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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.
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.
- 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:
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.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Teaching Ideas
Problem-Solving Task
MFAS Formative Assessments
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.
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.
Students are asked to write an equal addends equation that corresponds to a given array.
Original Student Tutorials Mathematics - Grades K-5
Help Destinee use arrays and repeated addition to find how many donuts that she has in this interactive tutorial.
Student Resources
Original Student Tutorial
Help Destinee use arrays and repeated addition to find how many donuts that she has in this interactive tutorial.
Type: Original Student Tutorial
Problem-Solving Task
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.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Task
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.
Type: Problem-Solving Task
