Multi-Digit and Fraction Computation

Lesson 1

Objective

Interpret division problems as the number of items in each group or the number of groups of a given number of items. Write corresponding multiplication and division problems.

Common Core Standards

Core Standards

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  • 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?

Foundational Standards

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  • 5.NBT.B.6

  • 3.OA.A.3

Criteria for Success

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  1. Understand and interpret a division problem as representing the number of equally sized groups of a set of objects or the number of objects in each equally sized group. 
  2. Write a contextual situation to represent a division problem.
  3. Write a corresponding multiplication problem for a division problem.
  4. Draw diagrams to represent division problems.

Tips for Teachers

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This lesson is approaching 6.NS.1. It reaches back to concepts students learned in earlier grades around multiplication and division in order for students to be able to extend on these concepts in following lessons in the unit.

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  • Problem Set
  • Student Handout Editor
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  • Vocabulary Package

 

Anchor Problems

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Problem 1

Luzmarie has 20 cards that she sorts into equal piles. To represent what she does, she writes the division problem $${20÷5=4}$$.

  1. Describe two different situations that Luzmarie’s division problem could represent. Draw a diagram to represent each situation.
  2. What multiplication problem(s) can you write to represent Luzmarie’s cards?

Guiding Questions

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Problem 2

For each problem, write a division and a multiplication problem to represent the situation. Then solve the problem and explain what it means. 

  1. You make 10 cups of pudding and pour it equally into 6 containers. How many cups of pudding are in each container?
  2. You mix yellow and blue paint to make 126 ounces of green paint. You pour the green paint into some smaller buckets, with 18 ounces in each one. How many buckets did you fill?
  3. A recipe for pancakes calls for 3 cups of flour for one batch. If you have 11 cups of flour, how many batches of pancakes can you make?
  4. A florist is arranging 13 dozen flowers into vases. Each vase can hold 15 flowers. How many vases can be completely filled? How many more flowers are needed to fill the last vase?

Guiding Questions

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Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Given a division problem, have students write contexts to represent the problem. Keep the dividend and divisor whole numbers, but the quotient can be a fraction. For example: Write a situation to represent $${124 ÷ 3 = ?}$$
  • Write related multiplication problems to division problems. For example, write a corresponding multiplication problem to $${15÷8= ?}$$ or $${240÷8= ?}$$
  • Include problems similar to Anchor Problem #2; encourage students to draw diagrams to support and demonstrate their thinking.
  • This may also be a good opportunity to review skills from Units 1 and 2.
  • MARS Formative Assessment Lessons for Grade 6 Interpreting Multiplication and DivisionThis reviews the concepts of multiplication and division using story problems and concrete models; it’s a good intro to working with more fractions later on.

Target Task

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Seventy-two students in the sixth-grade class are going on a field trip to the aquarium. The math teacher writes this division problem to represent how the students will be grouped for the field trip: $${72÷6= ?}$$

Abe says, “This means that there are 6 students in each group.”
Sam says, “This means there are 6 groups of students.” 

Who is correct? Explain your reasoning and draw a diagram to support your answer.

Mastery Response

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