Thursday, November 12, 2015

Thursday Tool School: Understanding Fractions- Benchmark Fractions

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. 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. 

We all know that fraction concepts have plagued our students for many years. For some reason, students struggle to understand how to make sense of the value of a fraction. 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. 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?" 

It took some time, but I began to notice that my students' understanding of fractions developed into the deeper understanding I had envisioned. (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. Two-sixths is closer to zero, not one whole.)

It's important to note that students don't just develop this understanding without beginning with the conceptual models. Students need lots of opportunities to make the comparisons using fraction tools before being able to make a visual estimation from the formal notation. See the examples below of how to use fraction strips to compare to a benchmark. 

Today's resource supports the following Common Core State Standard for Math: 
5.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. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 

Note: The one whole and two half strips are included for reference.

This conceptual model illustrates that the fraction one-eighth is closer to zero. 

This conceptual model illustrates that the fraction seven-twelfths is closer to one-half. 

This conceptual model illustrates that the fraction five-sixths is closer to one whole. 

Note: It is important to state here that confusion always arise with fractions that are close to one-fourth or three-fourths. I usually tell students to round them both up to one-half and one-whole for a quick reference; however, you may choose to make them benchmarks in and of themselves.   

After students have explored the conceptual model, they can record their learning on a graphic organizer. The example below show a graphic organizer where students record the formal fraction notation in the correct column and then "sum up" their learning by answering a question related to the what they notice about the relationship of the parts of the fraction (the numerator and the denominator) and the benchmark fraction. 

Blank Activity Sheet
Free Resource Alert! Click here to get a free copy of the blank recording sheet. 

Sound Off! How do you use math tools to teach fractions in the classroom?


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