Gaining A Deeper Understanding of Place Value
Dianna J. SpenceGregg VelatiniNorth Georgia College & State University
ClarificationThe exercises we introduce today
are
FOR YOU(not for your students!)
We do not expect (or recommend) that you use these Base 6 activities with your elementary students.
You may choose to do similar Base 10 activities with your students.
Why?“If not for our students, why do
them?”◦To strengthen your own…
…understanding of number systems …awareness of students’ perspectives &
challenges
“Why not just show us these activities in Base 10?”◦Because you know too much!◦Helpful (as a teacher) to experience lack
of familiarity and limitations similar to those of your students
Learning a Number SystemSuppose our hands looked like
this…
Imagine learning to count on your fingers
Finger Counting
ONE TWO
THREEFOUR
FIVE SIX
1 23
4
5 10
“TEN”
Help is on the way!Base Six Blocks
unit
rod
Counting with Blocks
1
=
2 3 4
510 11 12
13 14 15 20 21
Representing 2-Digit NumbersBuild these numbers with your
blocks*All numbers below are written in Base 624 51 40
35 55
What comes next?What is the next number after
45?
What is the next number after 55?
50
100
Base Six Blocks Revisited
unit rod flatcube1 10 1001000
“giant rod”10000
Representing 3-Digit NumbersBuild these numbers with your
blocks*All numbers below are written in Base 6204 120 134
325 152
Identifying NumbersWrite the number represented in
each picture (answers should be in Base 6).
Modeling Simple Addition
23+12
35
Modeling Addition with Trades
23+15
42
More Addition with Trades
42+34120
Practice: Addition
32+33
21+15
30+43
102+45
214+54
105 40 113
151 312
Modeling Simple Subtraction
45-2421
Modeling Subtraction with Trades
41-2413
Practice: Subtraction
52-33
21-15
50-43
103-45
200-54
15 2 3
14 102
Modeling Simple Multiplication
2×412
Modeling 2-Digit Multiplication
12×11132
Notice Partial Products:100 (flat)20 (rods at top)10 (rods at right)2 (units)
2-Digit Multiplication w/ Trades
14×21334
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