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

Grade 3 Whole Numbers

3.NBT.A.2

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

Screenshot 2024-02-15 at 9.33.33 AM.png
Explanation of Addition and Subtraction Strategies Links to an external site.

  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.

 

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
Add and subtract multi-digit numbers. (4.NBT.4)

 

 

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