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Fraction of a Whole
Students will be able to use bar models and multiplication to find a fraction of a whole number.
- Hook students with a scenario: "My favorite TV show is 27 minutes long. Usually I watch it on Friday evenings, but last Friday I fell asleep after watching only ⅓ of the show. I want to finish watching it, but I need to figure out how many minutes I’ve already watched so I can start in the right place."
- Tell students that in order to figure out how many minutes were watched, we will have to find one-third of 27. So today, we are going to learn how to find fractions of a whole number.
Explicit Instruction/Teacher modeling(10 minutes)
- Restate scenario ("I watched ⅓ of a 27 minute show. How many minutes did I watch?").
- Write the problem on the board (⅓ of 27).
- Draw a bar and label it "27." Explain, "The whole TV show is 27 minutes, so this bar will represent the total length of the show."
- Beneath the first bar, draw a bar that is the same length and divide it into thirds. Explain, "I only watched one third of the show before falling asleep."
- Lightly shade one part, or ⅓, and tell students, this shaded part represents the part of the show you watched.
- Point out that there are three equal parts in the bottom bar. Remind students that the total length is 27, so in order to find out what each of the ⅓ parts is, we will have to divide 27 into three equal parts (27 ÷ 3).
- Call on a student to give the answer to 27 ÷ 3, and write the answer, 9, in each of the three parts of the bottom bar.
- Remind students that the shaded ⅓ represents the part you watched, and explain: with this bar model, we can see that ⅓ of 27 is 9. So, "I watched 9 minutes of my favorite TV show."
- Point to the unshaded portion of the bottom bar and ask students how many minutes are left in the show. Give students time to discuss with a partner, then call on a student to share (i.e., 9 + 9 = 18; 18 minutes are left in the show).
- Explain that a bar model is one way to find a fraction of a whole. It helps us visualize the whole number and it also shows the whole divided into equal parts.
Guided Practice(15 minutes)
- Guide students through another example of a bar model, like ⅚ of 12.
- After drawing and shading the bar model, write a repeated addition sentence (e.g., 2 + 2 + 2 + 2 + 2 = 10) and explain that since ⅙ of 12 is 2, and ⅚ are shaded, we need to add five parts, or sixths, to find the answer.
- Tell students that another way to find a fraction of a whole number is to multiply.
- Write ⅖ of 20 on the board.
- Explain, "When we multiply a fraction by a whole number, we can just multiply it by the numerator. The denominator remains the same (write 20 x 2/5 = 40/5)."
- Tell students that this is because a whole number is equal to itself over one (20 = 20/1).
- Point out that 40/5 is an improper fraction, and remind students that, in order to simplify the fraction, we must divide the numerator (40) by the denominator (5). Write 40/5 = 8 on the board.
- Write ⅖ of 20 = 8 and discuss the answer.
- Hand out the Multiplication: Fraction of a Whole worksheet and review the example problem.
- Instruct students to complete the first problem with a partner.
Independent working time(10 minutes)
- Have students complete the remaining problems on both worksheets independently.
- Circulate as students work and offer support as needed.
- Go over the worksheets as a class.
- Teach repeated addition as a precursor to multiplication.
- Provide completed bar models and have students write a repeated addition sentence to go with the models.
- Have students apply the strategies learned in the lesson to solve two-step word problems.
- Hand out a blank sticky note to each student.
- Write a problem on the board, like ⅗ of 10. Instruct students to solve this on their sticky note using the method of their choice.
- Collect the sticky note as an exit ticket and check for understanding.
Review and closing(10 minutes)
- Show students the "Multiply Fractions with Whole Numbers Song" video.