gaining a deeper understanding of place value

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