Students’ mastery of this skill will include an understanding of two types of contexts that can be represented using division. One is that (for example) 56 divided by 8 is the number of objects in each share when 56 objects are divided into 8 equal shares. The other is that 56 divided by 8 is the number of shares when 56 objects are partitioned into shares of 8 objects each. These two types of division contexts are often described as “partitive” and “quotative”, respectively. When constructing division problems, teachers often lean heavily towards the former; e.g., “If I have 15 cookies and want to divide them among five children, how many cookies can each child have?” It is important that teachers also introduce students to the other type of division context; e.g., “If I have 15 cookies and want to make gift bags of 5 cookies each, how many gift bags can I make?” Students should describe a context in which a number of shares or a number of groups can be expressed as a division statement. Further, students will eventually make the connection between division and multiplication.
Understanding the Standard:
- The use of drawings, pictures, and manipulative objects will aid in students’ understanding of division as the process of making equal shares from a whole number.
Common contexts should be used that easily lend themselves to whole number quotients that are typically partitioned into equal shares. For example, if you are packaging bottles of juice for an event into 6-packs, and you have 42 bottles, how many 6-packs do you have? Another example: how many dozens of eggs are there in 132 eggs? 132 ÷ 12 = 11. A third example: 42 ÷ 6 = 7 .49 days is how many weeks? 49 ÷ 7 = 7.
Questions to Focus Learning:
- Can students use drawings and pictures to accurately portray a division problem?
- Can students recognize contexts in which division takes place?
- Can students use division expressions to represent the two types of contexts in which division takes place (see summary above)?
Students have not yet had opportunities to make equal shares and begin to understand the primary focus of division. See 2.OA.C.3
At Grade Level:
Students can express quotients of whole numbers as parts of a group. They can do this by writing division statements.
Beyond This Standard:
Students can interpret quotients with larger numbers and compute quotients of whole numbers. Students may begin to interpret quotients that involve halves or other common fractions in the answer.