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 6 Overview: Exploring Multiplication

Unit 6 Overview: Exploring Multiplication

Overview

Unit Overview/Summary - FOCUS: 

This unit includes number and operations in base ten, geometry, and operations and algebraic thinking serve as a support in this unit. Learning in this unit will enable students to: 

  • Understand place value;  
  • Partition a rectangle into rows and columns; and 
  • Work with equal groups of objects to gain foundations for multiplication. 

Relevant Standards:

Major work of the grade is in bold.  

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

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

2.OA.C.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.  

2.OA.C.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 

2.G.A.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 

Examples and Explanations:

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.OA.C.3. Students explore odd and even numbers in a variety of ways including the following: students may investigate if a number is odd or even by determining if the number of objects can be divided into two equal sets, arranged into pairs or counted by twos. After the above experiences, students may derive that they only need to look at the digit in the ones place to determine if a number is odd or even since any number of tens will always split into two even groups 

Example:  Students need opportunities writing equations representing sums of two equal addends, such as: 2 + 2 = 4, 3 + 3 = 6, 5 + 5 = 10, 6 + 6 = 12, or 8 + 8 =16. This understanding will lay the foundation for multiplication and is closely connected to 2.OA.4. 

The use of objects and/or interactive whiteboards will help students develop and demonstrate various strategies to determine even and odd numbers.  

2.OA.C.4. Students may arrange any set of objects into a rectangular array. Objects can be cubes, buttons, counters, etc. Objects do not have to be square to make an array. Geoboards can also be used to demonstrate rectangular arrays. Students then write equations that represent the total as the sum of equal addends as shown below. 

 

                                  

 

4 + 4 + 4 = 12                     5 + 5 + 5 + 5 = 20  

Interactive whiteboards and document cameras may be used to help students visualize and create arrays. 

2.G.A.2. This standard is a precursor to learning about the area of a rectangle and using arrays for multiplication. An interactive whiteboard or manipulatives such as square tiles, cubes, or other square shaped objects can be used to help students partition rectangles.  

Rows are horizontal and columns are vertical. 

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: 

  • Working with addition and subtraction equations. 

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: 

  • Represent and solve problems involving multiplication and division. 
  • Solve problems involving the four operations, and identify and explain patterns in arithmetic.
  • Understand concepts of area and relate area to multiplication and to addition. 

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. 

  • What are efficient methods for finding sums and differences using even and odd properties of numbers? 
  • How can repeated addition be represented? 
  • What are some characteristics of whole numbers? 

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: 

  • Flexible methods of computation involve grouping numbers in strategic ways. (Equations for even numbers with equal-sized addends.) 
  • Even numbered objects can be modeled using pairs or rectangular arrays. 
  • Rectangles can be composed or decomposed from/into equal-sided squares to model repeated addition.  

What Students Will Know:

  • Rectangles can be partitioned into rows and columns.  
  • Whole numbers are odd or even.  
  • When pairing an even numbered group of objects, no members are left over. 
  • When pairing an odd numbered group of objects, one member is left over.  
  • An even number may be decomposed into two equal addends, e.g., 10 = 5 + 5; 8 = 4 + 4.  
  • Each row in an array has an equal number of objects.  
  • Each column in an array has an equal number of objects.  
  • Adding rows or columns of an array will result in the same solution.  
  • The number of objects in an array is the same when the array is turned (rotated). 

What Students Will Do:

  • Determine if a group of objects, up to 20, is odd or even.  
  • Justify your answer (odd or even).  
  • Write an equation to represent an even number as the sum of 2 equal addends. 
  • Find the total number of objects arranged in rectangular arrays by using repeated addition.  
  • Write the equation to represent the repeated addition.  
  • Section a rectangle into same size squares creating rows and columns.  
  • Count the number of tiles in a rectangle to determine the total number of squares in the rectangle.  
  • 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. 
  • Partition rectangles into rows and columns of same-size squares.  
  • Represent a group of objects as odd or even by creating models, drawing pictures, and writing equations.  
  • Use strategies to determine if a group of objects has an odd or even number of members. 
  • Identify whole numbers between 0 and 25 as odd or even.  
  • Generalize a rule for why a number is odd or even.  
  • Write an equation to represent an even number as the sum of two equal addends. 
  • Explore rectangular arrays by creating models.  
  • Discuss and write addition equations to represent the total number of objects in an array as the sum of equal rows or equal columns, e.g., 3 + 3 = 6 and 2 + 2 + 2 = 6. 

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 

  • column 
  • equal 
  • even 
  • horizontal 
  • odd 
  • row 
  • vertical 

Content Vocabulary 

  • addend 
  • doubles 
  • equal groups 
  • equation 
  • pair 
  • partition 
  • remainder 

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-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.2.8 Describe how reasons support specific points the author makes in a text.  
  • 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.2.5 Create audio recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings.

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.

Entrepreneur: Lemonade Stand

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  

  • Concrete models of rectangular arrays to model even and odd quantities. 

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