Curriculum  /  Math  /  4th Grade  /  Unit 3: Multi-Digit Division  /  Lesson 4

Multi-Digit Division

Lesson 4

Math

Unit 3

4th Grade

Lesson 4 of 16

Objective

Divide two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies.

Common Core Standards

Core Standards

  • 4.NBT.B.6 — Find whole-number quotients and remainders with up to four-digit dividends and one-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.

Criteria for Success

  1. Divide two-, three-, and four-digit numbers by one-digit numbers using a variety of mental strategies, including:
    1. Finding partial quotients and adding them together (e.g., $$276 \div 6 = (240 + 36) ÷ 6 = (240 \div 6) + (36 \div 6)$$), and
    2. Adjusting the dividend to a compatible or “friendly” number and adjusting from there (e.g., $$276 \div 6 = (300 – 24) \div 6 = (300 \div 6) – (24 \div 6)$$).
  2. Understand and explain why various mental strategies work (MP.3).
  3. Understand that partial quotients can be found in more than one way (e.g., $$276 \div 6 = (120 \div 6) + (120 \div 6) + (30 \div 6) + (6 \div 6)$$). 

Tips for Teachers

  • This lesson explores strategies students may use for particular computational problems before they jump into generalizable methods and algorithms in later lessons. As Bill McCallum notes on his blog, “the distinction between a strategy and an algorithm is that an algorithm is general, it works in all possible cases, whereas a strategy might be specialized” (Mathematical Musings, Algorithms Grades 2-5).  He goes on to say that the progression towards fluency with any computation begins with strategies, then algorithms (note the plurality), then the standard algorithm. 
  • In this unit, students will not be explicitly asked to estimate quotients, since the NBT Progression states that in Grade 5, “estimating the quotients is a new aspect of dividing by a two-digit number” (NBT Progression, p. 18). However, the friendly number strategy mentioned here is essentially dependent on the ability to estimate using friendly, or compatible, numbers, e.g., adjusting $$158\div8$$ to be $$160\div8$$. All of the dividends in this lesson are fairly close to the compatible number to which they are adjusted, but not always the number that the dividend would be rounded to. Thus, students will be well set up to use compatible numbers to estimate or as a strategy to assess the reasonableness of their answer, if you choose to make this connection. If not, students will depend on using multiplication to check their answer to assess the reasonableness of their answer in this unit, with explicit instruction on estimating quotients coming in Grade 5 Unit 2. 
  • Problem Set #1 and #2 provide an array of Number Talks, similar to Anchor Task #2. You may decide to use these tasks in a similar way to Anchor Task #2, using them as a whole class and restricting the use of paper and pencil, forcing the use mental math to solve and therefore encouraging the use of the mental strategies discussed in the lesson. Or, if Anchor Tasks #1 and #2 take up much of the lesson block, you can use them as a source for problems for upcoming fluency blocks so that students can gradually develop the use of each strategy.
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Anchor Tasks

25-30 minutes

Problem 1

Three different students solved the problem $$ 232 \div 8$$. Your teacher will assign you one of the strategies below. Explain what the student did and whether the strategy they used works. Be prepared to share your thinking. 

Student A

Student B

Student C

Guiding Questions

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Student Response

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References

Book: Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 4 by Jo Boaler, Jen Munson, and Cathy Williams (Jossey-Bass, 2017) — pp. 195-202

Problem 2

Solve.

$$40\div4$$

$$80\div4$$

$$83\div4$$

$$50\div5$$

$$150\div5$$

$$10\div5$$

$$140\div5$$

$$30\div3$$

$$21\div3$$

$$51\div3$$

Guiding Questions

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Student Response

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References

Book: Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5 by Sherry Parrish (Math Solutions, 2010) — pp. 286-292

Problem Set

15-20 minutes

Discussion of Problem Set

  • How did each scaffolding problem help you solve the final problem in each part of #1 and #2? 
  • Is Jillian’s calculation in #3 correct? How do you know? How did you use her strategy to solve $$222\div 6$$? 
  • Were there specific strategies that you found yourself relying on repeatedly in #4? 
  • Which strategies seem to be useful for all computations? Which ones seem to be useful just in specific cases?

Target Task

5-10 minutes

Solve. Show or explain your work.

a.   $$87\div4$$

b.   $$294\div6$$

c.   $$4,256\div7$$

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

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

Next

Solve two-digit dividend division problems with no remainder or a remainder in the ones place with smaller divisors and quotients.

Lesson 5
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding and Interpreting Remainders

Topic B: Division of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Topic C: Multi-Step Word Problems and Patterns

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