10/5/2023 0 Comments Using benchmark fractions![]() Now is a good time to go back and ask students which tiles they could not use to make a fraction equivalent to 1/2 (thirds and fifths). Once they see it, though, the light bulbs go off! Next, I give them other denominators and ask what the numerator would need to be for the fraction to be equivalent to 1/2. Oddly enough, students rarely say that the numerator is half the denominator. Two times the numerator is the denominator (4 x 2 = 8).If you add the numerator again, you get the denominator (4 + 4 = 8).When students make them, I certainly record them, but I also challenge students to look for relationships between the numerator and denominator in each fraction Note: These are the relationships students usually see first. The denominators skip count by twos (4, 6, 8, 10, 12).The numerators are “in order” or count by ones (2, 3, 4, 5, 6).Now ask students a simple question: What do you notice? Be prepared for many different responses, but these are a few I usually hear: By not putting the fractions in order (2/4, 3/6, 4/8, etc.), students are more likely to focus on the relationship between the numerator and denominator, which is what you want. I like to highlight the students who use a more organized method and remind students that being organized often helps mathematicians do their work more efficiently.Īfter the students have found all of the fractions, write them on your whiteboard or an anchor chart. It’s always interesting to watch this process–some kiddos are very methodical, trying each of the pieces in order (eg., thirds, fourths, fifths, etc.), while others employ a more ‘helter skelter’ approach. Be sure to have the students work in pairs to facilitate mathematical discourse. Why is that important? Check out this post!Ĭhallenge students to use their tiles to find fractions that are equivalent to 1/2. If you don’t have access to fraction tiles, you can download printable ones here. When the students are using the tiles, I like them to draw a number line above the 1 whole tile (see picture) so they have a visual representation of the fact that proper fractions fall between 0 and 1 on the number line. My favorite manipulative for this exploration is fraction tiles, because you can easily connect them to fractions on a number line. ![]() Students should have many opportunities to explore fractions equivalent to 1/2 using hands-on materials. There is no additional cost to you, and I only link to books and products that I personally use and recommend. This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. Another useful strategy is to compare fractions to a benchmark of 1/2. The first post highlighted comparing fractions with like numerators or denominators, while the second post introduced a strategy for comparing fractions one unit fraction from a whole. ![]() In this series of blog posts, I am exploring 5 different strategies for comparing fractions. It begins to focus on the size of fractions in an important yet simple manner.” “Understanding why a fraction is close to 0, 1/2, or 1 is a good beginning for fraction number sense.
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