2nd Grade Math | Adding and Subtracting within 100

Unit Summary

In Unit 2, 2nd grade students build on their addition and subtraction work to develop and use strategies to add and subtract within 100 fluently. 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). By extending their fluency work within 20 from Unit 1, students will use some of the strategies and understandings from their work within 100.

In Topic A, students begin the unit by adding and subtracting with multiples of ten. This serves as a bridge from students Grade 1 work where they used place value understandings and properties of operations to add and subtract. They also build off their Unit 1 work and apply make a ten strategies to adding two-digit numbers within 50.

In Topic B, the focus is on strategies for adding within 100. In this topic students will use concrete manipulatives to represent their addition work and translate that to pictorial representations and then to more abstract representations. They will use their knowledge of tens and ones as they add as well. Students will also be introduced to the standard algorithm as a strategy but they are not expected to fluently use the standard algorithm in their Grade 2 math development.

In Topic C, students will focus on subtraction and similarly move through concrete representations to pictorial, using place value drawings, and later more abstract representations. Students will use their place value knowledge to subtract with up to one decomposition of a ten into 10 ones in order to subtract in situations where there are not enough ones. Students also explore how they can relate subtraction to addition in order to subtract.

Finally, in Topic C students build on the work with word problems by exploring compare problems within 100. They will build on their Unit 1 word problem work by continuing to use tape diagrams to represent the problem and using symbols to represent the unknown in their equations. In this topic students will culminate their work with exploring addition and subtraction within 100 by adding up to four two-digit numbers (2.NBT.B.6) and explain the strategies they used to solve addition and subtraction problems (2.NBT.B.9). Students also 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).

The work students explore in this unit provides students with a foundation for their work in future units in 2nd grade, most notably Unit 5 where they will extend their addition and subtraction strategies within 1,000. Students will continue to practice their fluency with 100 throughout their 2nd grade work as they solve word problems within 100, engage in work with measurement in Unit 3, and as they extend their place value understandings in Unit 4.

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Assessment

The following assessments accompany Unit 2.

Mid-Unit

Have students complete the Mid-Unit Assessment.

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, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help 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. 52-61 on Number and Operation in Base Ten and pp. 71-78 on Measurement and Data in the Progressions.
Read the following table that includes models used in this unit.

Number Bonds
base ten blocks	34 shown in base ten blocks
Tens and Ones Chart
Vertical Way

Essential Understandings

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

When adding and subtracting, know that 10 ones are equivalent to 1 ten therefore in addition situations, if there are more than 9 ones, know that a new ten is made. In subtraction situations, if there are not enough ones to subtract, a ten can be decomposed into 10 ones to subtract.
When adding and subtracting two-digit numbers students should think of them as numbers composed of tens and ones. These units allow students to think about properties of place value to add and subtract fluently.
When subtracting, students can think of addition and think of what addend needs to be added to the part that would equal the whole.
Make ten strategies that worked within 20, can be applied with tens to make 100 and also to make the next ten.
When adding up to four two-digit addends, addends can be flexibly decomposed and recomposed to add based on place value (adding tens and ones) or by finding benchmark numbers by making tens with addends.
Categorical data is a type of data that shows information by groups or categories. There are two ways of representing categorical data using picture graphs and bar graphs. Students will be able to both interpret and create graphs by using generated or given data.
Categorical data represented in bar graphs and picture graphs can be used to answer questions about general trends and simple put together or compare questions.

Vocabulary

Terms and notation that students learn or use in the unit

Materials

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

Optional: Hundreds Chart (1 per student)

Linking cubes (43 cubes total in at least two colors to show groups of 10 in alternating colors) — This is a teacher set. Optional sets can be provided to students as needed
Tens place value chart (1 per student or small group) — These should be laminated or in sheet protectors to reuse
Dry erase marker (1 per student)
Sheet protectors (1 per student)
Tape (1 roll per small group)
Paper base ten blocks (tens, ones) (5 tens and 7 ones per student)
Base ten blocks (10 tens and 20 ones per student or small group) — One additional set for the teacher
Dice (1 per student or small group) — For Problem Set use only
1-liter plastic bottle (1 per small group) — Students can use any container with a capacity of about 1 liter. See Lesson 10 Tips for Teachers for more information.
Optional: Demonstration analog clock (1 per teacher) — See Lesson 1 Tips for Teachers for more information.

