application of subquan to algebra: 3rd-8th grade and beyond
DESCRIPTION
NWMC12 3-8 presentation demonstrating the visual link of subQuan understanding and Algebra. Looks at the forms of numbers as seen on our website @ dreamrealizations.orgTRANSCRIPT
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.
Wha
t did
we
lear
n?
Recognizing place shapes �in different bases. W
hat d
id w
e le
arn?
Place Shapes Wha
t did
we
lear
n?
3 cubes, 2 squares, 1 seg, 4 ones
Coined subQuan �to avoid ‘ordered organized subitizing’
base 5
Wha
t did
we
lear
n?
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 !
Use place shapes to examine identical quantities
across bases.
Quantity ten shown in five bases
146 = 137 = 12 8 = 119 = 10A
Quantity hundred shown in three bases
144 8 = 1219 = 100A
(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
13319 = 1000A
Quantity one thousand shown in two bases
(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
146419 = 10000A
146417 = 100008 (4,096)
Use place shapes to examine identical subQuans
across bases.
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 >
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
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
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
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
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
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
Complements = 13A 7A
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
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!
subQuan the bridge data +1(6)1 +2 = + 8 +2(7)1 +2 = + 16 +3(8)1 +2 = + 26 +4(9)1 +2 = + 38
+1(x)2 -5(x)1 +2 = + q
Exit Exam
What is the equa+on for this subQuan metapa4ern?
What is the equa+on for this subQuan metapa4ern?
What is the equa+on for this subQuan metapa4ern?
This is one base of a subQuan metapa4ern. What is the equa+on for this metapa4ern?
Any ques+ons? Let’s visit one of our educa+onal
sims in Second Life IF our technology is behaving and we
have +me.
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.
Next session:
Session 3: Differences & Calculus Saturday @ 8:30am Grand Pacific Pender North
Ordered organized subitizing
ItOnlyTakes1.org
"We are here" Visit us in Second Life to experience the full effect of 3D visualization.