Grade 4 Whole Numbers

4.NBT.4

About the Math

Full Standard

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**4th Grade Students Learning 4th Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition and subtraction of whole numbers and fractions.

**3rd Grade Students Learning 4th Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition and subtraction.

Learning Targets

Estimate sums and differences before calculating to determine reasonableness of answers.
Count on to find the sum.
Count back to subtract.
Use partial sums to add.
Use think addition to find the difference.
Use compensation/adjusting to add or subtract more efficiently.
Explain and connect strategies to the standard algorithm for addition and subtraction
Add and subtract multi-digit numbers using the standard algorithm
Determine when an algorithm is efficient and when it is not

About the Math

Skills and concepts below are learning goals for this standard.

Estimate sums and differences before calculating to determine reasonableness of answers.

Estimating sums and differences before calculating enables students to develop greater accuracy and precision. Students should frequently be asked to estimate a sum or difference before calculating. They should also be asked to compare their results to estimates to determine if their work is reasonable.

Count on to find the sum.

Teaching of the counting on strategy begins in Kindergarten with one-digit addends. Counting on extends to larger numbers by breaking apart one addend and adding it to the other addend in chunks. Given 124+245, a student might start with 245+120 to get 365 and then add 365+4=369. A student might break apart 245=200+40+5 and start with 124+200=324, 324+40=364, 364+5=369.

Count back to subtract.

We can count back to find the difference. One can count back starting with the minuend and counting back the amount of the subtrahend. On the number line, we see 536 - 357 where 357 has been decomposed and counted back from 536. One could also find the difference between 536 and 357 on the number line if desired.

Use partial sums to add.

We can decompose addends and add the parts. Those partial sums can then be added to find the final sum.

The partial sums algorithm for adding 3-digit numbers breaks the addition problem into a series of easier problems based on place value. Answers to the simpler problems are added together to determine the final sum.

When adding 378 + 254 we can decompose each addend and add place values. For example,

300 + 70 + 8
+ 200 + 50 + 4
500 + 120 + 12 = 632

Then partial sums are added together. 500 + 120 + 12 = 632

Students can represent partial sums with physical tools and number lines. As students develop understanding, their focus should be shifted to decomposing one of the addends as it is usually more efficient.

Use think addition to find the difference.

Another option is to count up from the subtrahend. Here to find the difference of 536 - 179. One started with 179 and counted up to 536. The size of the jumps between these numbers can vary. Here, a jump of 21 was followed by 300, and then 36. Adding

those jumps together identifies the difference as 357.

Use compensation/adjusting to add or subtract more efficiently.

Numbers can be adjusted to compute more efficiently, This can be helpful in many situations. Consider 289 + 457. It can be thought of as 300 + 446 instead. The sums are the same. The latter is a more efficient computation because students can count on by 300. When adjusting addition expressions, an amount is given from one addend to the other. Adjusting subtraction functions differently. It is built on the notion of constant or same difference. Simply, 5 - 4 is the same as 4 - 3. Both are adjusted by 1. It can be used to solve something like 702 - 329. Instead, we can think of 699 - 326 finding a friendlier computation that requires no regrouping. When adjusting subtraction problems, BOTH numbers are adjusted in the same way.

Explain and connect strategies for adding and subtracting to the standard algorithms for those operations.

When introducing the standard algorithms, students should connect the above strategies to the algorithm noting how they are similar and different.

Add and subtract multi-digit numbers using the standard algorithm.

The standard algorithm adds the digits of each place value in ascending order beginning with the smallest place value. The standard algorithm subtracts the digits of each place value in ascending order beginning with the smallest place value.

Determine when an algorithm is efficient and when it is not.

Students who understand the algorithm must also know when it is efficiently used. Many computations are completed more efficiently using varied strategies and/or mental mathematics. For example, 324 + 1,400 can be added with an algorithm but many students can simply add 300 then 24 more. This is why so much time is spent in earlier grades decomposing numbers and adding multiples of tens, hundreds, and so on.

Progression of Standard within Grade 4

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Estimate sums and differences before calculating to determine reasonableness of answers. Count on to find the sum. Count back to subtract. Use partial sums to add. Use think addition to find the difference. Use compensation/adjusting to add or subtract more efficiently. Explain and connect strategies to the standard algorithm for addition and subtraction Add and subtract multi-digit numbers using the standard algorithm Determine when an algorithm is efficient and when it is not	Reinforce through work with problem solving.	Reinforce through work with problem solving.	Reinforce through work with problem solving.

