application of subquan to algebra: 3rd-8th grade and beyond

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.

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Recognizing place shapes �in different bases. W

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Place Shapes Wha

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3 cubes, 2 squares, 1 seg, 4 ones

Coined subQuan �to avoid ‘ordered organized subitizing’

base 5

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Wha

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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

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