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Fourth Grade                                                                                                9 Weeks
Addition, Subtraction, and Multiplication with Multi-Digit Whole Numbers


Students generalize their understanding of place value to 1,000,000 based upon foundational ideas with base-ten from grades K-3.  They will combine their base-ten understanding with the meanings and properties of operations to add, subtract, and multiply with multi-digit numbers.  Students extend their work from 3rd grade, fluently adding and subtracting within 1,000, to whole numbers up to 1,000,000, and begin to use an efficient/standard algorithm.  The major focus of 3rd grade was building fluency with single-digit multiplication and multiplying multiples of ten within 100.  During first quarter of 4th grade, students will extend their understanding of multiplication to multi-digit whole numbers, specifically working with two digits by one digit.  They will use methods based upon place value and properties of operations supported by suitable representations to multiply with multi-digit numbers.  Contexts for problem-solving that support the major work of adding, subtracting, and multiplying multi-digit whole numbers in this quarter include solving multi-step word problems involving real-world scenarios with measurement quantities (ex. area and perimeter).   

Lessons addressing the Unit Standards

Lessons listed below are in no particular order or instructional sequence.
..the needs of your students will determine your instructional path through this unit.

Multi-Day Lessons:

Experiences with Place Value  This document provides examples of a variety of place value experiences (lessons) you could use with your students to develop their understanding and fluency. 
(standards addressed: 4.NBT.1, 4.NBT2)

Elapsed Time Strategies  This document provides examples of a variety of strategies and experiences to use with your students for elapsed time.  (standards addressed: 4.MD.2)

Rounding Experiences  This document provides examples of strategies and experiences to use with your students for rounding. (standards addressed: 4.NBT.3)

Using Estimation  Students will use their understanding of rounding and estimation to complete these contextual tasks. (standards addressed: 4.NBT.3)

My Special Number  In these 2 or 3 lessons, students will sort factors and recognize characteristics of given numbers and be able to use these to solve problems. (standards addressed:  4.OA.4)

The Product Game  There are four lessons in this unit.  Students play the product game in the first lesson. In the second lesson, they make their own game boards. The task of creating a new game is challenging to most students. They learn a lot by experimenting and by making mistakes about what factors and products to include in a game. In the third lesson, students use Venn diagrams to represent the relationships between the factors or products of two numbers. The fourth lesson contains extensions and connections. (standards addressed:  4.OA.4)

Planning a Class Field Trip  In this unit of 8 lessons, teams of students plan trips. To put together their best travel plan, students study a map, consider different routes, visit Web sites to get airline schedules and costs, and analyze their data. Each team presents its travel schedule and budget to the class. Then teams analyze the different plans and discuss the best features of each one. Students collect data, organize data, and compute differences of multi-digit numbers. The sequence of lessons in this Unit Plan builds skills required for collecting, displaying, and using data to solve problem situations. Students collect and use numerical data from the Internet to estimate and calculate travel costs, to evaluate travel plans that meet specified conditions and to analyze possible flight plans to determine the best value.  (standards addressed:  4.MD.2)
Single Day Lessons:

Patterns in Place Value  Students will reason about place value and work to understand the patterns found in place value ideas.  They will also work to develop the next base 10 block. (standards addressed: 4.NBT.1, 4.OA.1)

