2nd Grade Math | Addition and Subtraction within 20

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 2 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).

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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

Suggestions for how to prepare to teach this unit

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

The central mathematical concepts that students will come to understand in this unit

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

Models and representations that students learn or use in the unit

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

The materials, representations, and tools teachers and students will need for this unit

Optional: Linking cubes (max 20 per student) – This could be some other small manipulative like square tiles
Four in a Row Game Board L (add and subtract within 10) (1 per pair of students)
Game piece or token (2 per pair of students) – These could be paper clips, individual linking cubes, etc.
Optional: Colored Pencils (2 per pair of students) – See Lesson 1 for more information
Four of a Kind Card Set G (+/- within 10) (1 set per group of 3 or more students)
Optional: Cardstock – Card sets can be printed on cardstock, if available
Hundreds Chart (1 per student)
Blank Hundreds Chart (1 per student)
Baggies of collections ranging in size up to (but not equal to) 100 objects (at least 1 per pair of students) – See Lesson 4 for more information
Counting Collections Recording Sheet (at least 1 per student)
Optional: Counting Collections Folder (1 per student) – See Lesson 4 for more information
Optional: Clipboards (1 per student)
Optional: Ten Frame Template (1 per student)
Four of a Kind Card Set H (+/- within 20) (1 set per group of 3 or more students)
Story Problem and Tape Diagram Sort Cards (1 per pair of students)
Equation Sort Cards (1 per pair of students)

Unit Practice

Lesson Map

Topic A: Adding and Subtracting within 10 and Counting

1

Lesson

Find the value of addition and subtraction expressions where the total is within 10.

Standards

2.OA.B.2

2

Lesson

Find the value that makes equations true where the total is 10.

Standards

2.OA.B.2

3

Lesson

Find the value that makes equations true where the total is less than or equal to 10.

Standards

2.OA.B.2

4

Lesson

Count by ones and tens within 200.

Standards

2.NBT.A.2

Topic B: Adding and Subtracting within 20

5

Lesson

Find the value that makes equations true where one part is 10 or a teen number.

Standards

2.OA.B.2

6

Lesson

Add within 20 by making a ten.

Standards

2.OA.B.2

7

Lesson

Subtract within 20 by going down over ten.

Standards

2.OA.B.2

8

Lesson

Subtract within 20 by thinking of it as an unknown-addend problem.

Standards

2.OA.B.2

9

Lesson

Add and subtract within 20 using doubles and near doubles.

Standards

2.OA.B.2

10

Lesson

Add and subtract within 20 and explain why strategies work.

Standards

2.OA.B.2

Topic C: Story Problems within 20

11

Lesson

Solve easy and middle difficulty add to, take from, and put together/take apart story problems using any way that makes sense to them.

Standards

2.OA.A.12.OA.B.2

12

Lesson

Solve easy and middle difficulty story problems using tape diagrams and equations.

Standards

2.OA.A.12.OA.B.2

13

Lesson

Solve add to and take from with start unknown story problems.

Standards

2.OA.A.12.OA.B.2

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

Number and Operations in Base Ten

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

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.

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.

Operations and Algebraic Thinking

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

Standards covered in previous units or grades that are important background for the current unit

Number and Operations in Base Ten

1.NBT.A.1

Number and Operations in Base Ten

1.NBT.A.1 — Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.B.2

Number and Operations in Base Ten

1.NBT.B.2 — Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

Operations and Algebraic Thinking

1.OA.A.1

Operations and Algebraic Thinking

1.OA.A.1 — Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.B.3

Operations and Algebraic Thinking

1.OA.B.3 — Apply properties of operations as strategies to add and subtract. Students need not use formal terms for these properties. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)
1.OA.B.4

Operations and Algebraic Thinking

1.OA.B.4 — Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
1.OA.C.6

Operations and Algebraic Thinking

1.OA.C.6 — Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
1.OA.D.7

Operations and Algebraic Thinking

1.OA.D.7 — Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.D.8

Operations and Algebraic Thinking

1.OA.D.8 — Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.

Future Standards

Standards in future grades or units that connect to the content in this unit

Number and Operations in Base Ten

2.NBT.A.1

Number and Operations in Base Ten

2.NBT.A.1 — Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
2.NBT.B.5

Number and Operations in Base Ten

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.

Operations and Algebraic Thinking

3.OA.D.8

Operations and Algebraic Thinking

3.OA.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

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.

Addition and Subtraction Within 20

Unit Summary

Assessment

Mid-Unit

Post-Unit

Unit Prep

Intellectual Prep

Intellectual Prep for All Units

Unit-Specific Intellectual Prep

Essential Understandings

Vocabulary and Models

Models

Materials

Unit Practice

Lesson Map

Common Core Standards

Core Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Future Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Standards for Mathematical Practice

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