![]() Letting fraction algorithms emerge through problem solving. Extending children’s mathematics: Fractions and decimals: Innovations in cognitively guided instruction. Australian Mathematics Teacher, 62, 28-40.Įmpson, S. Algebra students’ difficulty with fractions: An error analysis. In these examples, students use models to addīrown, G., & Quinn, R. The following two examples help us to see how student strategies for adding fractions can build from intuitions and familiarity with whole number operations. Several studies have shown “that if children are given the time to develop their own reasoning for at least three years without being taught standard algorithms for operations with fractions and ratios, then a dramatic increase in their reasoning abilities occurred, including their proportional thinking” (Brown & Quinn, 2006, p. By focusing on sense-making early on, rather than memorization of an algorithm, students will be able to extend this learning into algebraic contexts in secondary and post-secondary studies (Brown & Quinn, 2006 see also Wu, 2001) and build fluency with meaning. Junior grade students should be exposed to tasks that allow them to understand fraction operations in connection to whole number operations, beginning with the provision of ample time to allow students to construct their own algorithms for the operations (Huinker, 1998 Brown & Quinn, 2006). This increases student fluencyof addition and subtraction across all number systems. When students develop an understanding that the need for a common unit is universal for all addition and subtraction, they can more readily connect their understanding of whole number addition to other number systems, such as decimals and fractions, as well as algebraic operations. When fluency with equivalent fractions is developed, students are better able to consider addition of unlike fractional units by first relating each quantity to a common unit (common denominator) (Empson & Levi, 2011). A strong foundation in equivalence is also crucial to student understanding of addition and subtraction with fractions (Petit, Laird & Marsden, 2010). Prior to more formal exposure to fraction addition and subtraction, students need a solid understanding of fractions as quantity, as well as part-whole constructs of fractions (Petit, Laird & Marsden, 2010). Naming the unit fraction when counting helps students to see the parts of the fraction when composing and decomposing and to recognize, for example, that counting 6 one-fourth units is the same as adding 6 one-fourth units together. ![]() Daily Number Reasoning Templates make it easy to develop the big ideas all year long.Count unit fractions as a form of adding and subtracting fractions Remember how I suggested that we could combine decimal sense making with simple multiplication fact practice? Here is our chance! DOUBLE YOUR EFFORTS: Skip count by 3 tenths or 6 hundredths etc… before you get to decimal multiplication as well.
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