1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

Fractions: every sixth grader's best friend.

We know, we know. But in order to satisfy this standard, students will need to get up close and personal with fractions in more ways than one—so we'd encourage them to let go of their feud with fractions. It's about time they buried the hatchet.

We aren't saying it'll be easy. Even after years of adding, subtracting, and multiplying with fractions, some students still hold a grudge. And now they've got to divide fractions? When will it end? (Hint: never.)

For struggling students, we recommend using fraction models and number lines. That'll help students visualize and understand exactly what we mean when we divide two fractions: how many of the top fraction is contained in the bottom fraction.

In order to divide fractions either by whole numbers or other fractions, it pays to know that when we divide two fractions, we can just multiply the first fraction by the reciprocal of the second fraction—and make sure they're comfortable doing this with all types of fractions. Seriously, hit 'em with mixed numbers, improper fractions—the whole enchilada. You'll know they're good if they can rise from the ashes unscathed.

Once they're solid on the whole actually-dividing-the-numbers bit, we recommend allocating some class time to sharpening their skills of going between written language and fraction computation. In other words, they should be able to understand what fraction division means, solve real-world (or fantasy-world!) problems, and even create their own contexts for these types of problems.

In the end, this standard boils down to students being unafraid to divide fractions by fractions in a mathematical or real-world problem.