Author:
Connecticut Department of Education
Subject:
Mathematics
Material Type:
Unit of Study
Level:
Lower Primary
Grade:
2
Provider:
CT State Department of Education
Provider Set:
CSDE - Public
Tags:
Language:
English
Media Formats:
Text/HTML

Unit 3 Overview: Exploring Addition and Subtraction within 1000

Unit 3 Overview:  Exploring Addition and Subtraction within 1000

Overview

Unit Overview/Summary - FOCUS: 

This unit focuses on number and operations in base ten.   

Learning in this unit will enable students to: 

  • Use place value understanding and properties of operations to add and subtract. 

Relevant Standards:

Major work of the grade is in bold.  

The standards to be addressed during this unit of study include:   

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. 

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: 

a. 100 can be thought of as a bundle of ten tens — called a “hundred.” 

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).  

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.NTB.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. 

Examples and Explanations:

2.NBT.A.1. In this standard, students extend their place value understanding to the hundreds place as they are introduced to the idea that a bundle of 10 tens is a unit called a “hundred”. Unitize by making a hundred from a collection of ten tens In Grade 1 students worked on unitizing (grouping) 10 ones into a ten. In Grade 2 students extend this idea to unitize (group) 10 tens into a hundred. When students unitize tens as a whole unit (called “a hundred”), they are able to count groups as though they were individual objects. In Grade 2 this work extends beyond simple rote counting where they say 100, 200, 300. Rather, students are expected to examine a group of more than 10 base ten rods and group 10 of them together to make a hundred. After unitizing ten tens into a hundred when students are asked to determine the value of a pile of base ten blocks (or a picture of blocks) students should be able to count the group of 10 tens as hundreds.

Demonstrate that numbers 100, 200, … refer to a number of hundreds with 0 tens and 0 ones Students continue to apply their place value understanding from first grade as they are expected to build three-digit numbers that have only a non-zero number in the hundreds place. For example, 100 can be made of 10 groups of ten as well as 100 ones and 400 could be made of 4 hundreds or 40 tens or 400 ones.

Compose and decompose numbers using various groupings of hundreds, tens, and ones This part of the standard lays the groundwork for the use of place value concepts later in the year and in future grades in the context of adding and subtracting multi-digit numbers.

A document camera or interactive whiteboard can also be used to demonstrate “bundling” of objects. This gives students the opportunity to communicate their counting and thinking. 

2.NTB.B.7. There is a strong connection between this standard and place value understanding with addition and subtraction of smaller numbers.  Students may use concrete models or drawings to support their addition or subtraction of larger numbers.  Strategies are similar to those stated in 2.NBT.5, as students extend their learning to include greater place values moving from tens to hundreds to thousands.   

Interactive whiteboards and document cameras may also be used to model and justify student thinking. 

2.NBT.B.8. Students need many opportunities to practice mental math by adding and subtracting multiples of 10 and 100 up to 900 using different starting points. They can practice this by counting and thinking aloud, finding missing numbers in a sequence, and finding missing numbers on a number line or hundreds chart. Explorations should include looking for relevant patterns.  

Mental math strategies may include:  

• counting on; 300, 400, 500, etc.  

• counting back; 550, 450, 350, etc.  

Examples:  

• 100 more than 653 is _____ (753)  

• 10 less than 87 is ______ (77)  

• “Start at 248. Count up by 10s until I tell you to stop.”  

An interactive whiteboard or document camera may be used to help students develop these mental math skills. 

2.NBT.B.9.  Students need multiple opportunities explaining their addition and subtraction thinking. Operations embedded within a meaningful context promote development of reasoning and justification. 

Example:  

Mason read 473 pages in June. He read 227 pages in July. How many pages did Mason read altogether?  

  • Karla’s explanation: 473 + 227 = _____. I added the ones together (3 + 7) and got 10. Then I added the tens together (70 + 20) and got 90. I knew that 400 + 200 was 600. So I added 10 + 90 for 100 and added 100 + 600 and found out that Mason had read 700 pages altogether.  
  • Debbie’s explanation: 473 + 227 = ______. I started by adding 200 to 473 and got 673. Then I added 20 to 673 and I got 693 and finally I added 7 to 693 and I knew that Mason had read 700 pages altogether.  
  • Becky’s explanation: I used base ten blocks on a base ten mat to help me solve this problem. I added 3 ones (units) plus 7 ones and got 10 ones which made one ten. I moved the 1 ten to the tens place. I then added 7 tens rods plus 2 tens rods plus 1 tens rod and got 10 tens or 100. I moved the 1 hundred to the hundreds place. Then I added 4 hundreds plus 2 hundreds plus 1 hundred and got 7 hundreds or 700. So Mason read 700 books.  

Students should be able to connect different representations and explain the connections. Representations can include numbers, words (including mathematical language), pictures, number lines, and/or physical objects. Students should be able to use any/all of these representations as needed. 

