Understanding Division In Mathematics
Division is the process of separating a total into equal groups. It answers two key types of questions: “How many in each group?” and “How many groups can I make?”
Division involves three key components:
- Dividend: The number being divided
- Divisor: The number of groups or the size of each group
- Quotient: The result of the division, representing how many are in each group or how many groups can be made
For example, in 32 ÷ 4 = 8, 32 is the dividend (the total being divided), 4 is the divisor (the number of groups), and 8 is the quotient (the amount in each group).
Division also connects to other operations. It is the inverse of multiplication as you can see in the multiplication and division fact family:
Division also builds on repeated subtraction. For example, for 10 ÷ 2, subtract 2 repeatedly from 10 until you can’t subtract 2 anymore. The number of times you subtract 2, which is 5, represents the answer. NOTE: If there’s any amount left that’s smaller than 2, that amount is the remainder.
Why Is Division Important?
Division Builds Mathematical Understanding
Division helps strengthen number sense by teaching students how numbers can be composed and decomposed into equal groups or parts. This helps students develop a deeper understanding by visualizing how quantities can be distributed evenly.
Division also builds connections to multiplication, emphasizing the inverse relationship between these operations. Teachers can guide students to see 24 ÷ 6 not only as finding how many groups of 6 make up 24, but also as a way to verify or explain their reasoning by connecting it to multiplication, such as 6 × 4 = 24. These kinds of connections support fact fluency and help students understand the interplay between these operations.
Division prepares students for fractions, ratios, and proportional reasoning. Understanding division as splitting or grouping also lays the foundation for interpreting division with remainders, and dividing decimals.
Understanding Division Problems: Measurement and Sharing
Measurement Division
In measurement division problems, the divisor tells you the size of each group, and you need to find the number of groups. For example, if you have 24 candies and put 6 in each bag, 24 ÷ 6 asks, “How many bags can you make?”
Sharing (Partition) Division
In sharing problems, the divisor tells you the number of groups, and you need to find the size of each group. For example, if you share 20 apples equally among 4 people, 20÷4 asks, “How many apples does each person get?”
Strategies For Teaching Division
Using Concrete Models To Teach Division
Use manipulatives like counters or Unifix cubes and have students physically group items. Encourage students to also write the related multiplication equation, reinforcing the connection between the two operations.
Begin with 12 counters, and show 12 ÷ 3 = 4:
Use arrays to represent division visually by arranging objects into rows and columns.
Use number lines to show division as repeated subtraction, marking each step on the number line.
