FRACTIONS AND PROPORTIONAL REASONING IN KINDERGARTEN Natalie Ceccarelli Cari Potter Mikaela Humphreys

BUT WAIT THERE’S NO STANDARDS! de.aspx?sid=15http://ies.ed.gov/ncee/wwc/practicegui de.aspx?sid=15  Children can start learning about fractions from an early age – at a concrete level.  In kindergarten, students are learning to divide whole shapes and numbers into equal parts.  While students don’t directly learn about fractions, teachers lay the foundation for these skills later on.

FOUNDATIONAL STANDARDS IN KINDERGARTEN  Students begin to understand the concept of part-part-whole relationships as they learn about addition and subtraction.  CCSS.MATH.CONTENT.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. CCSS.MATH.CONTENT.3.NF.A.1  As students transition to learning about fractions in 3 rd grade, the emphasis begins with a focus on partitioning into equal parts, a foundational skill learned in kindergarten.  Students begin practicing fractions with physical manipulatives like food or realia in order to gain a concrete understanding.  Limited vocabulary like halves and whole are used instead of “1/8 th ” and “sixths”. CCSS.MATH.CONTENT.K.OA.A.2 CCSS.MATH.CONTENT.K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. CCSS.MATH.CONTENT.K.OA.A.3 CCSS.MATH.CONTENT.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1). CCSS.MATH.CONTENT.K.G.B.6 CCSS.MATH.CONTENT.K.G.B.6 Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?"

FRACTIONS AND MANIPULATIVES MIKAELA  Students form strong connections to the materials and tools they are taught with when a concept is first introduced.  Some of the complex ideas can be easier for students to understand through virtual manipulatives.  Physical manipulatives alike help students form concrete understanding of the idea of breaking a “whole” in equal parts and portioning equal pieces.  Using manipulatives consistently for non- fractional activities helps students gain understanding of numbers and number sense so they are better prepared when they are formally introduced to fractions.

2D SHAPES AND PROPORTIONAL THINKING CARI In Kindergarten, students are continually doing tasks, which will help develop the underlying concepts associated with fractions and some suggestions for models and images that help support ideas around fractions for primary grades. Standard: K.G.6. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rhombus?” “Can you join three triangles to make a trapezoid?

PROPORTIONAL FOUNDATIONAL SKILLS NATALIE Students come to kindergarten with a rudimentary understanding of basic fraction concepts. They can share a set of objects equally among a group of people and identify equivalent proportions of common shapes. Although fractions are typically introduced in first or second grade, there are activities that can be introduced in kindergarten which allow students to build on what they already know. These activities include equal sharing and proportional reasoning. Use equal-sharing activities to introduce the concept of fractions. Use sharing activities that involve dividing sets of objects as well as single whole objects: Splitting cookies evenly between children, using multiple shapes to build a whole shape. Covariation: When one quantity increases, another quantity increases. Examples include relationships between height and clothing size or foot length and shoe size. Patterns: Used as a fundamental approach to ratios. For example, in a pattern discuss how many triangles there are for each square. Proportional Reasoning: Balancing a seesaw or discussing the solution of a lemonade solution.

REFERENCES Boggan, M., Harper, S., Whitmire, A. (2010). Using manipulatives to teach elementary mathematics. Journal of Instructional Pedagogies, 3(1), 1-6. Brizuela, B. (2005). Young children’s notations for fractions. Educational Studies in Mathematics, 62(3), Cavalluzzo, L., Geraghty, T.M., steele, J.L., Holian, L., Jenkins, F., Alexander, J.M., & …CNA, C. (2014). “Using Data” to inform decisions: How teachers use data to inform practice and improve student performance in mathematics. Results from a Randomized Experiment of Program Efficiancy. CNA Corporation, Goodwin, K. (2008). The impact of interactive multimedia on kindergarten students' representations of fractions. Issues in Educational Research, 18(2), Lopez-Charles, Grace. "Teaching fractions with understanding: part-whole concept." NRICH (2011). Print. Pennant, J., & Woodham, L. (2013, November). Understanding Fractions. Retrieved January 25, 2016, from Pitta-Pantazi, D., & Christou, C. (2011). The Structure of Prospective Kindergarten Teachers' Proportional Small, M. (2014). Uncomplicating fractions to meet common core standards in math, K-7. New York, NY: Teachers College Press. Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., &... What Works Clearinghouse, (. (2010). Developing Effective Fractions Instruction for Kindergarten through 8th Grade. IES Practice Guide. NCEE What Works Clearinghouse.