An interactive whiteboard or document camera can be used to help students develop and explain their thinking. 

Transfer Goal: Aligned to district portrait or vision of the learner

Aligned to district portrait or vision of the learner 

In this unit students will develop the skills of perseverance, reasoning, and precision. This will be accomplished through focus on the following Standards for Mathematical Practice:  

  • Make sense of problems and persevere in solving them. 
  • Reason abstractly and quantitatively. 
  • Model with mathematics. 
  • Attend to precision. 
  • Look for and make use of structure. 
  • Look for and express regularity in repeated reasoning. 

Grade level content is in bold 

Coherence: 

How does this unit build on and connect to prior knowledge and learning?   

Students build on their previous understandings of: 

  • Place value.
  • Applying properties of operations and the relationship between addition and subtraction. 

How does this unit prepare students for future learning?   

The learning of this unit serves as a foundation for content that will be addressed in future years.  Specifically, students will utilize this learning to: 

  • Use place value understanding and properties of operations to perform multi-digit arithmetic. 

Essential Questions:

Essential Questions can be approached in multiple ways. There should be no more than 2-3 essential questions and they should align with your topics. Questions can be repeated throughout a course or over years, with different enduring understandings. 

  • Why can numbers be composed and decomposed and how is it beneficial? 
  • How does the position of a digit in a number affect its value? 

Enduring Understanding:

Enduring Understanding: The major ideas you want students to internalize and understand deeply. These understandings should be thematic in nature. They are not the end all, be all of the question. They are focused to align to the focus (unit overview). 

Students understand: 

  • When adding and subtracting numbers, the place and value of the digits is important for determining either the sum or the difference.  
  • When adding or subtracting, sometimes it is necessary to compose or decompose tens or hundreds. 
  • Numbers are composed of other numbers.
  • Place value is based on groups of ten.

What Students Will Know:

  • The value of digits. 
  • Place value names. 
  • Basic addition and subtraction computation and problem-solving strategies. 
  • The properties of addition (commutative, associative, and identity.) 

What Students Will Do:

Explain why addition and subtraction strategies work by applying knowledge of place value and the properties of operations using concrete objects, pictures and words (both oral and written).  

  • Add and subtract within 1000 using models, drawings, operation properties and/or the relationship between addition and subtraction using base 10 strategies.  
  • Relate the chosen strategy and explain the reasoning used.  
  • Mentally add 10 or 100 to a number between 100-900.  
  • Mentally subtract 10 or 100 to a number between 100-900.   
  • Generalize computation strategies of addition and subtraction that will apply to larger numbers.  
  • Create a model or draw a representation, and when appropriate, write an equation to record the addition or subtraction strategy. Use concrete models, drawings, place value, properties of operations, and other strategies for addition and subtraction within 1,000.  
  • Identify problems that require decomposing the tens or hundreds to find a solution.  
  • Listen to and ask questions about others’ strategies. 
  • Use mental strategies to add and subtract 10 or 100 from a given number 100−900. 
  • Explain why addition and subtraction strategies work by applying knowledge of place value and the properties of operations using concrete objects, pictures and words (both oral and written).

Embedded Financial Literacy Tasks

Connecting mathematical content with essential Financial Literacy concepts that are developmentally appropriate at this level, ensure that students build a foundation for Financial Literacy knowledge.

The resources below provide additional opportunities to consider to implement financial literacy at the elementary level.

Unit Specific Vocabulary and Terminology:

The purpose of vocabulary work should be to allow all students to access mathematics. Vocabulary is a way to provide opportunities for students to use mathematical language to communicate about how they solved a problem, describe their reasoning, and demonstrate understanding of mathematical content. Vocabulary is inclusive of key words and phrases.

Often multilingual learners/English learners (MLs/ELs) are perceived as lacking academic language and needing remediation. Research shows that MLs/ELs bring standards-aligned background knowledge and experiences to the task of learning, and they need opportunities to extend their language for academic purposes. When considering the language demand of a lesson (at the word level), you can check for cognates and polysemous words. Pointing out these words to students can help them activate and build background knowledge assumed in lessons. TESOL professionals can assist with the identification of cognates and polysemous words, and they can provide guidance about the background knowledge MLs/ELs bring or may need.

Academic Vocabulary 

  • Compare 
  • Mental math 
  • Operation 
  • Quantity 
  • Solve 

Content Vocabulary 

  • Addition 
  • Associative property 
  • Base ten 
  • Commutative property 
  • Difference 
  • Digit 
  • Hundreds 
  • Identity property 
  • Ones 
  • Place Value 
  • Properties of Addition 
  • Subtraction 
  • Sum 
  • Tens 

Vocabulary resources: 

English Math Vocabulary Cards

Spanish Math Vocabulary Cards

Chinese Math Vocabulary Cards

French Math Vocabulary Cards

Aligned Unit Materials, Resources and Technology:

High-quality instructional resources are critical for improving student outcomes. The alignment guidance is intended to clarify content and support understanding for clear implementation and coherence. 

