Arrays (sets of objects or numbers arranged in order, often in rows and columns) are helpful visuals as students begin to learn the early concept of multiplication, and formalize the skill of writing equations involving sums of equal addends (e.g., five rows of five columns can be written as 25 = 5 + 5 + 5 + 5 + 5). Here, students see equal groups of orderly arranged objects in rows and columns in the array, and orderly identical addends in their equations.
Understanding the Standard:
- The use of counters is helpful for students to build their own rectangular arrays to meet specifications (3 rows of 5). They can then write an addition sentence with repeated addends that is representative of an array built (5 + 5 + 5 = 15). While multiplication is not introduced until later, teachers can extend learning by showing students that addition and multiplication are related (3 rows of 5 = 3 x 5)
- Jumping on a number line is another visual activity that can aid students’ understanding of early multiplication concepts.
- The use of manipulatives and other technologies is encouraged.
- Students should be used to ten frames, and the ten frame of value 10 is a 2 by 5 array that equals 10. Students can begin here and build up to a 5 by 5 array. Each one should be expressed as an addition equation, and arrays other than 5 should also be written. For example, a 4 by 3 array can be expressed as 12 = 3 + 3 + 3 + 3.
Questions to Focus Instruction:
- Can students create a rectangular array that meets specific requirements?
- Are students able to express the counters in an array as repeated addition and then express it as a number sentence where the sum is the total number of objects in the array grouping?
- Students should write an equation to express the total as a sum of equal addends.
Students should have mastered skip counting and the ability to add repeated addends through 20.
At Grade Level:
Students will construct rectangular arrays to model a picture of equal groupings of objects up to arrays of 25. From here, they will write an addition sentence that is representative of the model.
While arrays are used in the early introductions of multiplication, students will further demonstrate their knowledge of multiplication with fluency through 100. Go to 3.OA.A.1
. to see the progression of related skills.