1. Marilyn Burn’s Fraction Kit MathSolutions.com
A kit like this should not be used as a “unit” but as something that is systematically used throughout a year or several years. Students understanding builds as you use the fraction kits to support understanding for more and more complicated issues involving fractions. By using this kit systematically (say every Friday) you build a deep connection for this kids and with the kids that you can use to discuss fractions in a meaningful and concrete way.
First thing you do is have the students cut the strips.
You have a blue whole
2 reds that are a whole
8 purples that are a whole
16 browns that are a whole
Discuss writing fractional names versus not putting fractional names on strips.
Burns recommends putting the fraction names on there.
I recommend NOT putting fractional names because I want students to internalize the names through making sense of the reasoning rather than memorizing the names through association. The lessons we have learned from Number Worlds that students actually understand number more deeply when they learn it NOT through memorization and mere association but through DEEP understanding of the concepts, tips me in the direction of letting the association come from understanding. Also allows you to have that conversation more often with students where you point to a strip and say “ what fraction is that? How do you know?” and get the kid to SHOW you why 1/8 is 1/8 or why ¼ is ¼.
Different games developed by Marilyn Burns.

2. Marilyn Burn’s Fraction Kit

3. How are your teachers teaching fractions?

4. Manipulatives and “Magical Hopes” Deborah Ball
1/6 + 1/6 = 2/6
Or is this 1/6 + 1/6 = 2/12? How do you explain this to a student?

5. Lee Stiff’s Fraction Squares
¾ /3
We’ve got a problem in this form—
need the same size pieces to add things…

6. ¾ + 1/3 9/12 + 4/12 Chop up the vertical by the horizontal
¾ /3
9/ /12
Chop up the vertical by the horizontal
and the horizontal by the vertical:
Don’t change the value, just the piece size

7. Problem #3 Division of Fractions
1 ¾ divided by ½
Give a Story Problem to show what is happening with this expression

8. Division of Fractions 2 1 Quantity Symbols Mathematical Structure
Concrete display of concept
Symbols
Simply record keeping!
Mathematical Structure
Discussion of the concrete
V. Faulkner and NCDPI Task Force adapted from Griffin

9. Division as Repeated Subtraction
Bean Party!

10. Division of fractions: measurement model
E How many ½ cups would go into a
1 ¾ cup container?
How many ½ cup scoops?
How many ½ cup servings?
½ of a ½
1 3/4
1/2 1
1/2
1/2

11. Structure 3 types of division 10/2
Measurement/Repeated Subtraction
“how many 2s can I get out of 10”
Partitive/Unitizing/Fair Shares “how many would 1 person get? Or “what would that mean in relation to 1?”
Product/Factor “If I have an area of 10 and one side is 2, how long is the other side?”
If I have 10 cups of beans and I give out 2 cup portions, how many servings will that provide? 2 10 2 ? 2 2 2
If 2 people find $10 how much will each person get ? ? 10 ? 5 10 ?
Division types adapted from Ma, Knowing and Teaching Elementary Mathematics, 1999

12. STRUCTURE: Division as Repeated Subtraction2 1
Why does the equal value “get bigger”?
Division as repeated subtraction
2 ½ / ½
Quantity:
Concrete display of concept
Verbal:
Discussion of the concrete
Symbols
Simply record keeping!
V. Faulkner and DPI Task Force adapted from Griffin