# Adding and Subtracting Within 100

Students develop strategies based on place value, properties of operations, and the operational relationship between addition and subtraction to add and subtract within 100 fluently. Students will use these strategies to add up to four two-digit numbers and explain why these strategies work. Students also explore categorical data.

Math

Unit 2

## 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 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

 number bonds base ten blocks 34 shown in base ten blocks place value chart vertical way bar graph picture graph 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?

### Essential Understandings

• 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

bar graph

categorical data

data

decompose

key

picture graph

To see all the vocabulary for Unit 2 , view our 2nd Grade Vocabulary Glossary.

### Materials

• 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

## 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

Topic B: Strategies for Adding within 100

Topic C: Strategies for Subtracting within 100

Topic D: Working within 100 and Categorical Data

## Common Core Standards

Key

Major Cluster

Supporting Cluster

### Core Standards

#### 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.
• 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.

#### 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.

• 1.MD.C.4
• K.MD.B.3

• 1.NBT.B.2
• 1.NBT.C.4
• 1.NBT.C.5
• 1.NBT.C.6

• 1.OA.A.1
• 1.OA.A.1
• 1.OA.A.2
• 1.OA.B.3
• 1.OA.B.4
• 1.OA.C.6
• 1.OA.D.8

• 3.NBT.A.2

• 4.NF.B.3.A

• 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.

Unit 1

Unit 3

Measurement

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