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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 (see resources for a bar model example)."
- 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/Interactive modeling(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 (i.e. 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.
- Hand out the Bar Models worksheet. Review the example problem with the class and then instruct students to complete the ‘Try it’ problem with a partner.
- Have students set the worksheet aside and 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 compare the answer to the matching ‘Try it’ problem on the Bar Model worksheet.
- 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 on their sticky note, using the method of their choice.
- Collect as an exit ticket and check for understanding.
Review and closing(10 minutes)
- Show students the Multiply Fractions with Whole Numbers Song video.