# Unit 2 Overview: Skip Counting and Place Value up to 1,000 Including Time and Money

## Overview

**Unit Overview/Summary - FOCUS: **

This unit focuses on number and operations in base ten and continued attention to Measurement and Data (time and skip counting of like coins/ bills).

Learning in this unit will enable students to:

- Understand place value
- Work with time and money

# Relevant Standards:

**Major work of the grade is in bold. **

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

**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.A.2 **Count within 1000; skip-count by 5s, 10s, and 100s.

**2.NBT.A.3. **Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

**2.NBT.A.4.** Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

2.MD.C.7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

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.NBT.A.1. **Understanding that 10 ones make one ten and that 10 tens make one hundred is fundamental to students’ mathematical development. Students need multiple opportunities counting and “bundling” groups of tens in first grade. In second grade, students build on their understanding by making bundles of 100s with or without leftovers using base ten blocks, cubes in towers of 10, ten frames, etc. This emphasis on bundling hundreds will support students’ discovery of place value patterns.

As students are representing the various amounts, it is important that emphasis is placed on the language associated with the quantity. For example, 243 can be expressed in multiple ways such as 2 groups of hundred, 4 groups of ten and 3 ones, as well as 24 tens with 3 ones. When students read numbers, they should read in standard form as well as using place value concepts. For example, 243 should be read as “two hundred forty-three” as well as two hundreds, 4 tens, 3 ones.

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.NBT.A.2 **Students need many opportunities counting, up to 1000, from different starting points. They should also have many experiences skip counting by 5s, 10s, and 100s to develop the concept of place value.

Examples:

- The use of the 100s chart may be helpful for students to identify the counting patterns.
- The use of money (nickels, dimes, dollars) or base ten blocks may be helpful visual cues.
- The use of an interactive whiteboard may also be used to develop counting skills.

The ultimate goal for second graders is to be able to count in multiple ways with no visual support.

**2.NBT.A.3.** Students need many opportunities reading and writing numerals in multiple ways.

Examples:

- Base-ten numerals 637 (standard form)
- Number names six hundred thirty seven (written form)
- Expanded form 600 + 30 + 7 (expanded notation)

When students say the expanded form, it may sound like this: “6 hundreds plus 3 tens plus 7 ones” OR 600 plus 30 plus 7.”

**2.NBT.A.4.** Students may use models, number lines, base ten blocks, interactive whiteboards, document cameras, written words, and/or spoken words that represent two three-digit numbers. To compare, students apply their understanding of place value. They first attend to the numeral in the hundreds place, then the numeral in tens place, then, if necessary, to the numeral in the ones place.

Comparative language includes but is not limited to: more than, less than, greater than, most, greatest, least, same as, equal to and not equal to. Students use the appropriate symbols to record the comparisons.

2.MD.C.7. In first grade, students learned to tell time to the nearest hour and half-hour. Students build on this understanding in second grade by skip-counting by 5 to recognize 5-minute intervals on the clock. They need exposure to both digital and analog clocks. It is important that they can recognize time in both formats and communicate their understanding of time using both numbers and language. Common time phrases include the following: quarter till ___, quarter after ___, ten till ___, ten after ___, and half past ___.

Students should understand that there are 2 cycles of 12 hours in a day - a.m. and p.m. Recording their daily actions in a journal would be helpful for making real-world connections and understanding the difference between these two cycles. An interactive whiteboard or document camera may be used to help students demonstrate 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, count (in this unit), recognize, 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.
- Coin/ bill identification.
- Working with equal groups of objects to gain a foundation for multiplication.
- Telling and writing time.

## 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 add and subtract.**- Use place value understanding and properties of operations to perform multi-digit arithmetic.
- Generalize place value understanding for multi-digit whole numbers.
- Represent and solve problems involving multiplication and division.
- Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- Solve problems involving money (with coins or bills).

# 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 the position of a digit in a number affect its value?
- How do units within a system relate to each another?
- How are various representations of time related?
- How do coin values effect how money is counted?

# 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:

- Numbers can represent quantity, position, location and relationships.
- Place value is based on groups of ten.
- Standard units provide common language for communicating time.
- Coins are counted according to their values.

# What Students Will Know:

**Place Value: **

- A group of ten tens is now referred to as a “hundred.”
- A three-digit number is made up of hundreds, tens, and ones.
- A numeral can stand for a different amount depending on its place or position in a number.
- Numbers are composed of other numbers.
- The digits to the left hold a larger value than the digit(s) to the right.
- Skip counting is a repeating pattern.
- Words can be used to represent numbers.
- When there are no ones and/or tens, the digit zero must be used in that ones and/or tens place to preserve the value of the number.
- Three-digit numbers can be composed and decomposed using multiple representations.
- Numbers written in expanded form can be expressed as an equation.
- Numbers have equivalent representations.
- Numbers can be compared.
- Symbols >, =, and < can be used to record the comparison between numbers.
- When comparing numbers, start with the greatest place value.
- The value of digits.
- Place value names.
- Basic addition and subtraction computation and problem solving strategies.
- The properties of addition (commutative, associative, and identity.)
- Quantity representations on a number line.

**Time: **

- The standard tools for time measurement.
- Hours and minutes.
- Time can be measured.
- Time can be measured to the nearest 5 minutes.
- Time can be measured using an analog clock or digital clock.
- Time can be recorded using hours and to the nearest 5 minutes, e.g., Twenty-five minutes after eleven is represented as 11:25.
- A day is measured as an interval of 24 hours.
- A day is divided equally into a.m. time and p.m. time.

