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 bdruken@fullerton.edu , amarzocchi@fullerton.edu, mvanderveldt@fullerton.edu Evaluation code: 580460 Funding provided by Titan PRIDE and Titan EDUCATOR

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 handle @CAMathCouncil and hashtag #cmcmath @CAMathCouncil #cmcmath

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

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

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 
. @CAMathCouncil #cmcmath

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

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). @CAMathCouncil #cmcmath

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

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

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

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 bdruken@fullerton.edu , amarzocchi@fullerton.edu, mvanderveldt@fullerton.edu @CAMathCouncil #cmcmath

___ ___ ___ ___________ 580460 Strongly Disagree Agree 0 1 2 3 Send your text message to this Phone Number: 37607 poll code for this session Speaker was engaging and an effective presenter (0-3) Other comments, suggestions, or feedback (words) ___ ___ ___ ___________ 580460 (1 space) (1 space) (no spaces) Speaker was well-prepared and knowledgeable (0-3) Session matched title and description in program book (0-3) Example: 580460 323 Inspiring, good content Non-Example: 38102 3 2 3 Inspiring, good content Non-Example: 38102 3-2-3Inspiring, good content

Exit Question Slide Title What is one practical take-away you can try in your own practice next week? @CAMathCouncil #cmcmath

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

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