Materials selection is a local control decision and these documents have been provided from participating publishers to assist districts in implementation. Use of the materials from these publishers is not required. These aligned core programs meet expectations as reported by edReports. Strong alignment of curricula and instructional materials have the potential to support student engagement and teacher growth. 

Opportunities for Interdisciplinary Connections:

ELA    

  • RI.2.1 Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.  
  • RI.2.3 Describe how characters in a story respond to major events and challenges.    
  • W.2.6 With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers.    
  • W.2.7 Participate in shared research and writing projects (e.g., read a number of books on a single topic to produce a report; record science observations).    
  • W.2.8 Recall information from experiences or gather information from provided sources to answer a question.    
  • SL.2.2 Recount or describe key ideas or details from a text read aloud or information presented orally or through other media.   

Computer Science 

  • IA-AP-08 Model daily processes by creating and following algorithms (sets of step-by-step instructions) to complete tasks. 

Critical Consciousness for Diversity and Equity:

Culturally relevant mathematics engages and empowers students. Opportunities for teachers to orchestrate discussions where students share not only connections to prior mathematics learned but also to their lived experiences must be provided. It is important to dig deep to find ways to link students’ home cultures and the mathematics classroom. Build authentic relationships with families through two-way, reciprocal conversations that acknowledge families’ cultures as assets for teaching and learning. As you plan to implement this unit, focus on designing experiences that have students at the center. In addition to keeping students engaged, ensure the learning experiences have a context that reflects lived experiences (mirror) or provide opportunities to view and learn about the broader world (window). 

One crucial link to students’ home cultures is through their language. Students’ language repertoires –all the languages and language varieties they use everyday– are a valuable resource to be engaged in the mathematics classroom. This approach is referred to as a translanguaging stance. It is based on a dynamic view of bilingualism that understands individuals as having one linguistic repertoire composed of various named languages (such as English and Spanish) and/or language varieties on which they draw to make meaning.

The following questions are intended to assist in promoting diverse voices and perspectives while avoiding bias and stereotyping:

  • How will students share their experiences with others while attending to the mathematics in the unit?
  • What opportunities are there for students to make connections from their life to the mathematics?
  • What do I know or need to learn about my students to create lessons free from bias and stereotypes?
  • In what ways can the mathematical thinking already taking place in the classroom and community be honored?
  • How is relevant background knowledge developed so that all students can access the mathematics of the unit?
  • What opportunities are there for students to use their full language repertoires during mathematical discussions and practice? Where can I create these opportunities?
  • What do I know or need to learn about students’ languages and how they use them? How can I learn this?

* Resources to support diversity and equity in the classroom please visit the DEI collection

Multilingual Learners/English Learners (ML/EL):

Mathematical symbols, expressions, and methods are not universal; ways of doing math differ across cultures. When working with diverse students, especially with those from different countries, it is important to be aware that these differences exist.

It is also important to remember that communicating about mathematical content and practices requires complex language. Since conceptual learning and language learning are interconnected and acquired through participation in meaningful activities, the research-based strategies listed below focus on making content comprehensible (accessible) and creating opportunities for student voice, both verbal and written.

Additional resources for ML/EL

CELP Standards--Linguistic Supports

ML/EL Support Collection for Math  

  • The use of visual tools such as number diagrams, number lines, base-ten manipulatives, etc. 

This unit presents opportunity to address the following CELP Standards: 

CELP Standard 1: Construct meaning from oral presentations and literary and informational text through grade-appropriate listening, reading, and viewing 

CELP Standard 2: Participate in grade-appropriate oral and written exchanges of information, ideas, and analyses, responding to peer, audience, or reader comments and questions 

CELP Standard 3: Speak and write about grade-appropriate complex literary and informational texts and topics 

CELP Standard 4: Construct grade-appropriate oral and written claims and support them with reasoning and evidence 

CELP Standard 5: Conduct research and evaluate and communicate findings to answer questions or solve problems 

CELP Standard 6: Analyze and critique the arguments of others orally and in writing 

CELP Standard 7: Adapt language choices to purpose, task, and audience when speaking and writing 

CELP Standard 8: Determine the meaning of words and phrases in oral presentations and literary and informational text 

CELP Standard 9: Create clear and coherent grade-appropriate speech and text 

CELP Standard 10: Make accurate use of standard English to communicate in grade appropriate speech and writing 

The document below provides guidance on these standards that is grade appropriate and broken down by language level descriptors which will assist the teacher in making the content of the unit accessible to all students.

Grade 2 Language Level Descriptors