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Progressing from Fair Sharing to Unit Fractions
Progressing from Fair Sharing to Unit Fractions
Unit fractions form the basis of all fractions. Any fraction can be represented or decomposed using unit fractions. Previously, teaching strategies and curriculum documents have largely ignored the role of unit fractions as the foundation to understanding fraction concepts. Representations that support the understanding of fractions with units have been minimally leveraged. Unit fraction learning can be found in the new math curriculum across the grades, up to and including Grade 9.
Using tools and representations, such as fraction strips, number lines, pattern blocks and relational rods, helps students develop their understanding concretely. Once students can see, and understand how fractions are broken down, it is easier for them to move to representational (pictorial) models, and eventually to abstract thinking.
Concrete, Representational, Abstract Model (CRA)
Concrete, Representational, Abstract Model (CRA)
The Concrete, Representational, Abstract (CRA) Model helps to structure an inclusive learning environment that can help to eliminate potential learning barriers or learning obstacles for students who have not yet developed a deep enough understanding of fraction concepts to work strictly in abstract concepts, manipulating algorithms. Used effectively, tools and representations not only make math concepts accessible to a wide range of learners but also give educators insight into students’ thinking. Because tools and representations draw on spatial reasoning and build “beyond language bridges”, they can be useful when teaching linguistically diverse students or students with special education needs.
Teachers are encouraged to use classroom or virtual manipulatives to allow students the opportunity to see the concepts as we teach fractions. It is also worth noting that the assessment questions and deliberate practice that can be found in Knowledgehook, are also structured using the CRA model. In the predeveloped questions and activities, concepts begin with a more structured concrete question, representational (pictorial) question types and into more abstract questioning.
How Tools and Representations support our focus on Think Alouds
How Tools and Representations support our focus on Think Alouds
Carefully chosen tools and representations provide a way for students to think through problems and communicate their thinking. When paired with discussion, they help demonstrate concepts and thinking. Visual representations provide an opportunity to talk about math, to examine mathematical relationships and to make the problem-solving process visible. Connections between the representations and the relevant mathematical ideas must be made explicitly, since the mathematical ideas are not in the representations themselves, but rather in students’ thinking about the mathematics.
Students who represent mathematical ideas in a variety of ways demonstrate a deeper understanding of these concepts, as each representation provides a different perspective. Similarly with Number Talks, opportunities for students to see and listen to a variety of perspectives provide for deeper understanding of concepts.
Quick Reference chart - Ontario Math Curriculum
Quick Reference chart - Ontario Math Curriculum
Math Curriculum Quick Reference Sheet 1.pdfMath Curriculum Quick Reference Sheet 2.pdfPage updated
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