12/15/2023 0 Comments Compare using benchmark fractions![]() ![]() Or, to use the “more and less than a benchmark” strategy to compare 2/10 and 3/4, each fraction can be compared to an equivalent form of 1/2 (i.e., 5/10 and 2/4). Once the denominators are the same, one can simply compare the size of the resulting numerators. For instance, to use the common denominator strategy to compare 2/5 and 3/8, each fraction can be rewritten as an equivalent fraction with a denominator of 40. Equivalence can be used to make fractions easier to compare.Representations that are useful for explaining the strategy.Situations in which the strategy is useful or questionable.It is easy to use and helps us to make sense of the numbers What fraction with a. The connections between the strategy and the definition of a fraction being used What does the numerator tell you The fraction 1/2 is a benchmark fraction.Three ideas to keep in mind when considering fraction comparison strategies:.In particular, it provides a foundation for anticipating and analyzing student thinking. Students must be able to determine and justify whether or not sums and differences of fractions are reasonable. Knowing different fraction comparison strategies, situations in which they are useful, and ways of representing and explaining them helps teachers facilitate student learning. Distance from a benchmark such as one-half or one whole (could be distances more than or less than).In the classroom: Provides resources to allow students to compare fractions with or witho ut a visual representation of the fractions the mathematics explicit. Requires students to construct a viable argument and use examples to justify their reasoning (MP3). More and less than a benchmark such as one-half or one whole Allows students to reason about the size of fractions by using benchmarks.Same number of parts, but parts of different sizes (common numerator).More of the same-size parts (common denominator).So we have 5/3 is greater than 10/7.This part explores four strategies for comparing fractions (Van de Walle et al., 2009): Or the smaller side, or the point, pointing to the smaller number. So we want the larger side or the opening on the larger number. So how do we write the symbol? Well we always want to open So we see that both 10/7 and 5/3 are between one and two, but which one of these is actually larger? Well we see 5/3 is further to the right on the number line than 10/7. How We Compare Fractions Same Numerator/Same Denominator FIND Common Numerator/ Common Denominator Using Visual Models-area model, fraction bars, number. So this is 1/7, this isĢ/7, 3/7, 4/7, 5/7, 6/7, this is 7/7, I could write that down, this is, one is the same thing as 7/7, 8/7, 9/7, 10/7 right over here. To split the part of the number line between zero and one or between each whole number And if we were to go over here, two would be the same thing as 6/3. This is 4/3, and then this right over here is going to be 5/3. So this is 1/3, this isĢ/3, this is 3/3, which is, of course, the same thing as one. So I'm marking off all of the- I'm marking off all of the thirds. Sections, one, two, and three, you see that right over here. Grade 4, students extend the use of these models to compare fractions with different numerators and denominators using several strategies: find equivalent fractions, if the denominator is the same compare the numerator, if the numerator is the same compare the denominators, and using a benchmark of ½ and 1. ![]() And then the space from one to two is split into three equal The space from zero to one is split into three equal If two fractions have equivalent numerators, then the fraction with the lesser denominator has a greater value. You see right over here, this is 1/3, this is 2/3, the thirdsĪre being marked off in blue right over here. We have zero, one, two and, first, I divide the number line into thirds. start fraction, 1, divided by, 3, end fraction. start fraction, 8, divided by, 12, end fraction. ![]() start fraction, 4, divided by, 6, end fraction. start fraction, 3, divided by, 10, end fraction. That, I'm going to plot each of these on a number line and I encourage you to pause this video and try to do the sameīefore I work it out. Joe made a table to show the time it took him to walk to school on different days of the week. So which of these is going to be larger? And to help us with And a whole here wouldīe 7/7, this is 10/7. For example, if students were comparing 6/8 and. ![]() The fraction 5/3 to 10/7 or which- if we can figure out which one of these fractions is larger. Instead of taking the time to find a common denominator, students compare each fraction to a benchmark fraction. ![]()
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