Grade 2 · Operations · MAT-02-OPS-012
Build Equal Groups and Arrays
Arrange objects into equal groups and rectangular arrays.
Learning objectives
What you should be able to do
- Arrange objects into equal groups and rectangular arrays.
- Use repeated addition to describe arrays.
- Connect rows and columns to early multiplication reasoning without requiring formal multiplication mastery.
Prerequisite check
Make sure the foundation is ready.
Checks equal-group reasoning foundations.
Learn
Build the idea from meaning, not memorization.
Equal groups contain the same number in each group
Three groups of four means every group contains exactly four objects. Equal grouping prepares learners to reason multiplicatively.
Arrays organize equal groups into rows and columns
A rectangular array has equal-length rows and columns. A3-by-4 array contains3 rows of4, for12 objects total.
Repeated addition describes an array
Three rows of four can be written4+4+4=12. Four columns of three can be written3+3+3+3=12. Both describe the same array from different directions.
Arrays connect arithmetic and geometry
Arrays make equal groups visible and later support multiplication, area, factors, and distributive reasoning.
Interactive math lab
Change it. See what stays true.
Array Builder
Build equal rows and columns, then connect the grid to repeated addition.
- build equal groups
- set rows columns
- write repeated addition
- rotate array
Worked examples
Twenty different ways to see the concept work.
2 groups of3.
3+3=6Equal groups.
3 groups of4.
4+4+4=12Three equal rows.
4 groups of2.
2+2+2+2=8Repeated addition.
2 rows of5.
5+5=10Array total10.
5 rows of2.
2+2+2+2+2=10Same total, different orientation.
3 rows,3 columns.
93+3+3.
4 rows,3 each.
123 repeated4 times.
2 rows,6 each.
126+6.
Can groups2,2,3 be equal?
NoOne group differs.
Can3 rows of4 be rearranged to4 rows of3?
YesSame12 objects.
Array with2 rows4 columns.
84+4.
Array with4 rows4 columns.
164+4+4+4.
Array with5 rows3 columns.
153 added5 times.
Build12 as equal groups.
Examples3 groups4 or4 groups3 or6 groups2Multiple equal-group structures.
Build10 as5 pairs.
2+2+2+2+2Five equal groups of2.
Why rectangular?
Rows/columns stay equal in lengthStructure makes grouping visible.
Count array faster than ones.
Use rows×group-size idea or repeated additionOrganization reduces counting load.
What does a row represent?
One equal group in a row-based viewEach row contains same count.
What does column view show?
A different equal-group orientationSame total.
Explain3-by-4 total.
Three rows each with4:4+4+4=12Repeated equal groups.
Practice
Guided practice with hints
01Build3 groups of2.
Hint: Each group same size.
Answer: 6 objects
022 rows of4 total?
Hint: Add4+4.
Answer: 8
034 rows of3 total?
Hint: Add3 four times.
Answer: 12
04Are2,2,2,2 equal groups?
Hint: Compare sizes.
Answer: Yes
05Write repeated addition for3 rows5.
Hint: 5+5+5.
Answer: 15
06Why can3x4 and4x3 arrays use same12 objects?
Hint: Reorient rows/columns.
Answer: Total objects do not change.
Practice
Independent practice
012 groups of5 total
Answer: 10
023 groups of3 total
Answer: 9
034 rows2 each
Answer: 8
04Repeated addition for4 rows3
Answer: 3+3+3+3
05Are3,3,2 equal?
Answer: No
06Build12 two ways
Answer: Examples3x4 and2x6
075 rows2 each
Answer: 10
08Explain array
Answer: Objects arranged in equal rows and columns.
Common mistakes
Learn to catch the error, not just the answer.
Verify every group contains the same count.
Only objects inside the array contribute to total.
State both explicitly: e.g.,3 groups of4.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Arrange chairs, tiles, or objects in equal rows.
- Use arrays to count grouped items efficiently.
Challenge problems
Find three equal-group representations of12.
1x12,2x6,3x4 and reversals.
Why does rotating an array preserve total?
No objects are added or removed.
Can11 form2 equal groups of whole objects?
No; one object would remain.
How do arrays prepare for area?
They count equal rows and columns of square units.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Array Architect
Build requested equal groups and arrays, then write matching repeated addition.
Practice
Mastery check
013 groups4 total
Answer: 12
022 rows5 total
Answer: 10
03Repeated addition for4 rows2
Answer: 2+2+2+2
04Are4,4,4 equal groups?
Answer: Yes
05Can7 form2 equal groups?
Answer: No, one remains.
06Array definition
Answer: Equal rows and columns.
07Why rotate without changing total?
Answer: Same objects remain.
08How arrays help later?
Answer: They support multiplication and area reasoning.
Terminology
Words to know
- equal groups
- Groups containing the same number of objects.
- array
- An arrangement in equal rows and columns.
- row
- A horizontal line of objects.
- column
- A vertical line of objects.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.OA.C.4
Rectangular arrays and repeated addition.