Addition and Subtraction Within 20

Students extend their knowledge of addition and subtraction within 20 to fluently add and subtract within 20 using various strategies. This work is put into practice as students solve add to, take from, and put together/take apart word problem types using tape diagrams and equations to represent what is happening mathematically.

Math

Unit 1

2nd Grade

Unit Summary


Please Note: In March 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.

This introductory unit focuses on a variety of concepts that students will build throughout the year, including fluently adding and subtracting within 20; counting by ones and tens within 200; and solving add to, take from, and put together/take apart word problems with unknowns in all positions. Students will use appropriate tools, including linking cubes, number bonds, ten frames, tape diagrams, and equations, strategically throughout the unit MP.5 Use appropriate tools strategically.  and use them to make sense of problems and persevere in solving them MP.1 Make sense of problems and persevere in solving them.

In Grade 1, students added and subtracted fluently within 10 and added and subtracted within 20 using a variety of strategies such as counting on, making ten, going down over ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums such as using doubles facts (1.OA.C.6). Students also counted by ones within 120 (1.NBT.A.1) and by tens within 100 (1.NBT.B.5). Further, students solved add to, take from, and put together/take apart story problems with unknowns in all positions, though students were not yet expected to be proficient with start unknown problems (1.OA.A.1).

This unit starts off with returning to some of that Grade 1 material in Topic A, namely adding and subtracting within 10 (1.OA.C.6, 2.OA.A.2) as well as counting by ones and tens, though the count sequence is now extended to 200 (2.NBT.A.2). Topic B focuses on adding and subtracting within 20, revisiting all of the strategies seen in Grade 1, such as making ten or using doubles facts, as they now work towards fluency within 20, eventually knowing from memory all sums of two one-digit numbers and related subtractions (2.OA.B.2) by the end of the year. Finally, in Topic C, the focus turns to add to, take from, and put together/take apart story problems within 20, using tape diagrams and equations to represent them (2.OA.A.1). They also pay particular attention to start unknown situations since students are not yet proficient with those subtypes. 

This provides an important foundation for work in subsequent units and grades. Students will extend the count sequence to 1000 later in Grade 2, and even add and subtract within 1000 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction (2.NBT.B.7), demonstrating fluency for addition and subtraction within 100 (2.NBT.B.5). These multi-digit computations heavily rely on students knowing from memory all sums of two one-digit numbers and related subtractions, since multi-digit computations can be thought of as a series of single-digit computations, with one for each place in the given numbers. Lastly, students will build on their story problem work by studying compare problems with unknowns in all positions in Unit 3 and then solving two-step word problems later in the year. Beyond Grade 2, they’ll fluently add and subtract within 1000 in Grade 3 (3.NBT.A.2) and study numbers of even greater magnitude (up to 1 million) in Grade 4 (4.NBT.A), where they will also gain fluency with the addition and subtraction algorithm (4.NBT.B.4).

Assessment


The following assessments accompany Unit 1.

Mid-Unit

Have students complete the Mid-Unit Assessment after Lesson 10.

Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Expanded Assessment Package

Use student data to drive instruction with an expanded suite of assessments. Unlock Mid-Unit Assessments and Answer Keys to help assess progress with unit content and inform your planning.

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. 44–51, Appendices 1 and 2 of the Progressions

Essential Understandings

  • There are patterns in the numbers when counting by ones and tens. When counting by ones, the ones digit of the number increases by 1 each time, and similarly when counting by tens, the tens digit of the number increases by 1 each time. It can be particularly challenging to count when crossing a decade or hundred number since multiple digits change with that crossing. 
  • Making a ten and going down over ten to add and subtract within 20 rely on (1) knowing the partner that makes 10 for any number, (2) students’ fluency with addition and subtraction within 10, and (3) understanding teen numbers as 10 + n
  • 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 concrete objects, tape diagrams, and equations helps students to conceptualize and solve them.

Vocabulary and Models

Models

Model Example
number bond

A number bond for 10 = 3 + 7

tape diagram

Example: Armando buys 16 peppers for a barbecue. 7 of the peppers are red and the rest of the peppers are orange. How many orange peppers did Armando buy?

ten frame

Double ten frames showing 8 + 3

Materials

Unit Practice


Lesson Map


Topic A: Adding and Subtracting within 10 and Counting

Topic B: Adding and Subtracting within 20

Topic C: Story Problems within 20

Common Core Standards


Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

Number and Operations in Base Ten

  • 2.NBT.A.2 — Count within 1000; skip-count by 5s, 10s, and 100s.

Operations and Algebraic Thinking

  • 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.
  • 2.OA.B.2 — Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. See standard 1.OA.6 for a list of mental strategies.

Foundational Standards

Number and Operations in Base Ten

  • 1.NBT.A.1
  • 1.NBT.B.2

Operations and Algebraic Thinking

  • 1.OA.A.1
  • 1.OA.B.3
  • 1.OA.B.4
  • 1.OA.C.6
  • 1.OA.D.7
  • 1.OA.D.8

Future Standards

Number and Operations in Base Ten

  • 2.NBT.A.1
  • 2.NBT.B.5

Operations and Algebraic Thinking

  • 3.OA.D.8

Standards for Mathematical Practice

  • CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

  • CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

  • CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

  • CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

  • CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

  • CCSS.MATH.PRACTICE.MP6 — Attend to precision.

  • CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

  • CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Read Next

Addition and Subtraction Within 20
Lesson 1
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