Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University

Clarification The 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 System Suppose our hands looked like this… Imagine learning to count on your fingers

Finger Counting ONETWO THREE FOUR FIVESIX “TEN”

Help is on the way! Base Six Blocks unit rod

Counting with Blocks 1 =

Representing 2-Digit Numbers Build these numbers with your blocks *All numbers below are written in Base

What comes next? What is the next number after 45? What is the next number after 55?

Base Six Blocks Revisited unit rodflat cube “giant rod” 10000

Representing 3-Digit Numbers Build these numbers with your blocks *All numbers below are written in Base

Identifying Numbers Write the number represented in each picture (answers should be in Base 6).

Modeling Simple Addition

Modeling Addition with Trades

More Addition with Trades

Practice: Addition

Modeling Simple Subtraction

Modeling Subtraction with Trades

Practice: Subtraction

Modeling Simple Multiplication 2 ×4 12

Modeling 2-Digit Multiplication 12 × Notice Partial Products: 100 (flat) 20 (rods at top) 10 (rods at right) 2 (units)

2-Digit Multiplication w/ Trades 14 ×21 334