2.NBT.B.5 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

Fluently add and subtract within 100 using strategies 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:

2nd Grade Students Learning 2nd Grade Standards

Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition   Report Card Measurement Topic: Demonstrates understanding of subtraction	Report Card Measurement Topic: Demonstrates understanding of addition   Report Card Measurement Topic: Demonstrates understanding of subtraction

1st Grade Students Learning 2nd Grade Standards

Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition   Report Card Measurement Topic: Demonstrates understanding of subtraction	Report Card Measurement Topic: Demonstrates understanding of addition   Report Card Measurement Topic: Demonstrates understanding of subtraction

 

About the Math

Skills and concepts below are learning goals for this standard.

• Explain the meaning of addition and subtraction within 100 using physical tools, hundred charts, drawings, and number lines. 

Fluency is grounded in understanding. Developing an understanding of two-digit addition and subtraction begins with physical models. Those models should be connected to work with hundred charts and ultimately number lines. Know that work with number lines should include open number lines after students demonstrate an understanding of computation on a ticked number line. 

• Add within 100 using Partial Sums (when decomposing both addends by place value).

Partial sums is an efficient way to add. For partial sums, one can decompose both addends and then add the tens with the tens and the ones with the ones. For example, 44 + 23 can be thought of as 40 + 20 (60) and 4 + 3 (7). The partial sums, 60 and 7, are then added for a sum of 67. Students should use models, charts, and number lines to show understanding (when appropriate).

 

• Subtract within 100 using Count Back (decompose/break apart the subtrahend and count back to find the difference).

When counting back, students can decompose the subtrahend and count back to find the difference. For example, 44 - 12, one can decompose 12 into 10 and 2 counting back by 10 and then 2. When subtracting larger numbers, such as 54, students can decompose and count back by tens (5 jumps of 10) but should shift to larger jumps (a jump of 50) once understanding is evident.

• Add within 100 using Count On (decomposing one addend and counting on to find the sum).

Decomposing one addend and counting on is typically more efficient than using partial sums (decomposing both addends). For the problem above, 44 + 23, one can decompose 23 into 20 and 3 and add on from 44, 44 + 20 = 64,  64 + 3 = 67. Students should understand that either addend can be decomposed. They should also be able to explain why they select one of the addends over another for decomposition.

• Find the difference of two numbers using Think Addition (counting up or by counting back to find the difference between two numbers).

This strategy models the "difference" type of subtraction rather than the "take away" type (see Count Back above). For example, given the problem 53 – 27, a student can count up (thinking addition, what added to 27 gets me to 53)... 27 + 20 = 47, 47 + 3 = 50, 50 + 3 = 53 and then add the amounts that were added 20 + 3 + 3 = 26 to find the difference. Similarly using the same problem, a student can find the difference between two numbers by counting back as follows: 53 – 20 = 33, 33 – 6 = 27 and the amounts subtracted are added together 20 + 6 = 26 to find the difference.

• Add and subtract within 100 using Compensation and Make Ten (adjusting numbers to add or subtract more efficiently).

Numbers can be adjusted to compute more efficiently, This can be helpful in many situations. Consider 34 + 49. It can be thought of as 33 + 50 instead (make ten). The sums are the same. The latter is a more efficient computation because students can count on by 50.  Students might also adjust by thinking of 34 + 49 as 34 + 50 = 84, and then adjust back 84 – 1 = 83.  Adjusting with subtraction can be used to solve something like 72 - 39. We can think of 73 - 40 to make an easier problem with the same difference of 23. Another student might only adjust one number in the problem, thinking of 72 – 39 as 72 – 40 = 22 and then adding 22 + 1 = 23 to account for the full difference.  

• Estimate the sum or difference of an addition or subtraction problem.

Estimation is critical for developing number sense and fluency. Students should consistently estimate sums and differences. This can be done by using compatible or friendly numbers. For example, 43 + 35 could be estimated as 80 as 40 + 40 is 80. 

Essential vocabulary for this standard includes: add, subtract, addition, subtraction, addend, sum, difference, adjusting, partial sums, partial differences, counting back, counting on,  and strategy. 

