Dividing with Unit Fractions

Prior to Lesson: Collect a chocolate bar for each pair of students. Any bar will work, but Hershey bars work the best due to the sections, they are already split into. Students should be paired in similar levels.

Diving by a Unit Fraction

1. Instruct students that they are going to work in pairs and in groups of four depending on the problem. Preconfigure the pairs and groups of four (2 pairs = 1 group of 4)

2. Begin by telling the students that they are to work as pairs and divide their bar in half. Have students volunteer ways to write dividing one whole by one half. Place emphasis on whether the fraction is the divisor or dividend. What do we have? What are we splitting between?

3. When we divided one whole by one half, what was our answer? How many 1/2 size pieces did we have? (2).

4. Now, instruct the students to put their bar back together and work as a group of 4. How many wholes do we have now? Have students volunteer ways to write dividing two wholes by one half. Again emphasize whether the fraction is the dividend or divisor.

5. When we divided two wholes by one half, what was our answer? How many 1/2 size pieces did we have?

6. Follow similar steps as 2 through 5, dividing by 1/4 and 1/8.

7. Have students record any observations or patterns they notice in their answers.

Diving a Unit Fraction by a whole number

1. Instruct students that they are going to work in pairs and groups of 4 to solve the problems.

2. Begin by telling the students that they need to use 1/2 of their bar. They can set the other half off to the side. Instruct them they are divide their 1/2 bar into two pieces as if they are sharing the bar. Have students volunteer ways to write dividing 1/2 by 2. Place emphasis on whether the fraction is the divisor or dividend. What do we have? What are we splitting between?

3. When we divided 1/2 by two, what is our answer? How much candy bar does each person get? How much of a whole do we have left? (1/4)

4. Now, instruct the students to work as a group of 4. We still only have 1/2, but now we need to share it among all 4 of you. Have students volunteer ways to write dividing 1/2 by four. Again emphasize whether the fraction is the dividend or divisor.

5. When we divided 1/2 by 4, what was our answer? How much of the whole did we each get?

6. Follow similar steps to divide by 8.

7. Have students record any observations or patterns they notice in their answers.

Focus Content Area Standards

CCSS.MATH.CONTENT.5.NF.B.7

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

CCSS.MATH.CONTENT.5.NF.B.7.A

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

CCSS.MATH.CONTENT.5.NF.B.7.B

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

CCSS.MATH.CONTENT.5.NF.B.7.C

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.