Revisit this standard during the year through routines, independent practice, discussions, and other activities.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Progression Across Grades
Grade 3	Grade 5
Add/subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction (3.NBT.2)	Fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.5) Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors (5.NBT.6) Add and subtract decimals (5.NBT.7)

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Instructional Materials for the various computation strategies can be found in Figuring Out Fluency Addition and Subtraction with Whole Numbers (this book has been provided to schools) as follows:

Book Cover for Figuring Out Fluency Addition and Subtraction with Whole Numbers

- Count On (Addition)/Count Back (Subtraction)-- pages 22-37
- Partial Sums (Addition)-- pages 61-78
- Think Addition (Subtraction)-- pages 104-119
- Make Tens/Hundreds (Addition)-- pages 40-56
- Compensation (Addition and Subtraction)-- pages 83-100
- Standard Algorithm (Addition and Subtraction)-- pages 120-126

Create opportunities for students to evaluate the accuracy of a given equation. Students should determine if the answers are correct or incorrect. If they are incorrect, they need to identify and correct the errors. The equations can be given on a worksheet, index cards, or on posters around the classroom.
While students are practicing adding and subtracting using the standard algorithm, another student or the teacher should use place value disks to model the meaning behind regrouping with the algorithm.
What two addends could equal a sum of 146? (e.g., 67, 298, 1,130, etc.)
What two numbers could you subtract to make a difference of 94? What could the two numbers be when regrouping is required? What could the two numbers be if no regrouping is required?
How many different ways can you solve 39+84? 73-25? What is similar/different between these strategies and the standard algorithm?
Do you think the standard algorithm is more efficient than other strategies? Why or why not?
What is the relationship between the standard algorithm and place value?
Using two 3-digit numbers, create two different addition equations with a sum between 300 and 400.
Using the digits 3, 5, 1, 8, 2 and 6, create a subtraction equation with the largest possible difference.
List 3 addends whose sum is between 2000 and 3000 (also good for enrichment).
Write an addition problem that has a sum of 3,697. Use two four-digit numbers.
Tell how you know that when you add 4,789 and 4,216 it will be less than 10,000.
Give students an addition sentence with missing digits. Have them find the missing digits. For example, 3,444 + 8_6 = 4,300. What number is missing from the addition sentence?

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 3 • Addition and Subtraction and Review Basic Facts (9s)

Add multi-digit numbers using partial sums or counting up.

Subtract multi-digit numbers using counting back or think addition:

Introduce the standard algorithm for addition and subtraction connecting it to representations and other strategies:

Module 4 • Addition and Subtraction and Review Basic Facts (4s)

Add/Subtract multi-digit numbers using compensation (adjusting):

Add/Subtract multi-digit numbers using the standard algorithm:

Additional Tasks

These links provide instructional ideas connected to this standard.

To regroup or not to regroup (Illustrative Math)
Where's the Beef (3 Act Task, G.Fletcher)
Miles of Tiles (InsideMathematics Task B)
Once Upon a Time (InsideMathematics Task B)
Making Sense of the Algorithm (Georgia Department of Education, pg. 53-56)
Reality Checking (Georgia Department of Education, pg. 57-64)
Lagoon Adventure.doc (Cache County, Utah lesson)
Bicyle Shopping Spree.doc (Cache County, Utah lesson)
Vacation Miles.docx (Cache County, Utah lesson)
My Mountain Ranges.doc (Cache County, Utah lesson)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	3-5
Hands on Standards	3-4	20-21
Brain-Compatible Activities for Mathematics	4-5	13-15
Developing Mathematics with Base Ten	2-6	44-46, 67-70
Math Intervention: Building Number Power	3-5	118-120, 124-128
Number Sense	3-4 4-6	87-90 40-42
Math In Practice Teaching Fourth-Grade Math	4	Module 4

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Tell Me A Story (HCPSS-adapted print resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

Add multi-digit numbers using partial sums and count on:

Subtract multi-digit numbers by using think addition or count back:

Add and subtract multi-digit numbers by using compensation (adjusting):

Add and subtract multi-digit numbers with the standard algorithm:

Problem Solving with Addition and Subtraction:

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Assessment

Learning Targets

rubric

Add multi-digit numbers using partial sums.
Adjust multi-digit numbers to add.
Subtract multi-digit numbers using partial differences by adding up or counting back.
Adjust multi-digit numbers to subtract.
Use number lines to add and subtract multi-digit numbers.
Explain and connect strategies for adding to the standard algorithm for addition.
Add multi-digit numbers using the standard algorithm.
Explain and connect strategies for subtracting to the standard algorithm for subtraction.
Subtract multi-digit numbers using the standard algorithm.
Determine when an algorithm is efficient and when it is not.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

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