2023 Early Hearing Detection & Intervention Conference
March 5-7, 2023 • Cincinnati, OH
6/21/2017 | 3:15 PM - 4:00 PM | Can You Explain Why We Invert and Multiply? Building Conceptual Understanding for Division with Fractions | Hobble Creek
Can You Explain Why We Invert and Multiply? Building Conceptual Understanding for Division with Fractions
The Core Standards in Mathematics suggest various representations that can be used to build conceptual understanding of fractions in mathematics. These tools include physical objects, number lines, rectangular arrays, area models, fraction strips, and other visual models. In early grades, repeated subtraction is used to build conceptual understanding of division with integers. This strategy can also be used to build conceptual understanding of division with fractions using representational models. In this session, you will learn how to use repeated subtraction to build conceptual understanding of division of whole numbers, fractions and rational expressions (fractions with polynomials) using a variety of visual representations. Lesson plans and activities that have been used to increase conceptual understanding of fractions with struggling students in both middle school classes and in developmental algebra courses in college will be shared. By the end of the session, you’ll be able to explain WHY we invert and multiply!
- Participants will be able to use multiple representations to solve problems involving division with whole numbers, fractions, and rational expressions.
- Participants will understand the progression of division across grades/standards, and see that strategies and algorithms for division with whole numbers also work with division of fractions and rational expressions.
- Participants will be able to explain why "invert and multiply" works as a shortcut for dividing fractions.
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Presenters/Authors
Cathy Callow-Heusser
(), Utah State Office of Education, cathy.callow-heusser@schools.utah.gov;
Catherine Callow-Heusser received her doctorate in Educational Research and Evaluation from USU, where she has worked 20 of the past 30 years as an instructor, instructional designer and researcher/evaluator of programs serving struggling students and students with disabilities. Dr. Callow-Heusser served as Director of Developmental Mathematics at USU from 2013-2015 and has taught math at the middle and high school levels. She was principal investigator on a National Science Foundation (NSF) Math-Science Partnership (MSP) evaluation technical assistance grant and has served as a consultant on numerous NSF and Department of Education MSP grants. She also served as the external evaluator of the Bureau of Indian Education’s (BIE) Reading First, BIE READS! and Math Counts grants, and as a technical assistance provider and coach to many Bureau of Indian Education schools. She joined the Utah State Office of Education as an Education Specialist in 2015.
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