Standard 3 : Develop an understanding of multiplication.



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General Information

Number: MA.2.AR.3
Title: Develop an understanding of multiplication.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 2
Strand: Algebraic Reasoning

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.2.AR.3.1: Represent an even number using two equal groups or two equal addends. Represent an odd number using two equal groups with one left over or two equal addends plus 1.
Clarifications:
Clarification 1: Instruction focuses on the connection of recognizing even and odd numbers using skip counting, arrays and patterns in the ones place.

Clarification 2: Addends are limited to whole numbers less than or equal to 12.

MA.2.AR.3.2: Use repeated addition to find the total number of objects in a collection of equal groups. Represent the total number of objects using rectangular arrays and equations.
Clarifications:
Clarification 1: Instruction includes making a connection between arrays and repeated addition, which builds a foundation for multiplication.

Clarification 2: The total number of objects is limited to 25.



Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.2.AR.3.AP.1: Explore the concept of odd and even by pairing objects to represent an even number using two equal groups or represent an odd number by using two equal groups with one left over. Group of objects may not exceed 20.
MA.2.AR.3.AP.2: Explore using repeated addition to find the total number of objects represented in a collection of equal groups (e.g., 3 groups of 2 objects) or in a rectangular array (e.g., 3 rows of 2 objects). Total objects may not exceed 20.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Original Student Tutorials

Name Description
Destinee Dragon’s Donut Troubles: Arrays:

Help Destinee use arrays and repeated addition to find how many donuts that she has in this interactive tutorial.

Beach Buddies: Even or Odd? :

Come explore even and odd numbers of objects and learn to determine if a group of objects has an even or odd number in this beach-themed, interactive tutorial.

Formative Assessments

Name Description
Counting By Rows or Columns:

Students are asked to make an array from pennies and then skip count to find the total number of pennies and write an addition equation to represent the array.

All Your Penguins in a Row:

Students are asked count by rows or columns to determine the total number in an array and then write an addition equation to represent the array.

Writing an Equal Addends Equation:

Students are asked to write an equal addends equation that corresponds to a given array.

Counting an Array:

Students are asked to find the total number of objects in a 3 x 4 array.

Showing a Collection as Odd or Even:

Students are asked to determine if each of two collections has an odd or even number of objects, and to explain how they made their decisions.

How Do You Know if a Number is Even or Odd?:

Students are asked to determine if a given number is even or odd.

Is it Even or Odd?:

Students are asked to determine if a given number is even or odd.

Even Numbers as the Sum of Two Equal Addends:

Students are asked to write even numbers within 20 as the sum of two equal addends.

Lesson Plans

Name Description
Cookies for All:

This lesson allows students to use everyday objects to understand equal groups by representing a total number of objects using rectangular arrays and repeated addition equations. The lesson uses "The Doorbell Rang" by Pat Hutchins to engage students during the lesson and to make a connection by using literacy in mathematics. This lesson will provide a foundation for the conceptual understanding of division by creating equal groups using arrays and repeated addition.

Déjà Vu Addition, 2 plus 2 plus 2:

This lesson illustrates that when you have a rectangular array of objects, you can determine the sum of the objects by using a repeated addition equation. This builds a foundation for multiplication.

Odds and Evens Dodgeball:

Students will create groups of objects to determine if a number is even or odd.

Array Addition:

This is a lesson in which students will practice making rectangular arrays and writing equations, with and without story problems, using repeated addition to find the total number of objects in each array. This lesson is designed to help prepare students for multiplication.

I Array + You Array = Arrays!:

An engaging activity that includes using repeated addition to find the total number of objects in equal groups and representing the total number of objects using arrays and equations.

Odds and Evens:

This resource helps students identify numbers as odd or even using a variety of methods including creating pairs, skip counting by two’s, using number lines, and arrays. It also leads them to understand that all even numbers can be written as a sum of equal addends and odds can be written as the sum of equal addends plus one.

This resource can be conducted as one lesson or can be spread over multiple mini sessions if needed as noted within this resource as Lesson 1 and Lesson 2.

 

Perspectives Video: Teaching Ideas

Name Description
The Van de Walle Dot Matrix: A tool to support concepts from counting to multiplying polynomials:

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Dot Matrix sheet is available for dowload here.

Equations on the Math Balance:

Unlock an effective teaching strategy for teaching inequalities and equations with the math balance in this Teacher Perspectives video for educators.

Problem-Solving Tasks

Name Description
Red and Blue Tiles:

This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Counting Dots in Arrays:

Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions. This particular question also lays a foundation for students to understand the commutative property of multiplication in third grade. This task would be much more valuable if included in an appropriate place in an instructional sequence than as an isolated task.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

Title Description
Destinee Dragon’s Donut Troubles: Arrays:

Help Destinee use arrays and repeated addition to find how many donuts that she has in this interactive tutorial.

Beach Buddies: Even or Odd? :

Come explore even and odd numbers of objects and learn to determine if a group of objects has an even or odd number in this beach-themed, interactive tutorial.

Problem-Solving Tasks

Title Description
Red and Blue Tiles:

This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Counting Dots in Arrays:

Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions. This particular question also lays a foundation for students to understand the commutative property of multiplication in third grade. This task would be much more valuable if included in an appropriate place in an instructional sequence than as an isolated task.



Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Problem-Solving Tasks

Title Description
Red and Blue Tiles:

This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Counting Dots in Arrays:

Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions. This particular question also lays a foundation for students to understand the commutative property of multiplication in third grade. This task would be much more valuable if included in an appropriate place in an instructional sequence than as an isolated task.