In these contextual problems, students use their place value understanding to work toward development of the standard algorithm with multi-digit addition and subtraction.  (standard addressed: 4.NBT.4)
Addition task: Big Fred Fans
Subtraction task: Out with the Old 
Making Your First Million In this lesson, one of a multi-part unit from Illuminations, students attempt to identify the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition until a million is reached. Additionally, they use critical thinking to analyze situations and to identify mathematical patterns that enable them to develop the concept of very large numbers. (standards addressed: 4.NBT.1)
What Counties Are Your Favorite?  In this lesson, one of a multi-part unit from Illuminations, students use their knowledge to gather data on ten of their favorite counties (places they might like to live, visit, etc.) within a specific state. Students hone their place value skills by representing numbers in various ways, including standard, written, and expanded form.  (standards addressed: 4.NBT.2)
Tasks for Measurement and Data (4.MD.2)
Connections & Companion Guide
In the following tasks, students use the context of  measurement and data to engage in multiple standards in the unit. These tasks are great for formative assessments, as they encompass  many of the unit standards. (Characters in these tasks will reoccur throughout the year.) 
Are We There Yet?  (standards addressed: 4.MD.2)
Jackson's Lawn Service  (standards addressed: 4.MD.2, 4.NBT.4)
Summer Vacation  (standards addressed: 4.MD.2, 4.NBT.2)
What's the Temp?  (standards addressed: 4.MD.2, 4.NBT.3, 4.NBT.4)
Illustrative Mathematics Tasks  The following task comes from the Illustrative Mathematics site (headed by Bill McCallum, co-author of CCSSM).  Illustrative Mathematics provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.
Ordering 4-Digit Numbers  (standards addressed: 4.NBT.2)

Lessons, Tasks and Investigations  The following lessons were written by the Georgia Department of Education and correspond with the standards in this unit.  Some lessons may require additional days. 
Place Value and Operations with Multi-Digit Numbers
Relative Value of Places
Number Scramble
Ticket Master
Estimation as a Check
Making Sense of the Algorithm
Reality Checking

Factors and Multiples
The Factor Game
Investigating Prime and Composite
Prime vs. Composite
Finding Multiples
Factor Findings
The Sieve of Eratosthenes

Area and Perimeter
Area and Perimeter

1st Quarter

Essential Questions

How does my understanding of place value and properties of operations help me multiply multi-digit whole numbers?

Mathematical Practices

What does this look like in 4th grade?

Click below for explanations and illustrations of each standard for elementary school.

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning

What is the standard algorithm?
This document provides explanations, strategies, misconceptions and ways to address misconceptions regarding "the standard algorithm" - 4.NBT.4

Open Response Formatted Tasks/Assessments

Shuttle Bus

Travel Time

Using Estimation

Problem Solving Resources
CCSS Problem Situations CGI Problem Types
Addition & Subtraction Addition & Subtraction
Multiplication & Division   Multiplication & Division 
Problem Solving - 3 Part Plan

Problems to pose that address the unit standards
*documents are in Word to enable instructional adjustments, number changes, etc.

True/False Statements   (standards addressed: 4.NBT.1, 4.NBT.2)

Promoting Rounding   (standards addressed: 4.NBT.3)

Multi-Digit Addition/Subtraction   (standards addressed: 4.NBT.4)

Contexts involving Measurement Units   (standards addressed: 4.MD.2) 

Additional Resources for Problem Solving  

  Check out this page if you need  help with your instructional moves during problem solving, video resources of classrooms in action, and other engaging activities.

Number Talks

Additional Resources
Click here to find out more and for resources with Number Talks

Addition and Subtraction   (standards addressed: 4.NBT.4)



Resource Guide for using Number Talks with Unit 1

SMART Notebook and Other Technology Resources

Place Value Warm-Ups  SMART Notebook
Engage students in conversations about place value. Problems can be used as daily warm ups or as multiple problems in a lesson.
(standards addressed 4.NBT.2, 4.NBT.3)

Over or Under  SMART Notebook
Engage students in mental math with estimation.
(standards addressed 4.NBT.3, 4.NBT.4)  
Factorize - Illuminations Interactive

This student interactive, from Illuminations, allows students to visually explore the concept of factors by creating rectangular arrays with an area equal to the product of the factors. They can choose whether or not to use the commutative property when identifying factors. (standards addressed:  4.OA.4)

Literature Connections

  *Share any connections you find!


Games and Activities

Choose a Number Project
Finding Multiples
Prime Number Hunt
Common Multiples
Find the Factor
Numeral, Word and Expanded Form

4. NBT.3
Round to the Nearest Ten
Round to the Nearest Hundred

Additional Resources

Progression documents for standards in this unit:

Number & Operations in Base Ten

Operations & Algebraic Thinking

Measurement & Data