1. Dividing a fraction by a fraction: Bridging 5.NF.7 to 6.NS.1
6.NS.1 From a Conceptual Understanding to Developing the Algorithm

2. What is the pattern?
Maybe change 3 to 55 the numbers have to be larger to challenge the advanced students.
Pose the questions as “How many servings of ½ are in 3 containers?” etc.
In looking across these problems and looking for a pattern, students will notice they are multiplying by the denominator of the second fraction. For example, in the third example, a student might say, “You get five for every whole container, so 5 x 8 is 40.”
Van de Walle, “Elementary and Middle School Mathematics: Teaching Developmentally,” pg 334

3. What is the pattern?
Have students solve these problems and compare these responses to the problems in the first set. Notice that if there are 40 one-fifths in 8, then when you group the fifths in pairs (two-fifths), you will have half as many – 20. Stated in servings, if the serving is twice as big, you will have half the number of servings.
Van de Walle, “Elementary and Middle School Mathematics: Teaching Developmentally,” pg 334

4. Vitamin C Servings
The serving size for a toddler’s daily vitamin C is ¾ cup of orange juice. If there are 2 ¼ cups of orange juice, how many servings of vitamin C are there for a toddler? 1. Write the problem as a division problem. 2. Use a picture, fraction circles or a number line to solve. 3. Use the algorithm to solve. Compare your answers.

5. Review
ons/v/dividing-mixed-numbers-and-fractions

6. Tic-Tac-Toe Directions: Pair up with a classmate.
2. Determine who will be “x” and who will be “o.”
3. The “x” person will solve the first problem, and then have the “o” person check it. If it was solved accurately, then the player gets to take a turn on the board. If not, the player loses a turn.
4. Then the “o” person will solve the next problem, have the “x” person check it, and take a turn. If the player does not solve it correctly, that player loses a turn.

7. In your own words…
In your own words, write the steps for dividing a fraction by a fraction. What do you do when you have a mixed number divided by a fraction? Or a mixed number divided by a mixed number?