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Application�of �
subQuan to Algebra Please contact us if you wish for us to present this class via the internet directly into your classroom. Fee arrangements
made via professional development or grants.
![Page 3: Application of subQuan to Algebra: 3rd-8th grade and beyond](https://reader034.vdocument.in/reader034/viewer/2022052623/559cf8c01a28abda298b459e/html5/thumbnails/3.jpg)
Wha
t did
we
lear
n?
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Recognizing place shapes �in different bases. W
hat d
id w
e le
arn?
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Place Shapes Wha
t did
we
lear
n?
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3 cubes, 2 squares, 1 seg, 4 ones
Coined subQuan �to avoid ‘ordered organized subitizing’
base 5
Wha
t did
we
lear
n?
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Wha
t did
we
lear
n? Forms of subQuans
Standard Form
43537 Expanded Form +4(7)3 +3(7)2 +5(7)1 +3
Place Shape Form�4 Cubes, 3 Squares, 5 Segs, 3 Ones base 7 �
Word Form !four three five three base seven !
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Use place shapes to examine identical quantities
across bases.
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Quantity ten shown in five bases
146 = 137 = 12 8 = 119 = 10A
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Quantity hundred shown in three bases
144 8 = 1219 = 100A
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(8+2)2 = +1(8)2 +4(8)1 +4 = + 100 (9+1)2 = +1(9)2 +2(9)1 +1 = + 100 (10)2 = +1(A)2 +0(A)1 +0 = + 100
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13319 = 1000A
Quantity one thousand shown in two bases
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(9+1)3 = +1(9)3 +3(9)2 +3(9)1 +1 = + 1000 (10)3 = +1(A)3 +0(A)2 +0(A)1 +0 = + 1000
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146419 = 10000A
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146417 = 100008 (4,096)
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Use place shapes to examine identical subQuans
across bases.
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subQuan Metapattern:
+1(6)1 +0 = + 6 +1(7)1 +0 = + 7 +1(8)1 +0 = + 8 +1(9)1 +0 = + 9 +1(A)1 +0 = + 10 +1(x)1 +0 = + q
One ro
The first seg equation >
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subQuan Metapattern:
+1(6)1 +4 = + 10 +1(7)1 +4 = + 11 +1(8)1 +4 = + 12 +1(9)1 +4 = + 13 +1(A)1 +4 = + 14 +1(x)1 +4 = + q
One four
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subQuan Metapattern: +3(6)1 +5 = + 23 +3(7)1 +5 = + 26 +3(8)1 +5 = + 29 +3(9)1 +5 = + 32 +3(A)1 +5 = + 35 +3(x)1 +5 = + q
Three five
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Herman goes for a
jog.
+4(6)1 +3 = + 27 +4(7)1 +3 = + 31 +4(8)1 +3 = + 35 +4(9)1 +3 = + 39
+4(x)1 +3 = + q
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subQuan Metapattern: +1(7)2 +0(7)1 +0 = + 49 +1(8)2 +0(8)1 +0 = + 64 +1(9)2 +0(9)1 +0 = + 81 +1(A)2 +0(A)1 +0 = + 100 +1(x)2 +0(x)1 +0 = + q
One ro ro
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subQuan Metapattern: +1(7)2 +4(7)1 +6 = + 83 +1(8)2 +4(8)1 +6 = + 102 +1(9)2 +4(9)1 +6 = + 123 +1(A)2 +4(A)1 +6 = + 146 +1(x)2 +4(x)1 +6 = + q
One four six
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subQuan Metapattern: +3(7)2 +0(7)1 +5 = + 152 +3(8)2 +0(8)1 +5 = + 197 +3(9)2 +0(9)1 +5 = + 248 +3(A)2 +0(A)1 +5 = + 305 +3(x)2 +0(x)1 +5 = + q
Three ro five
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Complements = 13A 7A
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Is there another subQuan Metapattern?
+1(6)1 +1 = + 7 +1(7)1 +2 = + 9 +1(8)1 +3 = + 11 +1(9)1 +4 = + 13 +1(A)1 +5 = + 15
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subQuan metapattern: +2(6)1 -5 = + 7 +2(7)1 -5 = + 9 +2(8)1 -5 = + 11 +2(9)1 -5 = + 13 +2(A)1 -5 = + 15 +2(x)1 -5 = + q
Two, negative five!
Seg complements!
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subQuan the bridge data +1(6)1 +2 = + 8 +2(7)1 +2 = + 16 +3(8)1 +2 = + 26 +4(9)1 +2 = + 38
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+1(x)2 -5(x)1 +2 = + q
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Exit Exam
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What is the equa+on for this subQuan metapa4ern?
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What is the equa+on for this subQuan metapa4ern?
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What is the equa+on for this subQuan metapa4ern?
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This is one base of a subQuan metapa4ern. What is the equa+on for this metapa4ern?
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Any ques+ons? Let’s visit one of our educa+onal
sims in Second Life IF our technology is behaving and we
have +me.
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Application�of �
subQuan to Algebra Please contact us if you wish for us to present this class via the internet directly into your classroom. Fee arrangements
made via professional development or grants.
![Page 37: Application of subQuan to Algebra: 3rd-8th grade and beyond](https://reader034.vdocument.in/reader034/viewer/2022052623/559cf8c01a28abda298b459e/html5/thumbnails/37.jpg)
Next session:
Session 3: Differences & Calculus Saturday @ 8:30am Grand Pacific Pender North
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Ordered organized subitizing
ItOnlyTakes1.org
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"We are here" Visit us in Second Life to experience the full effect of 3D visualization.