3.NBT.2 - About the Math, Learning Targets, and Rigor

Full Standard

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

 

Measurement Topic

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

3rd Grade Students Learning 3rd 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.
• Use tools to show addition and subtraction.
• Recognize subtraction as takeaway and difference.

 

About the Math

• 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.  

• Use tools to show addition and subtraction.

Students can use a myriad of tools to represent addition and subtraction. Base ten blocks are one tool for students to use. Place value chips are another. Students should also have ample opportunities to work with number lines to represent their thinking and computation. Work with phsyical models should be connected to number lines and equations. Computation should be supported with representations, especially number lines.

• Recognize subtraction as takeaway and difference.

Subtraction means to take away. We might have 513 blocks and can take away 237. On a number line, we can count back 237 from 513. Subtraction also means to find the difference between two numbers. We can do this on a number line. Here, the difference between 513 and 237 on the number line indicates the difference between the two numbers.

 

Some may believe that these strategies are too complicated or inefficient. The fact is for many students (and adults) the strategies help students understand the mathematics.

 

3rd-grade students can work with the traditional algorithm. This should only happen after students are able to demonstrate understanding of the mathematics concepts. Students who use the traditional algorithm are still expected to estimate their sums and differences. They should also be able to explain what is happening with the algorithm.

 

Math In Minutes:  The video links below demonstrate strategies for addition and subtraction.

• Decomposition of Numbers Links to an external site.
• Addition With A Number Chart Links to an external site.
• Subtraction With A Number Chart Links to an external site.
• Addition On A Number Line Links to an external site.
• Addition: Partial Sums Links to an external site.
• Subtraction:  Take Away and Difference Links to an external site.
• Selecting Appropriate Mathematics Tools Links to an external site.

 

Progression of Standard within Grade 3

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. Use tools to show addition and subtraction. Recognize subtraction as takeaway and difference.	Reinforce through work with problem solving.	Reinforce through work with problem solving.	Reinforce through work with problem solving.

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades

Grade 2	Grade 4
Fluently +/- within 100 (2.NBT.B.5) Add and subtract within 1,000. (2.NBT.7)	Add and subtract multi-digit numbers. (4.NBT.4)

 

 

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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:
  

  

   

• • 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

• Karen solved an equation and found a sum of 152. (Teacher can change sum to be aligned with the expectation of the quarter.) What 2 addends could she have added? Karen created a subtraction sentence with a difference of 276, what could be the subtrahend and minuend?
• When adding two numbers, what do you notice about the relationship between the addends as one of the addends increases?
• Sam adds 2 numbers together that equal 64. Adam says that he can make 64 as a difference between 2 numbers. What could Sam and Adam’s numbers be? (Numbers can be made to fit students needs as well as more challenging by quarter.)
• Solve 348 + 292 = using as many different strategies as you can. Solve 712 - 285 = using as many different strategies as you can.
• Use the digits 2, 5, 0, 9, 6, and 7 to make two 3-digit numbers with the greatest sum. Now use the digits to make two 3-digit numbers resulting in the smallest difference.
• Create an addition sentence involving two 3-digit numbers whose sum is greater than 1,000 but less than 2,500.
• List 10 equations this picture might be describing.

 

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.

 

Additional Tasks

  These links provide instructional ideas connected to this standard. 

• The Water Boy Links to an external site.  (3 Act Task, Graham Fletcher) Links to an external site.
• Three Other Way Links to an external site.s (Georgia Dept. Of Ed., pages 16-21)
• Miles of Tiles (Task B) Links to an external site.  (Georgia Dept. Of Ed., pages 16-21)
• Once Upon a Time (Task B) Links to an external site.(Georgia Dept. Of Ed., pages 16-21)
• Disco Day Links to an external site. (Finance in the Classroom lesson seed)
• Basic Weekly Budget Links to an external site. (Finance in the Classroom lesson seed, scroll down)

 

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 Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematic	K-3	140 (Digit Change, Activity 5.16, pg 140) 146 (Numbers, Squares, Sticks, and Dots, Activity 5.21) 146 (50 and Some More, Activity 5.22) T147 (he Other Part of 100, Activity 5.23) 149 (Mystery Mats, Activity 5.27) 165 (Ten-Frame Adding and Subtraction,Activity 6.1) 184-185 (Expanded Lesson: Exploring Subtraction Strategies)
	Nimble With Numbers	2-3 3-4	82-86
	Hands On Standards(1-2)	1-2	48-49 (Subtracting Without Regrouping) 50-51(Subtracting With Regrouping) 52-53 (Decomposing Numbers)
	Math Intervention: Building Number Power	K-2   3-5	137-146 59-63 33-43 64-68 74-79
	Math In Practice Teaching Third-Grade Math	3	Module 6 & 7

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Centers

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

• Race to 500 Download Race to 500
    (HCPSS-adapted resource)
• 3 Digit Subtraction Download 3 Digit Subtraction
  (HCPSS-adapted resource)
• Double Trouble Download Double Trouble
  (HCPSS-adapted resource)
• Partial Sums (+) Break Apart Addition Squares Download Partial Sums (+) Break Apart Addition Squares
  (HCPSS-adapted resource)
• Count On (+)/Count Back(–) Number Line Addition and Subtraction Download Count On (+)/Count Back(–) Number Line Addition and Subtraction
  (HCPSS-adapted 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.

• Count On Addition Show on a Number Line Links to an external site.
• Partial Sums for Addition Links to an external site.
• Count Back to Subtract Links to an external site.
• Use Think Addition to Subtract Links to an external site.
• Use Make Tens/Hundreds to Add Links to an external site.
• Use Compensation to Add Links to an external site.
• Use Compensation/Adjustment to Subtract Links to an external site.
• Estimating and Adding Links to an external site.
• Estimating and Subtracting Links to an external site.
• Which Strategy Makes Sense? Links to an external site.
• Addition Links to an external site.
• Subtraction Links to an external site.

 

• Addition within 1000 (performance task) Links to an external site.
• Add Within 1000 Links to an external site.
• Add Within 1000_2 Links to an external site.
• Subtract Within 1000 Links to an external site.
• Subtract Within 1000_2 Links to an external site.
• Subtract Within 1000_3 Links to an external site.
• Add and Subtract Within 1000 Links to an external site.
• Add and Subtract Within 1000_2 Links to an external site.
• Add and Subtract Within 1000 3 Links to an external site.
• Add and Subtract Within 1000 4 Links to an external site.

One-Step Word Problems Involving Addition or Subtraction:

• One-Step Word Problems Addition and Subtraction c Links to an external site.
• Solve One-Step Within 100 Links to an external site.
• Solve One-Step Within 100_2 Links to an external site.
• Solve One-Step Within 100_3 Links to an external site.
• Solve One-Step Within 100_4 Links to an external site.

 

 

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Learning Targets

• Estimate sums and differences before calculating to determine reasonableness of answers.
• Represent addition and subtraction with base ten models and number lines.
• Use partial sums to add (decomposing one or both addends).
• Find the difference of two numbers by counting up or by counting back.
• Subtract within 1,000 using partial differences when decomposing the subtrahend.
• Adjust numbers to add or subtract more efficiently.
• Recognize subtraction as takeaway and difference.
• Count up or count back to find the difference.

 

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 Links to an external site.

 

 

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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