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 1 Overview: Fact Strategies (Addition and Subtraction) Up to Twenty and Money Identification

Unit 1 Overview: Fact Strategies (Addition and Subtraction) Up to Twenty and Money Identification

Overview

Unit Overview/Summary - FOCUS: 

This unit focuses on Operations and Algebraic Thinking, Number and Operations in Base Ten and attention to Measurement and Data (foundational money concepts of coin/bill identification and recognition).  

Learning in this unit will enable students to: 

  • Represent and solve problems involving addition and subtraction 
  • Add and subtract within 20 
  • Use place value understanding and properties of operations to add and subtract 
  • Work with money concepts (coin and bill identification) 

Relevant Standards:

Major work of the grade is in bold.  

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

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. 

2.NBT.B.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. 

2.MD.C.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 

Examples and Explanations:

2.OA.A.1. Word problems that are connected to students’ lives can be used to develop fluency with addition and subtraction. Examples below describe the four different addition and subtraction situations and their relationship to the position of the unknown.  

Examples:  

  • Take-from example: David had 63 stickers. He gave 37 to Susan. How many stickers does David have now? 63 – 37 =  
  • Add-to example: David had $37. His grandpa gave him some money for his birthday. Now he has $63. How much money did David’s grandpa give him? $37 + = $63  
  • Compare example: David has 63 stickers. Susan has 37 stickers. How many more stickers does David have than Susan? 63 – 37 = o Even though the modeling of the two problems above is different, the equation, 63 - 37 = ?, can represent both situations (How many more do I need to make 63?)  
  • Take-from (Start Unknown) David had some stickers. He gave 37 to Susan. Now he has 26 stickers. How many stickers did David have before? (? - 37 = 26)

It is important to attend to the difficulty level of the problem situations in relation to the position of the unknown.  

  • Result Unknown problems are the least complex for students followed by Total Unknown and Difference Unknown.  
  • The next level of difficulty includes Change Unknown, Addend Unknown, followed by Bigger Unknown.  
  • The most difficult are Start Unknown, Both Addends Unknown, and Smaller Unknown.  

Second grade students should work on ALL problem types regardless of the level of difficulty. Students can use interactive whiteboard or document camera to demonstrate and justify their thinking.  

This standard focuses on developing an algebraic representation of a word problem through addition and subtraction -the intent is not to introduce traditional algorithms or rules.  

2.OA.B.2.   This standard is strongly connected to all the standards in this domain. It focuses on students being able to fluently add and subtract numbers to 20. Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.  

Mental strategies help students make sense of number relationships as they are adding and subtracting within 20. The ability to calculate mentally with efficiency is very important for all students. Mental strategies may include the following:  

  • Counting on  
  • Making tens (9 + 7 = 10 + 6)  
  • Decomposing a number leading to a ten ( 14 – 6 = 14 – 4 – 2 = 10 – 2 = 8)  
  • Fact families (8 + 5 = 13 is the same as 13 - 8 = 5)  
  • Doubles  
  • Doubles plus one (7 + 8 = 7 + 7 + 1)  

However, the use of objects, diagrams, or interactive whiteboards, and various strategies will help students develop fluency. 

2.NBT.B.9.  Students need multiple opportunities to explain their thinking when solving problems using addition and subtraction. 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. 

2.MD.C.8.  Since money is not specifically addressed in kindergarten, first grade, or third grade, students should have multiple opportunities to identify (in this unit), count, recognize (in this unit), and use coins and bills in and out of context. They should also experience making equivalent amounts using both coins and bills. “Dollar bills” should include denominations up to one hundred ($1.00, $5.00, $10.00, $20.00, $100.00). 

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 and the properties of operations to add and subtract. 
  • Representing and solving problems involving addition and subtraction. 
  • Adding and subtracting within 20.
  • 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: 

  • Solve problems involving the four operations, and identify and explain patterns in arithmetic.
  • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
  • Use place value understanding and properties of operations to add and subtract. 

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. 

  • How does place value and composing and decomposing numbers lead to understanding of addition and subtraction? 
  • How do visual representations depict addition and subtraction?  
  • What does it mean to be fluent? 
  • How do coins represent different values? 

