# Unit 4 Overview: Fluency with Addition and Subtraction within 100 and Problem Solving with Money

## Overview

**Unit Overview/Summary - FOCUS: **

This unit focuses on number and operations in base 10. There is continued attention to measurement and data (problem solving with money) as well as operations and algebraic thinking.

Learning in this unit will enable students to:

- Understand place value.
- Use place value understanding and properties of operations to add and subtract.
- Work with money both in and out of context

# 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.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.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.

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.B.2. **Automaticity should be grounded in efficient strategies such as: doubles, 5-wise (5+2, 5+4), decomposing to create a ten and leftovers (8+6 = 8+2+4), relationships between addition and subtraction, related combinations, known combinations. Once conceptual understanding is achieved, students can practice for automaticity.

**2.NBT.A.1. **The following list shows the number of pencils that each teacher has. Each box holds 10 pencils. • Mrs. Abernathy- 10 boxes and a bag of 1 pencil • Mrs. Bulgogi- 12 boxes and a bag of 5 pencils • Mrs. Oh- 11 boxes and a bag of 9 pencils.

How many pencils does each teacher have?

- Give a student access to a pile of base ten blocks. Ask students the following:
- Can you make a pile that equals 200? (2 hundreds blocks)
- Can you make a pile that equals 400? (4 hundreds blocks)
- Can you make a pile that equals 700? (7 hundreds blocks)

Ms. Smith asked her students to use base ten blocks to represent the number 212.

- Molly used two hundreds, one ten, and two ones.
- Zack used 212 ones.
- Salvador showed 212 a different way using 2 hundreds and other base ten blocks. What could Salvador have done?
- Possible Response: 2 hundreds and 12 ones

**2.NBT.B.5.** 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. Students should have experiences solving problems written both horizontally and vertically. They need to communicate their thinking and be able to justify their strategies both verbally and with paper and pencil.

Addition strategies based on place value for 48 + 37 may include:

- Adding by place value: 40 + 30 = 70 and 8 + 7 = 15 and 70 + 15 = 85.
- Incremental adding (breaking one number into tens and ones); 48 + 10 = 58, 58 + 10 = 68, 68 + 10 = 78, 78 + 7 = 85
- Compensation (making a friendly number): 48 + 2 = 50, 37 – 2 = 35, 50 + 35 = 85

Subtraction strategies based on place value for 81 - 37 may include:

- Adding Up (from smaller number to larger number): 37 + 3 = 40, 40 + 40 = 80, 80 + 1 = 81, and 3 + 40 + 1 = 44.
- Incremental subtracting: 81 -10 = 71, 71 – 10 = 61, 61 – 10 = 51, 51 – 7 = 44
- Subtracting by place value: 81 – 30 = 51, 51 – 7 = 44

Properties that students should know and use are:

- Commutative property of addition (Example: 3 + 5 = 5 + 3)
- Associative property of addition (Example: (2 + 7) + 3 = 2 + (7+3) )
- Identity property of 0 (Example: 8 + 0 = 8)

Students in second grade need to communicate their understanding of why some properties work for some operations and not for others.

Commutative Property: In first grade, students investigated whether the commutative property works with subtraction. The intent was for students to recognize that taking 5 from 8 is not the same as taking 8 from 5. Students should also understand that they will be working with numbers in later grades that will allow them to subtract larger numbers from smaller numbers. This exploration of the commutative property continues in second grade.

Associative Property: Recognizing that the associative property does not work for subtraction is difficult for students to consider at this grade level as it is challenging to determine all the possibilities.

**2.NTB.B.6. **Students demonstrate addition strategies with up to four two-digit numbers either with or without regrouping. Problems may be written in a story problem format to help develop a stronger understanding of larger numbers and their values. Interactive whiteboards and document cameras may also be used to model and justify student thinking.

**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.

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

Students should solve story problems connecting the different representations. These representations may include objects, pictures, charts, tables, words, and/or numbers. Students should communicate their mathematical thinking and justify their answers. An interactive whiteboard or document camera may be used to help students demonstrate and justify their thinking.

Example:

A student is given 1 quarter, 2 dimes and 3 pennies.

- How many cents would he/she have?
- What could be another way to show the same amount of money with different coins?
- Example: Jack buys a toy for 58¢ and hands the clerk $5.00. What change should he get back?

# 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:

**Properties of operations to add and subtract.****Adding and subtracting within 20.****Use place value understanding and properties of operations to add and subtract.**- Place value.
- Adding and subtracting within 1000 using strategies based on place value and properties of operations.
- The relationship between addition and subtraction.
- Identifying, recognizing, and counting coins and dollar bills.

