3.OA.A.2*This standard is part of a major cluster

StandardInterpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Standard UnpackedThis standard focuses on two distinct models of division: partition models and measurement (repeated subtraction) models. Partition models provide students with a total number and the number of groups. These models focus on the question, “How many objects are in each group so that the groups are equal?” A context for partition models would be: There are 12 cookies on the counter. If you are sharing the cookies equally among three bags, how many cookies will go in each bag? Measurement (repeated subtraction) models provide students with a total number and the number of objects in each group. These models focus on the question, “How many equal groups can you make?” A context for measurement models would be: There are 12 cookies on the counter. If you put 3 cookies in each bag, how many bags will you fill?

*For this standard, students should have ample opportunities using manipulatives and create drawing models to support their reasoning.

Division can be thought of in two ways. Division as sharing means you are given a total amount and a number of groups; the goal is to find the number in each group so that all groups have an equal amount. Division as repeated subtraction means you are given a total amount and the amount in each group. The goal is to find the number of groups. This can be modeled by removing equal amounts from the initial amount until none are left.

Example Division as Sharing (Partition Model):

You have 15 cars and would like to share them with two friends. How many cars will each person get if you share the cars with yourself and your friends equally? In this

example the student knows that there are 15 total object and three people to share them with (groups). The student could reason, or manipulate the set by discovering that each group will contain five cars. A student might understand this immediately, or need to place one car into each group until they have all been divided.

Example Division as Repeated Subtraction: You have 15 cars. You have separated them into groups of 5. How many groups are there? For this example a child might begin to place the objects into groups of five to determine there are 3 total groups. The child might be thinking in terms of subtraction for example, removing groups of five from the total group until none remain.

Common multiplication and division situations are shown in the table below. There are three major types, shown as rows of Table 3. The Grade 3 standards focus on Equal Groups and on Arrays. As with addition and subtraction, each multiplication or division situation involves three quantities, each of which can be the unknown. Because there are two factors and one product in each situation (product = factor x factor), each type has one subtype solved by multiplication (Unknown Product) and two unknown factor subtypes solved by division.

Equal groups problems can also be stated in terms of columns, exchanging the order of A and B, so that the same array is described. For example: There are B columns of apples with A apples in each column. How many apples are there? In the row and column situations (as with their area analogues), number of groups and group size are not distinguished.

Questions/ Activities to check for understanding and increase rigor:

• I have 24 total marshmallows divided into more than one bag. Each bag has the same amount. How many bags could I have? How many would be in each bag? Create a model and justify your thinking.

• How many ways can I share 36 equally? Create a model and justify your thinking.

• Explain the relationship between multiplication and division? Use models, drawings, and/or examples to support your answer.

• Think of an example in life when 42 ÷ 6 would be used with the sharing method of division (42 into 6 equal groups) and when it would be used with the measurement method (42 divided into groups of 6). Note: students do not need to know the vocabulary of sharing and measurement methods, but should be exposed to both.

• If the quotient is 6, what could your possible one-digit dividend and one-digit divisor be? List 3 different possibilities. Create a model and justify your thinking.

• How many people could share 32 M&M’s equally? Explain all possibilities

ELD Standard #3: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Mathematics.

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Share thinking about whole number quotients using key words from a word wall.

Share thinking about whole number quotients using key phrases from a word bank or word wall with a partner.

Share thinking about whole number quotients using simple sentences with a sentence frame in a small group.

Share thinking about whole number quotients using complex sentences in cooperative groups.

Share thinking about whole number quotients using a variety of simple & complex sentences independently.

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