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: 

  • Addition and subtraction can be represented on various models such as number lines, picture graphs, and bar graphs.  
  • Fluency means being efficient, accurate, and flexible with addition and subtraction strategies. 
  • When adding and subtracting numbers, the place and value of the digits is important for determining either the sum or the difference.   
  • Coins have different values. 

What Students Will Know:

Problem Solving: 

  • Basic addition and subtraction computation and problem solving strategies. 
  • The properties of addition (commutative, associative, and identity.) 
  • Unknown quantities can be represented in different places in an equation/number model.

Fluency: 

  • How to fluently add and subtract within 20.  

Money: 

  • Monetary unit representations. 
  • Monetary symbols ($ and ¢). 
  • A penny is worth 1 cent (1¢). 
  • A nickel is worth 5 cents (5¢). 
  • A dime is worth 10 cents (10¢). 
  • A quarter is worth 25 cents (25¢). 
  • An amount of dollars is represented with the dollar symbol ($). 
  • The size of a coin does not determine its value. 
  • The dollar symbol and cent symbol are not used simultaneously, i.e., do not use decimal notation. 

What Students Will Do:

Problem Solving: 

  • Solve one-step word problems within 100 involving situations of adding to, taking from, putting together, taking apart, and comparing involving results unknown using objects, drawings, and equations with a symbol for the unknown number.  
  • Solve two-step word problems within 100 involving situations of adding to, taking from, putting together, taking apart, and comparing involving start unknown using objects, drawings, and equations with a symbol for the unknown number.  
  • Solve problems using addition and subtraction within 100. 
  • Solve for an unknown (represented by an empty box or picture) in any position. 
  • Create a model or draw a picture and use an equation to represent the problem situation. 
  • Use and explain different strategies or properties of operations. 
  • 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). 

Fluency: 

  • Use efficient mental strategies to compute accurately and flexibly within 20.  
  • Explain why some strategies may be more efficient than others.  
  • Use number relationships to help students develop mental strategies. (Mental strategies may include the following: counting on, making 10, decomposing a number, using the relationship between addition and subtraction, creating equivalent but easier or known sums, etc.) 
  • Generalize computation strategies of addition and subtraction that will apply to larger numbers.  

Money (coin identification and recognition): 

  • Recognize and name a penny. 
  • Identify that a penny’s value is equal to 1 cent (1¢). 
  • Recognize and name a nickel. 
  • Identify that a nickel’s value is equal to 5 cents (5¢). 
  • Recognize and name a dime. 
  • Identify that a dime’s value is equal to 10 cents (10¢). 
  • Recognize and name a quarter. 
  • Identify that a quarter’s value is equal to 25 cents (25¢). 
  • Recognize a 1 dollar bill ($1.00), a 5 dollar bill ($5.00), a 10 dollar bill ($10.00), a 20 dollar bill ($20.00), and a 100 dollar bill ($100.00). 

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 

  • Equation 
  • Place Value 
  • Solve 
  • Sum 
  • Unknown 
  • Compare 
  • Difference 
  • Operation 
  • Quantity 
  • Symbol 
  • Cent sign 
  • Coin 
  • Currency 
  • Dime 
  • Dollar (bill) 
  • Dollar sign 
  • Money 
  • Nickel 
  • Penny 
  • Quarter 
  • Unit 
  • Value 

Content Vocabulary

  • Addition 
  • Associative Property 
  • Bar Graph 
  • Commutative Property 
  • Identity Property 
  • Picture Graph 
  • Properties of Addition 
  • Subtraction

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:

Computer Science  

  • 1A-AP-09 Model the way programs store and manipulate data by using numbers or other symbols to represent information.  

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 

 

Opportunities for Application of Learning:

Defined Learning provides an open access online library of standards-aligned project-based lessons to help students meet the expectations of the Standards. Each project is based on a situation in a relevant career to help students connect classroom content to career pathways. This supplemental resource is available at no cost to teachers and districts. Create an account and log in to access this free resource to support your curriculum.

Camp Counselor

The tasks below provide additional opportunities to apply the content of this unit.

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, tape diagrams, number lines, picture graphs, and bar graphs to represent and solve problems. 
  • The use of manipulatives such as play money. 
  • Visual representation of symbols on an Anchor chart or visuals. 

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