Lesson 1 | Multi-Digit and Fraction Computation | 6th Grade Mathematics

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

The core standards covered in this lesson

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?

Foundational Standards

The foundational standards covered in this lesson

5.NBT.B.6

Number and Operations in Base Ten

5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
3.OA.A.3

Operations and Algebraic Thinking

3.OA.A.3 — Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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.
Write a contextual situation to represent a division problem.
Write a corresponding multiplication problem for a division problem.
Draw diagrams to represent division problems.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

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

a. Describe two different situations that Luzmarie’s division problem could represent. Draw a diagram to represent each situation.

b. 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.

a. You make 10 cups of pudding and pour it equally into 6 containers. How many cups of pudding are in each container?

b. 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?

c. A recipe for jambalaya calls for 3 cups of rice for one batch. If a restaurant uses 11 cups of rice, how many batches of jambalaya did the restaurant make?

d. 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

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or 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 Division — This 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.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 2

Lesson Map

Topic A: Dividing with Fractions

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.

6.NS.A.1

Divide a fraction by a whole number using visual models and related multiplication problems.

6.NS.A.1

Divide a whole number by a fraction using visual models.

6.NS.A.1

Use visual models and patterns to develop a general rule to divide with fractions.

6.NS.A.1

Solve and write story problems involving division with fractions.

6.NS.A.1

Solve problems involving division with fractions.

6.NS.A.1

Topic B: Computing with Decimals

Add and subtract decimals using the standard algorithm.

6.NS.B.3

Multiply decimals using strategies, and develop an understanding of the standard algorithm.

6.NS.B.3

Multiply decimals using the standard algorithm.

6.NS.B.3

Divide multi-digit whole numbers using the standard algorithm.

6.NS.B.2

Divide numbers with decimal quotients. Divide decimals by whole numbers.

6.NS.B.2 6.NS.B.3

Divide decimals by decimals using the standard algorithm.

6.NS.B.3

Solve problems involving decimals using all four operations.

6.NS.B.3

Topic C: Applying the Greatest Common Factor and the Least Common Multiple

Use prime factorization to represent numbers as products of prime factors.

6.NS.B.4

Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.

6.NS.B.4

Find the least common multiple of two numbers. Solve application problems using the least common multiple.

6.NS.B.4

Solve mathematical and real-world problems using the greatest common factor and least common multiple.

6.NS.B.4

Multi-Digit and Fraction Computation

Objective

Common Core Standards

Core Standards

The Number System

Foundational Standards

Number and Operations in Base Ten

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Word Problems and Fluency Activities

Lesson Map

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