Sums for Mixed Numbers and Improper Fractions
Students will be able to add like mixed numbers and improper fractions using the counting up strategy with number lines.
- Propose an addition problem like 12 + 6 and take student responses. Listen for a strategy that counts 6 up from 12.
- Introduce the counting up strategy to your class, making reference to anyone who mentioned it.
- Explain that the day's lesson takes the counting up strategy for addition, but counts up from a mixed number and adds an improper fraction.
Explicit Instruction/Teacher modeling(10 minutes)
- Review the definition of a mixed number (a whole number mixed with a fraction such as 1 and 2/3) and an improper fraction (a fraction in which the numerator is greater than the denominator such as 5/3). Invite students to give you an example of each type of number and share it verbally with a table partner.
- Display a sample problem on the document camera and have students consider how they would solve it (e.g., 2 1/4 + 5/4). Record students' responses. Tell students that today you will show them three steps to follow to add like mixed numbers and improper fractions. Review these steps and model how to go through each one with the sample problem.
- Step 1: Estimate a good length for a number line and draw it with denominator sized partitions. (Draw a number line divided into fourths from 2 to 4.)
- Step 2: Identify your mixed number on the line. (Circle 2 1/4.)
- Step 3: Add by counting up based on the numerator from the improper fraction from the mixed number point and identify where you end up. (Count up 5/4 from 2 1/4 to arrive to 3 2/4.)
Guided Practice(5 minutes)
- Hand out and preview the Adding Mixed Numbers and Improper Fractions on a Number Line worksheet.
- Work through the first exercise on the Adding Mixed Numbers and Improper Fractions on a Number Line worksheet with your students and answer any clarifying questions.
Independent working time(15 minutes)
- Release students to complete the remaining exercises independently or in strategic partnerships.
- Remind students to follow the three steps as outlined on the first page.
- Circulate the room to offer assistance as needed.
- Provide sheets with number lines pre-partitioned to the common denominators on the Adding Mixed Numbers and Improper Fractions on a Number Line worksheet.
- Students who need more practice using number lines can visualize and practice the counting up strategy with Number Line Addition 2 worksheet (see optional materials).
- Challenge students to demonstrate two extra problems where the whole number 1 is added to the improper fraction addend. Show what happens and explain any patterns or generalizations.
- Pick a problem, state one of the three steps in the adding process, and ask your class to hold up fingers that correspond to the stage.
- Deepen the discussion by having your student explain why the particular step is important to arriving at a sum.
Review and closing(5 minutes)
- Remind students that there are many strategies to add mixed numbers with improper fractions and they will have the opportunity to determine which strategy works best for them. The important takeaway to note is that students have an imaginary math "toolbox" with lots of methods and strategies to help them tackle any type of math problem. Today they added mixed numbers and improper fractions with the same denominator using a number line, and hopefully they will continue to practice this strategy with future problems.
- Read aloud the objective of the lesson and ask students to share their main learnings from the day's work.