**Money: **

- Coins such as pennies, nickels, dimes, and quarters can be counted.
- Dollar bills can be counted.

# What Students Will Do:

**Place Value: **

- Represent three-digit numbers as amounts of hundreds, tens, and ones using manipulatives, pictures and words.
- Represent 100 as a bundle of ten tens using manipulatives, pictures and words.
- Represent 200, 300, 400, 500, 600, 700, 800, and 900 as the appropriate number of hundreds using manipulatives, pictures and words.
- Count within 1000 starting from any number.
- Read numbers to 1000.
- Write numbers to 1000 in standard form and expanded form.
- Write number names to 1000.
- Compare two three-digit numbers based on placed value of each digit.
- Use these symbols correctly <, =, > in comparison. Identify 100 as the same as ten-tens.
- Represent three-digit numbers with proportional objects (e.g., base ten blocks, sticks, etc.) and drawings.
- Compose and decompose three-digit numbers into hundreds, tens, and ones with proportional objects.
- Explain the need for zero as a place holder, e.g. one hundred four is 104.
- Identify and explain the value of each digit within a three-digit number.
- Identify and write the place (ones, tens, hundreds) of each digit in a three-digit numeral.
- Recognize and describe visual patterns in word form and expanded form of whole numbers to 1,000.
- Recognize and describe word patterns of whole numbers to 1,000.
- Recognize that numerals between 1−1,000 have repeating patterns.
- Extend the counting sequence to 1,000 from different starting points.
- Describe patterns in skip counting and use those patterns to predict the next number in the counting sequence.
- Skip-count forward and backward from any number within 1,000 by ones, tens, and hundreds.
- Skip-count by fives forward and backward from any multiple of 5 within 1,000.
- Given a written or oral number name within 1,000, read and write the numeral.
- Explore numbers using equivalent representations, e.g., 310 is “three hundred ten ones,” “two hundreds plus eleven tens,” and “31 tens,” etc.
- Read three-digit numbers when shown a numeral, a model of the number, or a pictorial representation of the number.
- Read and write numbers in expanded form with multiple representations for the same number.
- Write numbers in expanded form as an equation.
- Use mathematical language (greater than, less than, equal to) to describe the relationship between numbers.
- Connect the mathematical language to the use of symbols >, =, and < to.
- Compare two three-digit numbers.
- Read comparative statements from left to right.
- Explore three-digit numbers to discover that the value of the hundreds place helps determine the size of a three-digit number.
- Generalize the understanding that the value of the hundreds place may help to compare two three-digit numbers.
- Compare two different numbers that result in two true inequality statements. For example, 572 is greater than 324 (572 > 324), and 324 is less than 572 (324 < 572).

**Time: **

- Tell time using analog and digital clocks to the nearest 5 minutes.
- Write time using analog clocks and digital clocks.
- Identify and label when a.m. and p.m. occur.
- Skip-count by 5s, and 10s.
- Explore analog clocks to locate 5 minute interval markings.
- Use skip counting to represent 5 minute intervals.
- Write time symbolically using a colon ( : ) to separate hours and minutes; use two digits after the colon, e.g., five minutes after two o’clock is represented as 2:05).
- Explore and discuss the number of hours in a day.
- The first half of a new day begins at midnight and is represented as a.m.
- The second half of a day begins at noon and is represented as p.m.

**Money (skip counting w/ like coins): **

- Count by ones using pennies.
- Count by 5s using nickels.
- Count by 10s using dimes.
- Count by 25 using quarters.
- Count by dollars using dollar bills (1 dollar bill, 5 dollar bills, 10 dollar bills, 20 dollars, 50 dollars, 100 dollar bills).
- Use pennies, nickels, dimes, and quarters as manipulatives to reinforce place value up to 100 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:

**Student Achievement Partners Mini-assessments: **

**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 **

- Compare
- Difference
- Mental math
- Operation
- Quantity
- Represent
- Solve
- Symbol
- a.m.
- analog
- clock
- digital
- p.m.
- Coin
- Dime
- Dollar (bill)
- Money
- Nickel
- Penny
- Quarter
- Value

**Content Vocabulary **

- Addition
- Associative
- Base ten
- Commutative
- Digit
- Hundreds
- Identity
- Ones
- Place Value
- Properties of Addition
- Remainder
- Subtraction
- Sum
- Tens
- Skip count
- Half
- Hour
- Interval
- Minute
- Quarter
- Skip count
- 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:

**Science **

**2-ESS1-1**Use information from several sources to provide evidence that Earth events can occur quickly or slowly.

**Computer Science **

**1A-AP-10**Develop programs with sequences and simple loops, to express ideas or address a problem.

**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.2.7**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.*

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

- Bundling and Unbundling
- Place Value Units
- Boxes and Carton of Pencils
- Counting Stamps
- Largest Number Game
- Looking at Numbers Every Which Way
- Making 124
- One, Ten, and One Hundred More and Less
- Regrouping
- Three composing/decomposing problems
- Curious Subtraction Task
- Saving Money 2
- Comparisons 2
- Comparisons 1
- Number Line Comparisons
- Ordering 3-digit Numbers
- Using Pictures to Explain Number Comparisons
- Ordering Time

# 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.
- Visual representation of symbols on an Anchor chart or other visuals.
- Build decade numbers while simultaneously reading numbers aloud will reinforce the meanings of the quantities
- The use of visual tools such as number diagrams/analog clocks and digital clocks.
- Time interval number labels.
- The use of manipulatives such as play money.

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.