1. Caldwell School District Elementary Session
DMT Project
Dr. Jonathan Brendefur
Dr. Kim Bunning
Sam Strother

2. Division With an Eye on the Horizon
After Andrews Middle School is built, it will hold 609 students. Each classroom must have 29 students. How many classrooms does the school need? (1,046 students, 26 in a class)

3. Solve and Mentally Record Your Thinking
420 ÷ 30
6 ÷ 1/3
2.8 ÷ 2
2.8 ÷ .2

4. Division & Fractions Based on the work of Martin Simon, PhD
Presented at PME-NA Conference 2007
New York University

5. Draw a diagram that models this problem
There is 7/8 of a cake. Each friend needs 1/8 of a cake. How many friends can share the cake?

6. Draw a diagram that models this problem
You are going diving. You have 2 tanks of air. Each dive takes 3/8 of a tank. How many dives can you complete?

7. Explain how you would draw a diagram to model this problem
12/25 yards of fabric are in the store. Each doll dress takes 4/25 yards of fabric. How many dresses can be made?

8. How would you create a diagram to solve this problem?
9/167 ÷ 3/167

9. How would you draw a diagram to model this problem?
9/103 ÷ 3 /103
Try the same thinking for this problem:
10/103 ÷ 3/103

10. Big Ideas: Teaching Strategies
Diagrams (models)
“Mental Run” or explanation (how would you make a diagram)
Abstraction and/or Generalization

11. Big Ideas: Instruction
Students should understand and learn whole numbers in a way that supports their understanding of fractions, decimals, percents, ratios and proportional thinking
Students should understand and learn whole numbers in a way that supports their understanding of algebra (i.e. generalizing)

13. 1 10
100
(102)
1,000
(103)

14. X2 1 X X3

16. Part-Part-Whole: Whole Unknown Part-Part-Whole: Part Unknown PPW: PU
Fractions in K-1
Part-Whole: Part Unknown Problems
Part-Part-Whole: Whole Unknown
PPW:WU
Part-Part-Whole: Part Unknown PPW: PU
Lindsey has 14 green markers and 12 yellow markers How many markers does she have in all?
Lindsey has 26 markers. 14 are green and the rest are yellow. How many are yellow?

17. Fractions in K-1 Packaging and Filling (Base-10 problems)
Seeds come in packs of 5. If you have 12 seeds, how many packs can you fill?
Seeds come in packs of 10. If you have 37 seeds, how many packs can you fill?
Each van holds 10 kids. How many vans are needed to carry 45 kids?

18. Fractions in K-1 Sharing and Ratios
6 friends want to share 12 cookies. How many cookies does each friend get?
3 kids can make 4 posters. How many posters can 6 kids make? 8 kids?

19. Fractions in K-1 Iterating and Partitioning
If this piece, , is½ what would 1 whole look like?
Find a way to fold a piece of paper into 4 equal parts….8 equal part…3 equal parts….6 equal parts….5 equal parts

20. Common Models for Fractions
Bar, Rectangle, Tape, Ribbon
Set 2
Linear
1/2
Area or Region

21. Division in K-1 Use problems similar to the fraction problems
Use multiplication and division simultaneously
Don’t emphasize notation…only problem solving and modeling
Label pictures with numbers

22. Multiplication and Division
(Groups of Members=?)
Measurement Division
(? of Members=Total)
Partitive Division
(Groups of ?=Total)
4 cars each have 6 students in them. How many students are there in all ?
24 students need to ride to the field trip with 6 students in a car. How many cars will be needed?
24 students need to ride in 6 cars with the same number of students in each car. How many students will be in a car?

23. Contact Sam Strother DMT Project boise.schoolfusion.us