Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College...
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Transcript of Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College...
![Page 1: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/1.jpg)
Gaining A Deeper Understanding of Place Value
Dianna J. SpenceGregg VelatiniNorth Georgia College & State University
![Page 2: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/2.jpg)
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.
![Page 3: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/3.jpg)
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
![Page 4: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/4.jpg)
Learning a Number SystemSuppose our hands looked like
this…
Imagine learning to count on your fingers
![Page 5: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/5.jpg)
Finger Counting
ONE TWO
THREEFOUR
FIVE SIX
1 23
4
5 10
“TEN”
![Page 6: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/6.jpg)
Help is on the way!Base Six Blocks
unit
rod
![Page 7: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/7.jpg)
Counting with Blocks
1
=
2 3 4
510 11 12
13 14 15 20 21
![Page 8: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/8.jpg)
Representing 2-Digit NumbersBuild these numbers with your
blocks*All numbers below are written in Base 624 51 40
35 55
![Page 9: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/9.jpg)
What comes next?What is the next number after
45?
What is the next number after 55?
50
100
![Page 10: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/10.jpg)
Base Six Blocks Revisited
unit rod flatcube1 10 1001000
“giant rod”10000
![Page 11: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/11.jpg)
Representing 3-Digit NumbersBuild these numbers with your
blocks*All numbers below are written in Base 6204 120 134
325 152
![Page 12: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/12.jpg)
Identifying NumbersWrite the number represented in
each picture (answers should be in Base 6).
![Page 13: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/13.jpg)
Modeling Simple Addition
23+12
35
![Page 14: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/14.jpg)
Modeling Addition with Trades
23+15
42
![Page 15: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/15.jpg)
More Addition with Trades
42+34120
![Page 16: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/16.jpg)
Practice: Addition
32+33
21+15
30+43
102+45
214+54
105 40 113
151 312
![Page 17: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/17.jpg)
Modeling Simple Subtraction
45-2421
![Page 18: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/18.jpg)
Modeling Subtraction with Trades
41-2413
![Page 19: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/19.jpg)
Practice: Subtraction
52-33
21-15
50-43
103-45
200-54
15 2 3
14 102
![Page 20: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/20.jpg)
Modeling Simple Multiplication
2×412
![Page 21: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/21.jpg)
Modeling 2-Digit Multiplication
12×11132
Notice Partial Products:100 (flat)20 (rods at top)10 (rods at right)2 (units)
![Page 22: Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University.](https://reader038.fdocuments.us/reader038/viewer/2022110206/56649d0e5503460f949e36c5/html5/thumbnails/22.jpg)
2-Digit Multiplication w/ Trades
14×21334