Multiplication and Division of Whole Numbers

Lesson 6

Math

Unit 2

5th Grade

Lesson 6 of 20

Objective


Multiply two-digit numbers by two-digit numbers.

Common Core Standards


Core Standards

  • 5.NBT.B.5 — Fluently multiply multi-digit whole numbers using the standard algorithm.

Foundational Standards

  • 4.NBT.B.4
  • 4.NBT.B.5
  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success


  1. Compute two-digit by two-digit products using the area model, the partial products algorithm, and the standard algorithm.
  2. Relate the area model, the partial products algorithm, and the standard algorithm. 
  3. Round to estimate two-digit by two-digit products.

Tips for Teachers


Students multiplied two-digit by two-digit whole numbers using the area model, the partial products algorithm, and/or the standard algorithm in Grade 4. However, because two-digit by two-digit multiplication is both more complex than all of the cases students saw in Lesson 5 and more closely related to the new cases they’ll see in Grade 5, a whole day has been dedicated to this case to review these methods, and in particular the standard algorithm, with this case before moving on to new, more cognitively complex cases in later lessons.

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Anchor Tasks


Problem 1

a.   Here are two ways to find the area of a rectangle that is 23 units by 31 units.

  1. What do the area models have in common? How are they alike?
  2. How are they different?
  3. If you were to find the area of a rectangle that is 37 units by 49 units, which of the two ways of decomposing the rectangle would you use? Why?

b.   You might be familiar with different ways to write multiplication calculations. Here are two ways to calculate $$23\times31$$.

  1. In Calculation A, how are each of the partial products obtained? For instance, where does the 3 come from? 
  2. In Calculation B, how are the 23 and 690 obtained? 
  3. Look at the area models in Part (a). Which area model corresponds to Calculation A? Which one corresponds to Calculation B?
  4. How are the partial products in Calculation A and the 23 and 690 in Calculation B related to the numbers in the area models? 

Guiding Questions

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References

Open Up Resources Grade 6, Unit 5, Lesson 7, Teacher Version7.2: Connecting Area Diagrams to Calculations with Whole Numbers

Grade 6, Unit 5, Lesson 7, Teacher Version is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 7, 2018, 11:15 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

a.   Label the area model to represent $$37\times49$$ and to find that product. 

  1. Decompose each number into its base-ten units (tens, ones, etc.) and write them in the boxes on each side of the rectangle. 
  2. Label regions A, B, C, and D with their areas. Show your reasoning. 
  3. Find the product that the area model represents. Show your reasoning. 

b.   Here are two ways to calculate 37 × 49. Each number with a box gives the area of one or more regions in the area model. 

  1. In the boxes next to each number, write the letter(s) of the corresponding region(s). 
  2. In Calculation B, which two numbers are being multiplied to obtain 333? Which two are being multiplied to obtain 1,480? 

Guiding Questions

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References

Open Up Resources Grade 6, Unit 5, Lesson 7, Teacher Version7.4: Using the Partial Products Method

Grade 6, Unit 5, Lesson 7, Teacher Version is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 7, 2018, 11:15 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

Estimate the following products. Then solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help.

a.   $$73\times84$$

b.   $$48\times67$$

Guiding Questions

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References

Open Up Resources Grade 6, Unit 5, Lesson 7, Teacher Version7.4: Using the Partial Products Method

Grade 6, Unit 5, Lesson 7, Teacher Version is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 7, 2018, 11:15 a.m..

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #2e and #2f. How did you assess reasonableness for both problems? If you round both factors to the nearest ten in both problems, you get the same estimate. Why does it make sense that the actual product in #2e is less than the estimate and the actual product in #3f is larger than the estimate? 
  • Look at #3. How did you determine which expression was equal to 36 × 94? How is this related to the area model? To the standard algorithm? 
  • Look at #4. How did you solve for the values of B and C? 
  • How did you determine where to place the digits in #7? 
  • Look at #8. What was the biggest product you were able to make? The smallest? How did you find those values? 

Target Task


Problem 1

Solve. Show or explain your work.

a.   21 × 14

b.   68 × 79

Student Response

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Problem 2

Yuri drew an area model to find the value of 47 × 35.

a.   Determine the number that each letter in the model represents and explain each of your answers.

b.   Write the product for 47 × 35.

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.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 5

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Lesson 7

Lesson Map

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

Topic A: Writing and Interpreting Numerical Expressions

Topic B: Multi-Digit Whole Number Multiplication

Topic C: Multi-Digit Whole Number Division

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