Introduction
The Common Core Mathematics standard states students should be able to understand a fraction as a number on the number line and represent fractions on a number line diagram. In my 14 years of teaching third grade, I have had difficulty explaining this concept adequately to my students! Many of my students think of a fraction as a combination of two whole numbers. The most popular strategies involve folding paper, identifying shaded portions on a partitioned shape, or placing fractions on a number line. All of these activities are a beginning, yet I know now that I can do better. My intent for this unit is to shepherd fractions from an area model to the number line as I begin to explain and represent fractions as a distance or measurement. As useful as the area models are for developing fractional understanding, students begin to over generalize and pigeon hole their understanding of a fraction as a piece of something instead of understanding that a fraction is a number in and of itself and that a fraction can be greater than 1.
In order to gain a thorough understanding of mathematical ideas, students need to be able to make connections and integrate their learning of concepts in a variety of ways. I will start this unit by allowing students to explore with manipulatives to put together and compare trains of blocks and rods of various lengths. Through the use of manipulatives, students can connect ideas to gain a deeper understanding. Student’s achievement grows when they have access to manipulatives and are explicitly taught how these manipulatives can assist their learning and how they connect to other representations. Manipulatives not only increase understanding but also allow students to make sense of problems, make and test conjectures about a problem, and justify their solutions, just to name a few benefits. I explain the importance of the use of manipulatives here because too many times by third grade, these enriching tools become scarce. This unit will include developing number sense through the use of base ten blocks and Cuisenaire rods. These tools are an excellent way to bring students from whole number understanding to the understanding of fractions. Using these rods will enable students to begin to make connections to measurement and lengths. Students will use the rods to measure a large variety of items found in and around the classroom. They will be putting the rods together and modeling addition. I will then lead them to actual measurement activities using specific units. During their investigations, students will begin to realize the need for numbers in between whole numbers. Our discussions of fractions will begin and since students discovered authentically the need for these numbers, they will have a connection to their learning. This unit will progress from recognizing fractions as a number and placing them on a number line. I will also begin to explain how to discover equivalent fractions. Students will obtain an understanding of fractions and this will aid them as they move into the arithmetic, (adding, subtracting, multiplying, and dividing) of fractions, however this will not be addressed in this unit.
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