Standard #: MA.2.AR.3.2


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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.



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 2
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Equation 
  • Rectangular array

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is to connect the idea of repeated addition as a way to represent equal groups. At this grade level, students are also introduced to the array as a model for arranging groups into equal rows and equal columns. 
  • Instruction includes the language of rows and columns to reinforce the number of groups and the number of objects in each group. The number of groups can be represented by the number of rows with the number of objects in each group being represented by the size of the row (the number of columns), or the number of objects in each group can be represented by the number of columns and the number of objects in a group represented by the size of a column (the number of rows).
  • Instruction includes the idea that a scattered collection can be arranged into equal groups in various ways without changing the total number (i.e., the Cardinality Principle). 
  • Instruction includes the use of number lines and counters.

 

Common Misconceptions or Errors

  • Students may mistakenly add the number of rows and columns instead of the number of objects in each row.
  • Students may count the array total as the perimeter instead of the area. 
  • Students may not recognize that when rows and columns are rearranged in arrays the total number of objects in the array remains the same.

 

Strategies to Support Tiered Instruction

  • Teacher provides opportunities to create multiple arrays for a specific number using two-color counters and write a repeated addition equation to represent the sum of the array.
    • For example, students build arrays for the number 24, count the number of objects in each row and write a repeated addition equation to represent the array. While each array will be different, the sum will always be the same, building understanding that the equation changes based on the number of objects in each row. 
arrays for the number 24
  • Teacher provides arrays cards to match multiple variations of an array that match a specific number. 
    • For example, students may see a variety of arrays for the number 24. Arrays are presented as arrays of 3 rows of 8, 8 rows of 3, 2 rows of 12, 12 rows of 2, 4 rows of 6, 6 rows of 4, and some non-examples of arrays for 24. By sorting the arrays into a group that represents 24, students develop an understanding that columns and rows can be rearranged and still represent the same sum. 
  • Teacher provides a template of an array for students to number the number of objects in each row and write a repeated addition equation to represent the array. 
    • Example:
number of objects in each row

 

Instructional Tasks

Instructional Task 1 (MTR.2.1, MTR.7.1

A teacher is putting chairs at a table for a class party. The teacher puts five chairs at each of the four tables. 
  • Part A. Use counters to represent the total number of chairs, and write a repeated addition equation to show the total number of chairs. 
  • Part B. Represent the chairs by putting counters into an array in more than one way.

 

Instructional Items

Instructional Item 1 

  • Part A. Draw three triangles in each of the groups below. 
  • Part B. Create an array to represent the total amount of triangles. 
  • Part C. Write a repeated addition equation to show the total number of triangles. 

4 groups

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
5012040: Mathematics - Grade Two (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712030: Access Mathematics Grade 2 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012005: Foundational Skills in Mathematics K-2 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))


Related Access Points

Access Point Number Access Point Title
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

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.

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.

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.

 

Original Student Tutorial

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.

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.

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 Task

Name Description
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

Original Student Tutorial

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.

Problem-Solving Task

Name Description
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

Problem-Solving Task

Name Description
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.



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