• 6.NS.A.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?
  

  The Number System

  6.NS.A.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?

  Search

• 5.NF.B.6
  

  Number and Operations—Fractions

  5.NF.B.6 — Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

  Search

• 5.NF.B.7
  

  Number and Operations—Fractions

  5.NF.B.7 — Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade

  Search

Do the Launch and Pose a Problem sections SERP's Poster Problem "No Matter How you Slice It."

Launch:

• Watch the video on slide 1.
• Can you explain how the slicer works? 
• According to the video, what is the thinnest slice this slicer can make?
• If you know the length of a block of cheese, can you determine how many slices it can make?
• Suppose you get a new block and you know how thick you want your slices. What do you need to know in order to tell how many sandwiches you can make?

Pose a Problem:

• Discuss slides 2, 3, and 4.
• Complete Handout #1.

Do the Workshop section of SERP's Poster Problem "No Matter How You Slice It", including Handout #2. Students can work in pairs or in small groups.

Handout #2:

Make up and solve two of your own slicing problems. In problem A, you should not have any cheese left over, and in problem B, you one must have some cheese left over. 

For each problem, you need to determine how much cheese you start off with: how long is your block of cheese? You also need to say how thick you want the slices of cheese to be—or you can decide how many slices you will need in total. Keep in mind that the thickness of each slice should be between $${\frac{1}{32}}$$ and $${\frac{1}{2}}$$ inches thick. 

After you create your problems, make a poster showing each problem and its solution. Each solution should include an explanation, at least one calculation, and a diagram.

There are other ways to think about division of fractions. Try these two questions. They both use division, but why? And how do you know what to divide by what? 

1. Analise’s hair grew $$1\frac{3}{4}$$ inches in $$3\frac{1}{2}$$ months. On average, how many inches did Analise’s hair grow per month?
2. Write your own story problem that involves division of fractions. Then solve your problem.