 

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 2

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
Explain the meaning of addition and subtraction within 100 using physical tools, hundred charts, drawings, and number lines. Add within 100 using partial sums when decomposing both addends (using tools as appropriate). Subtract within 100 using count back (with tools as appropriate). Add within 100 using count on (with tools as appropriate). Find the difference of two numbers using think addition (counting up or by counting back to find the difference of two numbers). Add and subtract within 100 using compensation (adjusting numbers to add or subtract more efficiently). Estimate the sum or difference of an addition or subtraction problem.	Explain the meaning of addition and subtraction within 100 using physical tools, hundred charts, drawings, and number lines. Add within 100 using partial sums when decomposing both addends (using tools as appropriate). Subtract within 100 using count back (with tools as appropriate). Add within 100 using count on (with tools as appropriate). Find the difference of two numbers using think addition (counting up or by counting back to find the difference of two numbers). Add and subtract within 100 using compensation (adjusting numbers to add or subtract more efficiently). Estimate the sum or difference of an addition or subtraction problem.	Revisit this standard through when problem solving with money and measurement.	Revisit this standard through when problem solving with money and measurement.

 

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 Throughout Year

Grade 1	Grade 3
Add within 100 (1.NBT.4)  Mentally find 10 more or 10 less than a two-digit number (1.NBT.5) Subtract multiples of 10 in the range 10-90 from multiples of 10 (1.NBT.6 )	Fluently +/- within 1,000 (3.NBT.2)

 

 

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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 20-37
  • Partial Sums (Addition)-- pages 58-78
  • Think Addition (Subtraction)-- pages 102-119
  • Make Tens/Hundreds (Addition)-- pages 38-56
  • Compensation (Addition and Subtraction)-- pages 80-100

• Provide base ten blocks or place value disks, a hundreds chart and place value mats. Have students add two two-digit numbers. Pose problems in context such as in the classroom there are 14 brown chairs and 27 blue chairs. How many chairs are in the classroom? Provide time for students to work with a partner to solve the problem with whatever tool they would like. They could use a number line as a tool as well as the blocks, disks, or hundreds chart. Invite students to share their model and their solution path. Pose questions such as what did you do first to solve the problem? How did you count your blocks/disks? Provide time for other students to share and make connections between how students solved the problem. 
• Show the students a number bond and have them identify the equations it represents. For example, 48 + 19 = 67,  19 + 48 = 67, 67 - 48 = 19 and 67 - 19 = 48. Create additional number bonds and have students identify the equations. Students can also create their own number bonds.
  
• Draw a number line such as the one below and ask students to identify the equation it represents.
  
• Display a representation such as the one below and ask students to identify the equation it represents.
  
• One way to add 28 + 34 is to add
  20 +  30 = 50
  8 + 4 = 12
  50 + 12 = 62
  What is another way to solve 28 + 34?
• LP says 55 - 26 is 31. Isaac says 55 - 26 = 29. Who do you agree with? Justify your response. 
• Sophie said you can solve 36 + 46 by solving 40 + 42.  Do you agree with her? Justify your response.
• Create five different equations that equal 36.
• The sum is 83, what could be the two two-digit addends? Give a different solution.
• Using one or two-digit numbers, write a subtraction equation with a difference of 42.
• Using a hundred chart, choose two numbers to add or subtract. Show how to use the chart to add or subtract them without using paper to solve.
• Use the digits 4, 2, 0 and 7 to create two two-digit numbers with the greatest sum, the smallest difference.
• Solve 35 + 58 = with two different strategies.
• Place the digits 1, 3, 4, 5, 6 and 8 in the blanks ( + = ) to make a true number sentence. Now find another solution using the same digits (only once). (36 + 45 = 81 and 18 + 36 = 54, might be more)
• What 2-digit numbers could you add to 763 so that you would still have a sum less than 800?
• Temperature Check - Page 106 in Figuring Out Fluency.  Teachers can use the slides Links to an external site. to support the introduction of this task.  The connection to Think Addition can be made as students find the difference between AM and PM temperatures.  *Note - Fall and Spring temperatures typically have a larger change from AM to PM.
• Sorting Estimates - Students work to sort expressions based on their estimated sums.  They should have the opportunity to justify their thinking and reasoning behind the placement of each expression.  Teachers can create their own expressions using index cards or use the options provided in the worksheet Links to an external site..  

