1. Station Teaching in Action: Unpacking the Meaning of Fraction
Slide Title
Station Teaching in Action: Unpacking the Meaning of Fraction
Bridget Druken, Ph.D., Dept. of Mathematics
Alison Marzocchi, Ph.D., Dept. of Mathematics
Michelle VanderVeldt Brye, Ph.D., Dept. of Elementary and Bilingual Education
California State University, Fullerton Brye, Michelle ,
Evaluation code:
Funding provided by Titan PRIDE and Titan EDUCATOR

2. Station Teaching in Action: Unpacking the Meaning of Fraction
Slide Title
Station Teaching in Action: Unpacking the Meaning of Fraction
When talking about our session on social media, please use the CMC twitter and hashtag #cmcmath
@CAMathCouncil #cmcmath

3. Slide Title Background Who Are We?
Alison, former high school teacher now assistant professor of mathematics education in CSUF math dept, teaches math content courses and credential courses, supervises single subject teacher candidates
Bridget, assistant professor of mathematics education in CSUF math dept, teaches math content courses and supervises single subject teacher candidates
Michelle, former elementary teacher now associate professor in CSUF elementary and bilingual education dept, teaches credential courses for multi-subject program and supervises multi-subject teacher candidates
@CAMathCouncil #cmcmath

4. Slide Title Motivation Where did this lesson idea come from?
Presented with funding opportunity from Titan PRIDE & Titan EDUCATOR for facilitating collaboration between math methods and content CSUF faculty
Resulted from lesson study between math content and math methods course instructors at CSUF
Iterated it five times; this is the sixth
Wanted to better understand CCSS fraction progression on meaning of fractions and a co-teaching strategy - station teaching
@CAMathCouncil #cmcmath

5. Slide Title Targeted CCSS Fraction Standards Meaning of fractions
a. Same sized pieces (Partitioning and shape vs. value): Understand the fraction 1/b as the quantity formed by 1 part when the whole is partitioned into b equal parts (3.NF.A.1). Recognize that equal shares of identical wholes need not have the same shape (2.G.A.3).
b. Iterating unit fractions: Understand the fraction a/b as the quantity formed by a parts of size 1/b (3.NF.A.1).
In other words, a indicates the number of copies of the unit fraction 1/b 
.
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6. Slide Title Targeted CCSS Fraction Standards
2. Different representations of fractions
Understand three diagram models for representing rational numbers: linear, area, and discrete (3.NF.A.2).
In other words, the whole can be a line segment, a shape (circle, rectangle, etc.), or a collection of objects or any one finite entity susceptible to subdivision and measurement
@CAMathCouncil #cmcmath

7. Slide Title Targeted CCSS Fraction Standards 3. Specifying the whole
Understand that the value of a fraction is dependent on the whole. In other words, the size of the pieces depends on the referent whole.
For example, the fraction ½ can be placed between 0 and 1 on a number line, and is different than finding ½ of a number (½ of 2, for instance).
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8. Slide Title Activity: Rotate Among Three Stations
Number Line Station (15 min.)
 Given two numbers, place a third!
Geoboards Station (15 min.)
 Prove you have fourths!
Counting Bears Station (15 min.)
 Determine how many bears in a family!
Q: When did you engage in each of the learning goals? What are benefits and limitations of station teaching?
@CAMathCouncil #cmcmath

9. Slide Title Group Discussion
Where did you engage in these learning goals? Be specific.
Learning Goal
Number Line
Geoboards
Counting Bears
1a. Meaning: same-sized pieces
Same size pieces don’t have to look exactly the same
Same equal groups (how many in each group // equal in a different way)
1b. Meaning: iterating unit fractions
Iterate unit fraction as accurately as possible (denom is size, numerator is # of pieces)
Iterate unit fractions to figure out whole
2. Different representations
linear
Area model
Set / discrete objects
3. Specifying the whole
The whole was 0 to 1
The whole matters! 1/2 of 1 not equal to ½ of 2.
@CAMathCouncil #cmcmath

10. Slide Title Benefits/Limitations of Station Teaching
Turn-and-talk to your pod: What are the benefits of station teaching for teaching math? Limitations? Be specific.
Benefits
Limitations
Get up and move around
Manipulatives for all!
Affordability of manipulatives
Fosters collaboration
Can be used in many ways – different concepts
Maximizing on time (fit more into a lesson)
Capitalize on the number of teacher
Be careful about the size of the groups and the makeup  careful grouping!
What if there’s only one teacher??
@CAMathCouncil #cmcmath

11. Thank You! Questions?
Questions about this station teaching lesson or lesson study? Feel free to contact us!
If interested in hearing more, we will be at AMTE in Orlando, FL and NCTM in San Antonio, TX. Feel free to come or refer-a-friend!
Funding provided by Titan PRIDE and Titan EDUCATOR.
Bridget Druken, Ph.D., Dept. of Mathematics
Alison Marzocchi, Ph.D., Dept. of Mathematics
Michelle VanderVeldt Brye, Ph.D., Dept. of Elementary and Bilingual Education
California State University, Fullerton Brye, Michelle ,
@CAMathCouncil #cmcmath

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13. Exit Question
Slide Title
What is one practical take-away you can try in your own practice next week?
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14. Slide Title Group Discussion
Where can you find evidence of each learning goal?
Learning Goal
Number Line
Geoboards
Counting Bears
1a. Meaning: same-sized pieces
Unit fractions need to be partitioned into same-sized pieces (e.g thirds are all equal lengths)
Same-sized value (fourths) not necessarily congruent shapes
Partition numerator up into that many groups to find size of each unit fraction
1b. Meaning: iterating unit fractions
Find ¼ of 1 and iterate (copy and paste) to 7/4
Four fourths make a whole
Find 1/3 of a family to iterate (copy and paste) to 8/3 of a family
2. Different representations
linear
area
discrete
3. Specifying the whole
The whole is the unit interval 0 to 1
The whole is the 4x4 grid
The whole is a family, which changes in size

15. Slide Title Benefits/Limitations of Station Teaching
What are the benefits of station teaching for teaching math? Limitations? Be specific.
Benefits
Limitations
Increased student engagement with manipulatives,
affordability of manipulatives,
capitalizing on more than one adult in room,
lowered student-to-teacher ratio,
More ‘noise’
Teacher can only monitor one station at a time
If limited # of teachers, students must be able to facilitate stations on their own (counting bears)
@CAMathCouncil #cmcmath