## 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.
- Develop understanding of fractions as numbers.

# 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 do visual representations depict addition and subtraction?
- What does it mean to be fluent?
- How can I use my understanding of place value and knowledge of coins & dollar bills to solve problems involving money?

# 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 is being efficient, accurate, and flexible with addition and subtraction strategies.
- Coins have different values and are counted according to their values.

# What Students Will Know:

- Properties of operations.
- Numbers are composed of other numbers.
- Relationship between addition and subtraction.
- There is a relationship between number lines and measurement tools.
- When adding and subtracting numbers, the place and value of the digits is important for determining either the sum or the difference.
- A number line diagram is similar to a ruler in that whole numbers are 1 unit apart.
- Each number on a number line denotes the distance from the labeled point from 0, not the number itself.
- Addition and subtraction strategies can be used to solve real-world measurement problems.
- A symbol can be used to represent an unknown number.

**Money: **

- Monetary unit representations.
- Monetary symbols ($ and ¢).
- An amount of dollars is represented with the dollar symbol ($).
- A collection of pennies, nickels, dimes, and quarters can be counted.
- The dollar symbol and cent symbol are not used simultaneously, i.e., do not use decimal notation.

# What Students Will Do:

- Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the number 0, 1, 2.
- Represent whole-number sums and differences within 100 on a number line diagram.
- Use number sentences or drawings to solve measurement word problems within 100.
- Write an equation using a symbol for the unknown number to represent the problem.
- Represent whole numbers as lengths from 0 on a number line diagram.
- Use number line diagrams to represent whole-number sums and differences within 100.
- Fluently add within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction.
- Fluently subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction.
- Use strategies to add and subtract within 100 efficiently, accurately, and flexibly.
- Generalize computation strategies of addition and subtraction that will apply to larger numbers.
- Use strategies to add up to four two-digit numbers.
- Use mental strategies to add and subtract 10 or 100 from a given number 100−900.
- Explain and justify why addition and subtraction strategies work.
- Explore and explain the use of addition and subtraction to solve real-world problems involving lengths (given in the same whole number units).
- Use drawings and equations with a symbol for the unknown number to represent the problem.
- Find the unknown length unit in real-world situations.
- Explore the relationship between number lines and whole number measurement tools.

**Money: **

- Solve word problems involving dollars within 100, and use the $ symbol appropriately.
- Solve word problems involving cents within 100, and use the cents symbol appropriately.
- Identify and use “₵” as a symbol to represent coin values.
- Identify and use “$” as a symbol to represent dollars.
- Find the value of a collection of quarters, dimes, nickels, and pennies.
- Compare collections of coins based on their values.
- Use pennies, nickels, dimes, and quarters as manipulatives to reinforce place value up to 100 cents.
- Solve word problems by adding and subtracting within 100, whole dollars with whole dollars, and cents with cents.

# 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.*

# Demonstration of Learning:

**Additional Assessment Samples: **

# 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 **

- Distance
- Fluent
- Length
- Operation
- Place Value
- Quantity
- Solve
- Symbol
- Unknown
- Cent sign
- Change
- Coin
- Currency
- Dime
- Dollar (bill)
- Dollar sign
- Money
- Nickel
- Penny
- Quarter
- Solve
- Unit
- Value

**Content Vocabulary **

- Addition
- Associative Property
- Commutative Property
- Difference
- Equation
- Identity
- Properties of Addition
- Remainder
- Subtraction
- Sum
- Place value
- Remainder
- Skip count

**Vocabulary resources: **

- Bilingual Glossaries and Cognates
- Using Cognates to Develop Comprehension in English
- Challenges for EL Students to Overcome
- Cognates and Polysemous Words
**Granite School Vocabulary Cards:**Each card has the word and a picture. They are designed to help all students with math content vocabulary, including ELL, Gifted and Talented, Special Education, and Regular Education students.

# 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.

**Science **

**2-ESS2-1**Compare multiple solutions designed to slow or prevent wind or water from changing the shape of the land.**2-ESS1-1**Use information from several sources to provide evidence that Earth events can occur quickly or slowly.

**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:

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

**Money: **

# 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 manipulatives, such as play money and base-ten manipulatives.

- Visual representation of symbols on an Anchor chart or visuals.
- Building decade numbers while simultaneously reading numbers aloud to reinforce the meanings of the quantities while visually connecting to specific monetary units and denominations.

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.