Objective
Multiply two-digit, three-digit, and four-digit numbers by one-digit numbers.
Common Core Standards
Core Standards
The core standards covered in this lesson
5.NBT.B.5— Fluently multiply multi-digit whole numbers using the standard algorithm.
Number and Operations in Base Ten
5.NBT.B.5— Fluently multiply multi-digit whole numbers using the standard algorithm.
Foundational Standards
The foundational standards covered in this lesson
4.NBT.B.4
Number and Operations in Base Ten
4.NBT.B.4— Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.5
Number and Operations in Base Ten
4.NBT.B.5— Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NBT.A.1
Number and Operations in Base Ten
5.NBT.A.1— Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.2
Number and Operations in Base Ten
5.NBT.A.2— Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Compute two-digit, three-digit, and four-digit by one-digit products using the area model, the partial products algorithm, and the standard algorithm.
- Relate the area model, the partial products algorithm, and the standard algorithm.
- Round to estimate two-digit, three-digit, and four-digit by one-digit products.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
- Studentsmultiplied up to four-digit by one-digit whole numbers using the area model, the partial products algorithm, and/or the standard algorithm in Grade 4. The intention of this lesson it to review these strategies, and particularly the standard algorithm, with these cases before moving on to multiplication with larger factors in later lessons.
- Throughout this topic, it is important to preserve place value when talking about products of multi-digit numbers. For example, when discussing the computation$$1,768\times4$$, the partial product of the 6 digit and the 4 digit should be referenced as “six tens times four” or “sixty times four” rather than “six times four.”
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Anchor Tasks
Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
Problem 1
Here is one way to find the area of a rectangle that is 43 units by 2 units.
You might be familiar with different ways to write multiplication calculations. Here are two ways to calculate 43$$\times$$2.
Calculation A Calculation B
a.In Calculation A, how are each of the partial products obtained? For instance, where does the 6 come from?
b.In Calculation B, how is 86 obtained?
c.Look at the area model. How are the partial products in Calculation A and the 86 in Calculation B related to the numbers in the area model?
Guiding Questions
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References
Open Up Resources Grade 6, Unit 5, Lesson 7, Teacher Version—7.2: Connecting Area Diagrams to Calculations with Whole Numbers
Grade 6, Unit 5, Lesson 7, Teacher Version is made available by Open Up Resourcesunder theCC BY 4.0license.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.Find the value of $$932\times4$$.
b.Swathi used the standard algorithm to find the value of $$932\times4$$. Here is her work.
- Where do you see $$2\times4$$in Swathi's work?
- What does the 1 on the equal line represent in Swathi's calculation? Where did it come from?
- Where did the digits 3 and 7 in the solution come from?
Guiding Questions
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References
Open Up Resources Grade 5 Unit 4 Lesson 6 Activity 1 “Compose a New Unit”
Grade 5 Unit 4 Lesson 6 Activity 1 “Compose a New Unit” is made available by Open Up Resourcesunder theCC BY 4.0license.Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Sept. 15, 2021, 11:49 a.m..
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.$$4,408\times5$$
b.$$5,731\times7$$
Guiding Questions
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Problem Set
15-20 minutes
Problem Set
Answer Keys
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Discussion of Problem Set
- Look at #4. Can the expression 8 x (3,000 + 600 + 5) be used to find the value of 3,605 x 8? Why or why not? What other expressions can be used to solve 3,605 x 8? How do you know?
- Look at #5. What is an example of when Nina’s claim is true? What is an example of when Nina’s claim is not true?
- What was the value of the question mark in #6? How did you figure that out?
- Look at #7. What is a possible number that Casey multiplies 178 by? Is there more than one right answer?
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Solve. Show or explain your work.
a.42 ×3
b.6 ×215
c.2,039 ×8
Student Response
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References
EngageNY Mathematics Grade 4 Mathematics > Module 3 > Mid-Module Assessment—Question #2a-c
Grade 4 Mathematics > Module 3 > Mid-Module Assessment of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 22, 2017, 1:59 p.m..
Modified by Fishtank Learning, Inc.
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
Extra Practice Problems
Answer Keys
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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.
Lesson 4
Lesson 6
