3 Dot Nf Dot 2 More Ideas From Vdw

Ideas Inspired by Teaching Student-Centered Mathematics

Zero, One-Half, or One (K-3, p.263) On the board or document camera, write a collection of 8 to 10 fractions. A few should be greater than 1, with the others ranging from 0 to 1. Let students sort the fractions into three groups: those close to 0, close to 1/2, and close to 1. For those close to 1/2, have them decide if the fraction is more or less than 1/2. The difficulty of this task largely depends on the fractions. The first time you try this, use fraction such as 1/20, 53/100, or 9/10 that are very close to the three benchmarks. On subsequent days, use fractions with most of the denominators less than 20. You might include one or two fractions such as 2/8, or 3/4 that are exactly in between the benchmarks. As usual, require explanations for each fraction.

Close Fractions (K-3, p.263) Have students name a fraction that is close to 1 but not more than 1. Next have them name another fraction that is even closer to 1 than that. For the second response, they have to explain why they believe the fraction is closer to 1 than the previous fraction. Continue for several fractions in the same manner, each one being closer to 1 than the previous fraction. Similarly, try close to 0 or close to 1/2 (either under or over). The first several times you try this activity, let the students use models to help with their thinking. Later, see how well their explanations work when they cannot use models or drawings. Focus discussions on the relative size of fractional parts.

About How Much? (K-3, p.263) Draw a picture like one of those in the figure 9.12 (or prepare some ahead of time for the overhead/document camera). Have each student write down a fraction that he or she thinks is a good estimate of the amount shown (or the indicated mark on the number line). Listen without judgment to the ideas of several students and discuss with them why any particular estimate might be a good one. There is no single correct answer, but estimates should be "in the ballpark." If children have difficulty coming up with an estimate, ask if they think the amount is closer to 0, 1/2, or 1.

Ordering Unit Fractions (K-3, p.264) List a set of unit fractions such as 1/3, 1/8, 1/5, and 1/10. Ask children to put the fractions in order form least to greatest. Challenge children to defend the way they ordered the fractions. The first few times you do this activity, have them explain their ideas by using models.

Line 'Em Up (K-3, p.266) Select four or five fractions for students to put in order from least to greatest. Have them indicate approximately where each fraction belongs on a number line labeled only with points 0, 1/2, and 1. Students should include a description of how they decided on the order of the fractions. To place the fractions on the number line, students must also make estimates of fraction size in addition to simply order the fractions.