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Make It Work! Adding Fractions with Unlike Denominators
Students will be able to add fractions with unlike denominators with sums between one and two.
- Have the students get into partners, and give each pair of students a set of pattern blocks (one hexagon, six triangles, two trapezoids).
- Explain to your students that the hexagon represents one whole.
- Instruct students to figure out how many triangles make up the hexagon by putting the triangles on top of the hexagon. Then, instruct students to work with partners to figure out how many trapezoids make up the hexagon.
- Tell students that there are three ways to make one whole by using these pattern blocks: one hexagon or six triangles or two trapezoids.
- Explain that when we look at how many total of each shape we have, that gives us the denominator, or the number below the line in a common fraction. Remind your class that a fraction is a number that represents parts of a whole.
- Tell your class that, today, they're going to find common denominators between two fractions so that they can add fractions with unlike denominators.
Explicit Instruction/Teacher modeling(15 minutes)
- Tell your class that the denominator represents the total number of equal parts the item is divided into. Refer back to the introduction for an example (six triangles and two trapezoids).
- Explain to students that when we have unlike denominators, we can't just add the numerators, or numbers above the line in a fraction, like we would when the denominators are the same. There are some extra steps that we have to take.
- Write an example on the board: 1/2 + 5/6.
- Explain to students that the denominators are different, but if we just added it like we normally do, we would come up with the answer of 6/6. Model this by putting the trapezoid (represents 1/2) and five triangles (represents 5/6) on top of the hexagon (representing one whole or 6/6). Explain that this shows that 1/2 + 5/6 can't make 6/6, or one whole.
- Model the example with the Fraction Strips worksheet. Separate one fraction strip into halves and the other into sixths. Show that it's not possible to add the numerators when the denominators are broken up differently—students need to find the least common denominator, or lowest common multiple of two numbers.
- Show students how to correctly find the common denominator of 2 and 6, and use new blank fraction strips to show the new fractions with the lowest common denominator of 6: 3/6 and 5/6.
- Add 3/6 + 5/6 to get the answer 8/6. Change the improper fraction to a mixed number: 1 and 1/6.
Guided Practice(10 minutes)
- Pass out copies of the worksheet Make It Work! Adding Fractions with Unlike Denominators and the worksheet Fraction Strips to each student.
- Have students continue working with a partner as they complete #1–#3 on the worksheet together. They should use the fraction strips just as you did in the direct instruction.
- Gather the class together after a few minutes of work time to go over and talk through the problems. Have the students come to the document camera to show their fraction strips and speak about their process. Encourage the class to give one another feedback during this part of the lesson.
Independent working time(10 minutes)
- Students will work independently to complete #4–#8 on the worksheet.
- Circulate, offering support where needed.
- Bring students to the teacher's table to work with pre-made fraction strips or tiles.
- For an extra challenge, students who have mastered adding fractions with unlike denominators can complete problems with two-digit denominators using fraction strips.
- Problems #4–#8 on the worksheet serve as an assessment of students' mastery of the standard.
- Your observation of student discussion and work can also serve as an assessment.
Review and closing(5 minutes)
- Go over two questions from the worksheet together, focusing on the problems that students struggled with or asked the most questions about.
- Call on volunteers to explain processes in the correct order for how to add fractions with unlike denominators.