Adding Fractions With Unlike Denominators

Subject: Mathematics

Grades: 4-5 (Ages 9-11)

NCTM Principles and Standards for School Mathematics

• Uses visual models, benchmarks and equivalent forms to add and subtract commonly used fractions
• Recognizes and generates equivalent forms of commonly used fractions
• Develops and uses strategies to estimate computations involving fractions in situations relevant to students’ experience
• Uses models, benchmarks and equivalent forms to judge the size of fractions
• Develops an understanding of fractions as parts of a unit whole and as divisions of whole numbers
   

Description

Students often struggle with adding and subtracting fractions with unlike denominators because they memorize a series of steps without a connection to number sense and the underlying concept of equivalent fractions. In this lesson, students will use Kidspiration Fraction Boxes™ to model addition of fractions with unlike denominators. By using the tool to build fractions and dynamically search for common denominators, students will develop their ability to reason flexibly with fractions. Their work with concrete models will enable them to retain and apply related procedures for operating on fractions with efficiency and understanding.

  Instructions
 

1. Open the lesson by presenting a situation that involves the addition of fractions with unlike denominators and uses student names from the class. For example, Brianna bought 5/6 of a pound of fudge and Jeremy bought 1/2 of a pound of fudge. The two of them would like to figure out how much fudge they have altogether. Record both fractions on the board. Ask students whether this situation calls for addition, subtraction, multiplication or division, and why. Then ask students to estimate much fudge the two students purchased altogether.
2. Open a new workspace in the Kidspiration Fraction Boxes Math Tool. Demonstrate how to use a Math Text Box and the Plus Sign and Fraction Frame buttons on the Bottom toolbar to write 5/6  + 1/2 . Bring a fraction box onto the workspace from the Math palette, and ask students how they might represent Brianna’s portion of fudge, 5/6 of a pound. What could the whole box represent? Discuss the meaning of the 5 and the 6, and show students how they can cut the whole (which represents 1 pound) into equal parts by using the up and down arrow buttons.

Ask students what each of these parts represents (1/6 of a pound), and how the parts could be colored to represent Brianna’s share. Demonstrate how to use a Color button on the Bottom toolbar to represent the amount of fudge that Brianna bought. Bring out another fraction box and repeat the process with a different color to represent the amount of fudge that Jeremy bought.

3. Ask students to refine their original estimates based on the model. Altogether, do you think they have less than a pound of fudge, about a pound, more than a pound, or more than two pounds? Why? Discuss any misconceptions about adding fractions, such as the common student error of adding these two fractions to get 6/8 .
4. Solicit suggestions from students as to how you might add Brianna and Jeremy’s portions of fudge. How can we add fractional amounts that are not the same size? There are several routes to a solution, and depending on the suggestions from students and your goal for the lesson, you may want to facilitate solving the problem a couple of different ways. Two common approaches to the problem are outlined below:

Method 1
Some students might suggest that 3/6 can “fit inside” of 1/2, or that 3/6 of Brianna’s pound of fudge can be “combined with Jeremy’s 1/2 pound to make 1 whole pound.” This concept of transferring a fractional quantity to “make a whole” can be demonstrated by multi-selecting 3/6 and dragging them to the empty 1/2 cell.
 

Note: A fraction box will only “accept” tiles if the fractional quantity being moved and the space to which it is moved are equivalent.

Does the model help us see how much fudge Brianna and Jeremy have altogether? Allow students to determine that the total amount is 1 2/6 pounds of fudge. If they are working on simplifying fractions, they can use the arrow buttons to “re-divide” the top fraction box and explore fractions that are equivalent to 2/6. Once they see that 2/6 is equivalent to 1/3, click on the button that says “3 Parts” to officially change the top fraction from sixths into thirds.

Method 2
A second way to show 5/6 + 1/2 is to use fraction boxes to model finding a common denominator. Begin by representing each fraction, as before.

Can we find an equivalent fraction for 1/2 that would make the pieces the same size as the sixths, allowing for addition? Show students how they can explore equivalent fractions with the up and down arrow buttons.

For example, 1/2 of a pound is equivalent to 2/4 of pound, but are Brianna’s and Jeremy’s pieces all the same size? Continue changing the divisions in the fraction box until students see that 1/2  is also equivalent to 3/6, and that both Brianna and Jeremy’s portion can be thought of in terms of sixths.

To officially cut the bottom fraction into sixths, instead of halves, click on the button that says “6 Parts.” Now that Brianna’s and Jeremy’s portions of fudge are both in sixths of a pound, the pieces can be easily combined. Drag tiles between fraction boxes to make 1 whole.

Ask students to determine, based on the model, how much fudge Brianna and Jeremy have altogether. If the expectation is that students also simplify their answers, for example, from 1 2/6 to 1 1/3 pounds, they can use fraction boxes to model simplification as described in Method 1.

Assessment

• Assess students on their contributions to the class example problem.
• Have students present their solutions to the assigned problems. Assess them on their ability to explain their reasoning and justify their solution through the use of a model.
• Check completed activities for clear modeling of each problem and correct solutions. See Adding Fractions Exemplar.kid from the previously downloaded Zip file for a sample completed activity.
   

 
Adaptations

• Before modeling each problem in the activity, have students record an estimate.
• Add context to the addition problems by modifying the activity to include word problems.
• Add pages to the activity to include subtraction problems. Students can use the Mark for Subtraction button to mark tiles with an X and represent “taking away.”
• The following activities can be used to differentiate instruction or extend the activity. All activities are located here: Kidspiration Starter>Activities>Math.
  
  • Students who need more practice adding and subtracting fractions with like denominators can complete the fraction boxes activity Fractions-Add and Subtract.kia.
  • Using fraction boxes in the Step Workspace can help students develop a process and a meaningful sequence of steps when adding fractions with like denominators. To complete similar problems in the step workspace, see Unlike Denominators-Adding.kia.
  • Fraction tiles can also help students visualize, understand and find common denominators. See the activity Finding Common Denominators.kia.