2.NBT.B.9 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

Explain why addition and subtraction strategies work, using place value and the properties of operations.

Measurement Topic

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

About the Math

Skills and concepts below are learning goals for this standard.

• Explain why different addition and subtraction strategies work. Strategies include Partial Sums (+), Count Back (–), Count On (+), Think Addition (–),  Make Tens/Hundreds (+), and Compensation (+ and –).

This learning target is closely related to 2NBT5 and 2NBT7 in that one cannot apply a specific strategy if they do not understand how the strategy works. For this learning goal, students should be able to show/prove how a particular strategy works with various representations (manipulatives, charts, number lines). They should also be able to explain why the strategy works.

Essential vocabulary for this standard includes partial sums, count back, count on, think addition, make tens/hundreds compensation(adjusting), commutative property, associative property, and identity property. 

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 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.

Tasks 

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

• Gather base ten blocks or place value disks and a place value mat for each student. Students could also choose to draw a number line or use a hundreds chart. You could use graphic organizers such as a part part total mat.  Pose addition or subtraction problems for the students to solve. Problems could be set in context. Discuss with the class what strategies they could use to solve the problem (partial sums, count on, count back, think addition, make a ten or hundred and compensation). Additionally, what tools could they use such as a hundreds chart or a number line. Discuss what a reasonable answer would be and then have them build a model or use a tool to solve the problem. To debrief the math thinking, have students share out how they solved the problem and make connections between different student models. If students have not done so, connect their model to an equation. Pose questions such as how did you use your understanding of tens and ones to solve the problem. Another question could be why do we subtract ones from ones and tens from tens. 
• After students have had multiple exposure with solving problems with manipulatives and are able to articulate the importance of place values in addition and subtraction, you could have them start to draw physical models to solve addition and subtraction problems. Ask students how they could draw base ten blocks and/or place value disks. Pose a problem in context, preferably. Discuss strategies, tools, and a reasonable answer and have students solve the problem in their journal. Have students share their model and make connections between various models. 
• How are addition and subtraction related?
• How would you explain the commutative property to someone from another planet?
• Which property do you think is most important? Why?
• How does the associative property help us when we add numbers?
• Why does it make sense to make another ten and add some more when we add 8 or 9 to another number?

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. [NOTE: NCTM Membership required for access to Illuminations lessons.]

• Dinosaur Museum Download Dinosaur Museum
  (Utah Core Academy Lesson)
• Fundraiser Download Fundraiser
  (Utah Core Academy Lesson)
• Sum Search Links to an external site. (NCTM Illuminations Lesson Seed)

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	146 (Numbers, Squares, Sticks and Dots, Activity 5.21)
	SuperSource: Base Ten Blocks	K-2	30-33 (Feed the Birds) 58-61 (Race for a Fla) 62-65 (Race to Clear the Mat) 66-69 (Subtraction Split) 70-73 (Sum It Up) 82-85 (What's the Difference?) 86-89 (Who's Got the Most?)
	Math Intervention: Building Number Power	3-5	139-143 (Commutative and Associative Properties
	Math In Practice Teaching Second-Grade Math	2	Modules 6 & 7

Centers

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

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.

• Explain Why Addition and Subtraction Strategies Work Two-Digit Numbers a Links to an external site.
• Explain Why Addition and Subtraction Strategies Work Two-Digit Numbers b Links to an external site.
• Explain Why Count Back Think Addition and Partial Sums Work Two-Digit Numbers Links to an external site.
• Explain Why Compensation Works Two-Digit Numbers Links to an external site.
• Explain Why Subtraction Strategies Work Three-Digit Numbers Links to an external site.
• Explain Think Addition Links to an external site.

• Solve Word Problem with Explanation Links to an external site.
• Explain the Commutative Property Links to an external site.
• Explain the Commutative Property_2 Links to an external site.
• Explain the Associative Property Links to an external site.
• Relate Counting Back and Think Addition Links to an external site.
• Apply Properties to Solve Equations Links to an external site.

Full Standard

Explain why addition and subtraction strategies work, using place value and the properties of operations.

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

2NBT9 Anecdotal Data Collection Tool (Addition) Links to an external site.

2NBT9 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.

2NBT Explain Think Addition

• Printable Task Links to an external site.
• Student Exemplars Links to an external site.