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Addition and Subtraction Within 100
Students add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction. Students apply this new computational understanding to solving comparison word problems as well as working with categorical data.
Math
Unit 2
2nd Grade
Unit Summary
Please Note: In July 2025, this unit and its lesson plans received a round of revisions. Teachers should pay close attention as they intellectually prepare to account for the updated pacing and content.
In Unit 2, 2nd grade students focus on adding and subtracting within 100. By the end of 2nd grade students are expected to fluently add and subtract within 100 using strategies based on place value, properties or operations, and the relationship between addition and subtraction 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. . Students will extend their work within 20 from Unit 1 to larger numbers in this unit, using some of the same strategies as well as learning new methods to compute.
In Topic A, students begin the unit by relating their work with counting in Unit 1 to the idea of adding and subtracting with multiples of ten and multiples of one. Then, in Topic B, the focus shifts to strategies for adding within 100. First, students connect and extend strategies like making ten to add within 20 from Unit 1 to make a multiple of ten to add within 100 (e.g., 46 + 29 can be made into the easier computation 45 + 30). Next, students develop general methods to add, starting with using concrete base ten blocks to add by place, then drawing pictorial base ten blocks, and finally writing more abstract equations to show how they solved.
In Topic C, students will focus on subtraction. They start with connecting some of their strategies to subtract within 20 from Unit 1 to subtract within 100 (e.g., to subtract 52 - 4, subtracting 52 - 2 to get to 50, then another 2 to get to 48). Then, they similarly move through using concrete manipulatives to subtract by place, then pictorial, and finally writing equations to record their work. The topic ends with a lesson where students add and subtract within 100 using a variety of strategies, giving students an opportunity to use appropriate tools strategically based on the numbers involved MP.5 Use appropriate tools strategically. .
Finally, in Topic D, students build on the work with word problems by solving compare problems within 100. They continue to use tape diagrams to represent the problem and use symbols to represent the unknown in their equations. Students then end the unit by exploring categorical data with picture graphs and bar graphs. Students learn about the structure of both graph types and learn to interpret and create them to answer and ask questions based on the given data 2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. .
The work students explore in this unit provides them with a foundation for their work in future units in 2nd grade, most notably Unit 5 where they will extend their addition and subtraction methods to within 1,000. Students will continue to build their fluency with 100 throughout their 2nd grade work in a variety of ways, including solving word problems within 100, adding and subtracting on the number line in Unit 3, and solving word problems involving money, among many other applications.
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Assessment
The following assessments accompany Unit 2.
Mid-Unit
Have students complete the Mid-Unit Assessment after Lesson 8.
Post-Unit
Use the resources below to assess student understanding of the unit content and action plan for future units.
Unit Prep
Intellectual Prep
Intellectual Prep for All Units
- Read and annotate "Unit Summary" and "Essential Understandings" portion of the unit plan.
- Do all the Target Tasks and annotate them with the "Unit Summary" and "Essential Understandings" in mind.
- Take the Post-Unit Assessment.
Unit-Specific Intellectual Prep
- Read pp. 52-61 of the Number and Operation in Base Ten Progressions.
Essential Understandings
- Many strategies that can be used to make computations within 20 easier can be extended to make computations within 100 easier. For example, just like 6 + 9 can be thought of as 5 + 10, 46 + 29 can be thought of as 45 + 30.
- Two-digit numbers are composed of tens and ones, and 10 ones are equivalent to 1 ten. Therefore in addition situations, if there are 10 ones, they are composed to make a ten. In subtraction situations, if there are not enough ones to subtract, a ten can be decomposed into 10 ones to subtract.
- Making sense of problems and persevering in solving them is an important practice when solving word problems. Key words do not always indicate the correct operation, so representing story problems with tape diagrams and equations helps students to conceptualize and solve them.
Materials
- Optional: Hundreds Chart (1 per student)
- Linking cubes (120 per student)
- Base ten blocks (10 tens and 20 ones per student or small group) — One additional set for the teacher
- Optional: Tens place value chart (1 per student or small group) — Some students may benefit from the use of a tens place value chart to organize their base ten blocks or linking cubes. These can be laminated or in sheet protectors to reuse, or students will need multiple copies.
- Dice (1 per student or small group) — For Problem Set use only
- Base Ten Block Subtraction Cards (1 per group of 4 students)
- Optional: Clipboards (1 per student)
Vocabulary and Models
Unit Vocabulary
bar graph
data
key
picture graph
To see all the vocabulary for Unit 2, view our 2nd Grade Vocabulary Glossary.
Models
| Model | Example |
| concrete base ten blocks | 34 shown in concrete base ten blocks |
| pictorial base ten blocks | 27 shown in pictorial base ten blocks |
| tape diagram | Example: The second grade classes made greeting cards for some patients at a nursing home. Last week they made 68. This week they made 49. How many more cards did they make last week than this week? |
| picture graph | |
| bar graph | |
Unit Practice
Lesson Map
Topic A: Addition and Subtraction with Multiples of Ten or One
Topic B: Addition within 100
Topic C: Subtraction within 100
Topic D: Word Problems and Categorical Data
Common Core Standards
Key
Major Cluster
Supporting Cluster
Additional Cluster
Core Standards
Measurement and Data
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2.MD.D.10 — Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
Number and Operations in Base Ten
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2.NBT.B.5 — Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
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2.NBT.B.9 — Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.
Operations and Algebraic Thinking
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2.OA.A.1 — Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Foundational Standards
Measurement and Data
-
1.MD.C.4
Number and Operations in Base Ten
-
1.NBT.C.4
-
1.NBT.C.5
-
1.NBT.C.6
Operations and Algebraic Thinking
-
1.OA.A.1
-
1.OA.D.7
-
2.OA.B.2
Future Standards
Number and Operations in Base Ten
-
3.NBT.A.2
Operations and Algebraic Thinking
-
3.OA.D.8
Standards for Mathematical Practice
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CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
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CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
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CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
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CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
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CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
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CCSS.MATH.PRACTICE.MP6 — Attend to precision.
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CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
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CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
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