Adding+and+subtracting+fractions

Adding and Subtracting Fractions
Students learn to add and subtract fractions by playing with fraction circles*. They have to spend lots of time working with fraction circles to model adding and "taking away." This is how they come to see why the procedure works for adding fractions when the denominators are the same. They recognize that two fractions with the same denominator are just pieces of a whole that has been cut into equal size pieces, so they're just adding (or subtracting) pieces. For example, think of a pizza cut into eighths (8 pieces). 3/8 of a pizza plus 4/8 of a pizza means "3 pieces + 4 pieces = 7 pieces" or 7 eighths.

When one denominator is a multiple of the other, students need to be able to generate equivalent fractions, and then use what they know about adding or subtracting when the denominators are the same. They should learn the process of scaling up or scaling down to create equivalent fractions with denominators that are multiples. To do this, they need to understand conceptually what equivalent fractions are. Their early work with fraction circle pieces involves finding equivalent fractions (other names for the same size pieces). See Fraction Basics and "Equivalent Fractions" in the Adding and Subtracting section of the Student Packet.

When the denominators are not multiples, students first need to learn to estimate the size of the sum or difference. Let students spend considerable time working on #12 in the Basic Fraction Concepts (an assessment) section of the Student Packet. This is where their experience with fraction circles is very valuable.

When the denominators are not multiples, the GLCEs suggest that the easiest starting point is to use the denominator that is the product of the two denominators. However, if they are using fraction bars to model the operation, say 1/4 + 5/6, they might easily find that the 1/12’s bars can be used to reconstruct both 1/4 and 5/6, getting 13/12 rather than 26/24 as an answer. Either answer is acceptable. Don’t confuse students at this point with LCM while they’re still learning to add fractions. (You probably don’t need to introduce LCM at all, or GCF either.) If students use the product of the two denominators as the common denominator, then you can focus on scaling down to “reduce” the answer, if you want.

For those students who are ready to move ahead, they can learn to scale up both fractions until they find equivalent fractions with the same denominators.

**Assignment:** Have your students work through the section of the Student Packet on Adding and Subtracting Fractions. As you plan the lessons, decide which tasks should be done in groups of 2, which should be done individually, and where you should have whole class discussions. Allow students to work at the tasks without giving them answers. Let them use fraction manipulatives, or encourage them to make drawings. Don't just tell them the procedure (algorithm) - let them get to the point where it is obvious, by the work they've done with drawings. Then record your observations, suggestions for improvements, interesting comments or solutions by students, etc. in the discussion tab for this page.


 * The fraction circles shown on this webpage are just an example of what you can purchase. This course does not endorse any particular manufacturer or make a profit from any sales. You can also purchase them at The Teacher Store, 6001 S. Pennsylvania Ave., Lansing.