Unit Practice

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson Map

Topic A: Adding & Subtracting with Multiples of Ten

1

Add and subtract 1 and 10 to or from two-digit numbers within 100.

2.NBT.B.5

2

Add and subtract multiples of ten to two-digit numbers.

2.NBT.B.5

3

Use make a ten strategies to add two-digit numbers within 50.

2.NBT.B.5

Topic B: Strategies for Adding within 100

4

Use base ten blocks to represent adding within 100.

2.NBT.B.5

5

Use math drawings to represent adding within 100.

2.NBT.B.5

6

Use place value knowledge to add within 100.

2.NBT.B.5

7

Use properties of operations and other strategies to add within 100.

2.NBT.B.5

8

Relate the standard algorithm for addition to other methods to add and explain thinking.

2.NBT.B.5 2.NBT.B.9

Topic C: Strategies for Subtracting within 100

9

Use base ten blocks and place value drawings to represent subtracting within 100.

2.NBT.B.5

10

Relate addition and subtraction to subtract within 100.

2.NBT.B.5

11

Use place value knowledge to subtract with one decomposition.

2.NBT.B.5

12

Use properties of operations to subtract within 100.

2.NBT.B.5 2.NBT.B.9

13

Relate subtraction with place value drawings to the standard algorithm.

2.NBT.B.5 2.NBT.B.9

14

Relate subtraction with place value drawings to the standard algorithm in situations with one decomposition and explain thinking.

2.NBT.B.5 2.NBT.B.9

Topic D: Working within 100 and Categorical Data

15

Represent and solve compare story problems within 100 (Day 1).

2.NBT.B.5 2.OA.A.1

16

Represent and solve compare story problems within 100 (Day 2).

2.NBT.B.5 2.OA.A.1

17

Use place value strategies to add 4 two-digit numbers within 100.

2.NBT.B.6

18

Use flexible strategies to add 4 two-digit numbers within 100.

2.NBT.B.6

19

Use strategies to add and subtract within 100 and explain thinking.

2.NBT.B.5 2.NBT.B.9

20

Interpret and create picture graphs and answer related questions.

2.MD.D.10

21

Interpret and create bar graphs and answer related questions.

2.MD.D.10

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

Measurement and 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.

Measurement and 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.

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.

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.
2.NBT.B.6 — Add up to four two-digit numbers using strategies based on place value and properties of operations.

Number and Operations in Base Ten

2.NBT.B.6 — Add up to four two-digit numbers using strategies based on place value and properties of operations.
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.

Number and Operations in Base Ten

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

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.

Foundational Standards

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

Measurement and Data

1.MD.C.4

Measurement and Data

1.MD.C.4 — Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
K.MD.B.3

Measurement and Data

K.MD.B.3 — Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Limit category counts to be less than or equal to 10.

Number and Operations in Base Ten

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:
1.NBT.C.4

Number and Operations in Base Ten

1.NBT.C.4 — Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.C.5

Number and Operations in Base Ten

1.NBT.C.5 — Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
1.NBT.C.6

Number and Operations in Base Ten

1.NBT.C.6 — Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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.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.A.2

Operations and Algebraic Thinking

1.OA.A.2 — Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, 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.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

3.NBT.A.2

Number and Operations in Base Ten

3.NBT.A.2 — Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Number and Operations—Fractions

4.NF.B.3.A

Number and Operations—Fractions

4.NF.B.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.

Adding and Subtracting Within 100

Unit Summary

Assessment

Mid-Unit

Post-Unit

Unit Prep

Intellectual Prep

Intellectual Prep for All Units

Unit-Specific Intellectual Prep

Essential Understandings

Vocabulary

Materials

Unit Practice

Lesson Map

Common Core Standards

Core Standards

Measurement and Data

Measurement and Data

Number and Operations in Base Ten

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

Foundational Standards

Measurement and Data

Measurement and Data

Measurement and Data

Number and Operations in Base Ten

Number and Operations in Base Ten

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

Operations and Algebraic Thinking

Future Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations—Fractions

Number and Operations—Fractions

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Standards for Mathematical Practice

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