 

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. 

• Saving Money 2 Links to an external site.(Illustrative Math) 
• The Pringle Ringle Links to an external site. (3 Act Task, G.Fletcher)
• Addition~There's More Than One Way Links to an external site. (Utah Education Network Lesson Seed)
• Tim's Bakery Download Tim's Bakery
  (Utah Core Academy Lesson)
• Taki Challenge Download Taki Challenge
  (Utah Core Academy Lesson)
• Box Tops Download Box Tops
  (Utah Core Academy Lesson)
• 2-digit Addition Game Download 2-digit Addition Game
  (Utah Core Academy Lesson)
• Story Problems, Revisited, Pg. 46 Links to an external site. (Georgia Department of Education)

 

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 Mathematics	K-3	165 (Ten-Frame Adding and Subtracting, Activity 6.1)
	Math In Practice Teaching Second-Grade Math	2	Modules 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.

• 52 Less Download 52 Less
  (HCPSS-adapted resource)
• Number Line Addition and Subtraction Download Number Line Addition and Subtraction
  (HCPSS-adapted resource)
• Discover the Difference Download Discover the Difference
   (HCPSS-adapted resource)
• Double Trouble Download Double Trouble
  (HCPSS-adapted resource)
• Pictures with Base Ten Download Pictures with Base Ten
  (HCPSS-adapted resource)
• Race to 100 Download Race to 100
  (HCPSS-adapted resource)
• Searching for the Sum Download Searching for the Sum
  (HCPSS-adapted resource)
• Spin and Solve Download Spin and Solve
  (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.

Important Note for 2NBT5: Below you will find strategy specific options as well as options for overall adding and subtraction. There are instructional uses for both types of evaluation items. When considering grading and reporting, it is important to remember the measurement topic is wholistic "demonstrates understanding of addition/subtraction" AND the measurement topic also includes standards beyond 2NBT5 (see the crosswalk). A student's grade for the quarter should reflect their overall progress toward "demonstrating understanding of addition/subtraction". 

 

• Add Using Partial Sums Links to an external site.
• Subtract Using Count Back Links to an external site.
• Subtract Two-Digit Using Count Back b Links to an external site.
• Add Using Count On Links to an external site.
• Subtract Using Think Addition Links to an external site.
• Add Using the Make Ten Strategy Links to an external site.
• Add Two-Digit with Count On and Make Ten Links to an external site.
• Subtraction Using the Compensation Strategy Links to an external site.
• Add Two-Digit Numbers B Links to an external site.
• Subtract Two-Digit Numbers B Links to an external site.
• Add and Subtract Two-Digit Numbers a Links to an external site.
• Add and Subtract Two-Digit Numbers b Links to an external site.
• Add Using Base Ten Pictures Links to an external site.
• Subtract Using Base Ten Pictures Links to an external site.
• Add and Subtract Using Base Ten Pictures Links to an external site.
• Subtract Using a Number Line Links to an external site.
• Add and Subtract Using a Number Line Links to an external site.
• Add and Subtract Using a Number Line 2 Links to an external site.
• Partial Sums A Links to an external site.
• Partial Sums B Links to an external site.
• Partial Sums C Links to an external site.
• Word Problem Links to an external site.
• Subtract with Two Different Strategie Links to an external site.s
• Add and Subtract Two-Digit Numbers Links to an external site.
• Add Efficiently (performance task) Links to an external site.
• Subtract Efficiently (performance task) Links to an external site.

 

 

 

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Full Standard

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

 

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

 

2nd Grade Students Learning 2nd Grade Standards by Measurement Topic

 

1st Grade Students Learning 2nd Grade Standards by Measurement Topic

 

2NBT5 Anecdotal Data Collection Tool (Addition) Links to an external site.

2NBT5 Anecdotal Data Collection Tool (Subtraction) Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification. 

 

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Rubric for Tasks (pdf) Links to an external site.

 

Exemplars for this standard

Use the links below to access a task for this standard as well as student work samples that are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.

Add Two-Digit Numbers, Printable Task Links to an external site.

Student Exemplars Links to an external site.

 

Subtract Two-Digit Numbers, Printable Task Links to an external site.

Student Exemplars Links to an external site.

 

 

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