent Problems
=
3128 47
Cut in half
Cut in half
Math facts for 47
47 x 20 = 940
47 x 40 = 1880
47 x 10 = 470
Partial
Quotients
47 x 5 = 235
Math "requires creativity, original thinking, and ingenuity."
Generic Rectangles
Shifting
+1/9
2 2/3
-1/9
2 6/9 - 1/9
= 2 5/9
How many 2/7 are there in 5?
Count the number of 2/7's, shown as pairs of like-colored stars
6 Blue + 6 Yellow + 5 Red = 17
Remainder: 1 Red star = 1/2 pair = 1/7
5 2/7 = 17 R1/7 = 17 1/2
Draw a picture
Decomposing
12/30
5/30
17/30
Full transcript