![]() ![]() ![]() ![]() Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. In early grades, this might be as simple as writing an addition equation to describe a situation. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Later, students learn to determine domains to which an argument applies. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. They justify their conclusions, communicate them to others, and respond to the arguments of others. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. Thursday Tool School: Understanding Fractions- Par.MI.3 Mathematical practicesĬonstruct viable arguments and critique the reasoning of others.Thursday Tool School: Understanding Fractions- Ben.Transformation Tuesday: Getting Started with Math.What I'm Reading Wednesday: Making Number Talks Ma.Thursday Tool School: Understanding Fractions- Com.Note: The one whole and two half strips are included for reference. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Today's resource supports the following Common Core State Standard for Math:ĥ.NF.A.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. See the examples below of how to use fraction strips to compare to a benchmark. Students need lots of opportunities to make the comparisons using fraction tools before being able to make a visual estimation from the formal notation. It's important to note that students don't just develop this understanding without beginning with the conceptual models. Two-sixths is closer to zero, not one whole.) ![]() (An understanding that prevents the dreaded one-third plus one-third equals two-sixths because using benchmark fractions will allow students to see that one-half plus one-half equals one whole. It took some time, but I began to notice that my students' understanding of fractions developed into the deeper understanding I had envisioned. Each time I presented a fraction, I posed the question, "Is this fraction closer to zero, one-half, or one whole?" And, I often added, "How do you know?" A few years back, in an effort to try to help my fourth graders really make connections between the value of a fraction and the formal fraction notation, I taught them how to compare the fraction to a benchmark. For some reason, students struggle to understand how to make sense of the value of a fraction. We all know that fraction concepts have plagued our students for many years. This week, I want to talk about using benchmark fractions to better help students make connections between the value of the fraction and the formal fraction notation. Last week, I discussed how to use fraction tools to help students learn to connect a fractional part to the whole and then to the formal fraction notation. ![]()
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