Adding and Subtracting Within 1,000

Students add and subtract within 1,000 using strategies based on place value, properties of operations, and the operational relationship between addition and subtraction in order to add and subtract within 1,000. Students will use these strategies to add up to two 3-digit numbers concretely, pictorially and abstractly and explain why these strategies work. 

Math

Unit 5

2nd Grade

Unit Summary


In Unit 5, 2nd grade students build on their addition and subtraction work from adding and subtracting two 2-digit numbers and patterns within 10 to develop and use strategies to add and subtract within 1,000. By the end of 2nd grade students are expected to have a plethora  of strategies and generalizable methods in order to add and subtract 3-digit numbers within 1,000 (2.NBT.B.7). In this unit, students are introduced to adding and subtracting 3-digit numbers within 1,000 using the standard algorithm, however students are not expected to be fluent or show proficiency with the standard algorithm until Grade 4. By extending their adding and subtracting work within 100 from Unit 2, students will use some of the strategies and understandings in their work within 1,000. This helps students with their work throughout their grade 2 mathematics and beyond. 

In Topic A, students begin the unit by adding multiples of tens or hundreds. This is a continuation of the work done in Unit 2 where they added multiples of tens fluently within 100. Similarly, they also build off their Unit 1 and 2 work by applying strategies of compensation to adding three-digit numbers in order to get to a benchmark hundred. 

Topic B focuses on methods for adding within 1,000. In this topic students use concrete manipulatives to represent their addition work. From there, they use their knowledge of concrete models to draw pictorial representations. Then finally, students move to more abstract representations, including the standard algorithm. Students use their knowledge of hundreds, tens, and ones as they show up to two compositions of a new hundred and a new ten. 

In Topic C, students begin the topic by subtracting multiples of tens or hundreds. As similar work was completed in Topic A of this unit, students will also maintain a constant difference in order to subtract without needing to regroup.

In Topic D, students focus on subtraction within 1,000 and similarly move through concrete representations to pictorial, using place value drawings, and later more abstract representations to solve. Students use their place value knowledge to subtract with up to two decompositions of a hundred into 10 tens and ten into 10 ones in order to subtract in situations where there are not enough tens or ones. Students also explore how they can relate subtraction to addition in order to subtract as well as continue to practice abstract adding using the standard algorithm to check their work. 

Finally, in Topic E students build on their work with word problems by solving more difficult problem types of one-step story problems as well as harder subtypes of two-step story problems. They  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. They also use their knowledge of solving twice for two-step story problems from Unit 4 (2.OA.A.1). By the end of second grade students should be proficient in two-step word problem combinations of two middle difficulty problem types with addition and subtraction. Also, in this topic students will use their skills of making new hundreds in the context of  adding up to four two-digit numbers and going beyond 100 (2.NBT.B.6) and explain the strategies they used to solve addition and subtraction problems (2.NBT.B.9). 

The work students explore in this unit provides them with a better understanding of numbers and patterns first brought on in the foundation for their work in Unit 2. Students will continue to practice their fluency with 100 throughout their 2nd grade work as they continue to solve word problems within 100. 

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Assessment


The following assessments accompany Unit 5.

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

concrete base ten blocks

134 shown in base ten blocks

pictorial base ten blocks

368 + 106 = ?

place value chart

number line

545 + 30 = ?

arrow notation

529 + 40 = ?

expanded form notation $$\begin{array}{crcrcrcc} &400&+ &30&+ &5 &&&\\ + \ \ \ &200&+ &70 &+ &3 &&&\\ \hline &600&+ &100&+ &8 &= &708\end{array}$$
totals below for addition

totals below for subtraction $$ \begin{array}{cccccccc} &\overset{300}{\cancel{400}} &+ &\overset{110}{\cancel{10}} &+ &6 &&&\\ - \ \ \ &100 &+ &80 &+ &40 &&&\\ \hline &200 &+ &30 &+ &2 &= &232 \end{array}$$
standard algorithm for addition

standard algorithm for subtraction

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 and 10 tens are equivalent to 1 hundred, therefore in addition situations, if there are more than 9 ones, know that a new ten is made and if there are more than 9 tens a new hundred is made. In subtraction situations, if there are not enough ones to subtract, a ten can be decomposed into 10 ones to subtract and if there are not enough tens to subtract a hundred can be decomposed into 10 tens in order to subtract. 
  • When adding and subtracting three-digit numbers students should think of them as numbers composed of hundred, tens and ones in the purpose of adding or subtracting units. These units allow students to think about properties of place value to add and subtract fluently and allow students to compose or decompose units effectively. 
  • When subtracting, students can think of addition and think of what addend needs to be added to the part that would equal the whole.

Materials

  • Optional: Completed Blank Hundreds Chart to 1000 (1 per group) — From Unit 4 as a resource
  • Base ten blocks (10 hundreds, 18 tens, 18 ones per student)
  • Empty Number Line (1 per student) — These should be laminated or in sheet protectors to reuse
  • Hundreds place value chart Work Mat Template (1 per student) — These should be laminated or in sheet protectors to reuse
  • Dry erase marker (1 per student)
  • Sheet protectors (1 per student)
  • Thousand Cube (Teacher only)
  • Dice (1 per student) — Used in problem set

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 with Mental Strategies

Topic B: Adding within 1,000

Topic C: Subtracting with Mental Strategies

Topic D: Subtracting within 1,000

Topic E: Story Problems and Explaining Addition and Subtracting Thinking

Common Core Standards


Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

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.7 — Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
  • 2.NBT.B.8 — Mentally add 10 or 100 to a given number 100—900, and mentally subtract 10 or 100 from a given number 100—900.
  • 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.

Foundational Standards

Number and Operations in Base Ten

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

Operations and Algebraic Thinking

  • 1.OA.A.1
  • 1.OA.D.8

Future Standards

Number and Operations in Base Ten

  • 3.NBT.A.2
  • 4.NBT.B.4
  • 4.NBT.B.5
  • 4.NBT.B.6

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.

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Unit 4

Place Value with Numbers to 1,000 & Money

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