Topic Seven: Meanings of Division

Pacing (Duration of Unit):

Desired Results

Transfer:
Standards for Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Established Goals:
3.OA.2 Interpret a 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 share 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.

3.OA.3 Use multiplication]and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 X ?=48, 5 =?÷ 3, 6 X 6=?

3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷8 by finding the number that makes 32 when multiplied by 8.

Student I Can Statements:
  • I can explain division as a set of objects partitioned into an equal number of shares.
  • I can identify parts of division equations (dividend, divisor, and quotient)
  • I can interpret quotients in division ( 32 ÷ 4 = 8 can be 4 groups with 8 items in each group or 8 groups with 4 items )
  • I can determine the unknown number in multiplication and division problems such as in the following examples: 8 x 9 = ?, 8 x ? = 48, ? x 3 = 27, 28 ÷ 7 = ?, ? ÷ 6 = 3, and 35 ÷ ? = 7.
  • I can explain the relationship between multiplication and division.
  • I can turn a division problem into a multiplication problem with an unknown factor.

Prerequisite Standards:
3.OA.1 Interpret product of whole numbers, e.g., interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 X 7.
Big Ideas:

Operation Meanings and Relationships
There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.

Practices, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • What are the different meanings of division?
  • How is division related to other operations?
Students will know...
  • Some real-word problems involving joining or separating equal groups or comparison can be solved using division.
  • Sharing involves separating equal groups and is one way to think about division.
  • Repeated subtraction involves separating equal groups and is one way to think about division.
  • Any division problem can be thought of as multiplication fact with a missing factor. Then, an answer can be found using a multiplication table.
  • Sharing and repeated subtraction both involve separating equal groups and are two ways to think about division.
  • Frequently word problems can often be shown by using objects to act it out or by using a picture or [[#|diagram]] in order to understand and solve the problem.

Vocabulary:
division

Students will be skilled at...
  • modeling to solve division problems involving sharing and recording solutions using division sentences.
  • modeling to solve division problems involving repeated subtraction and record solutions using division number sentences.
  • using multiplication tables to find answers to division problems.
  • solving word problems by [[#|writing]] equations that represent the problem situations.
  • writing and solving number stories involving division.
  • solving problems by using objects and drawing a picture.

Assessment Evidence

Performance Assessment:
Other Evidence:

Learning Plan

Learning Activities:

7-1 Some real-word problems involving joining or separating equal groups or comparison can be solved using division. Sharing involves separating equal groups and is one way to think about division.

7-2 Some real-word problems involving joining or separating equal groups or comparison can be solved using division.
Repeated subtraction involves separating equal groups and is one way to think about division.

7-3 Any division problem can be thought of as multiplication fact with a missing factor. Then, an answer can be found using a multiplication table.

7-4 Frequently word problems can often be shown by using objects to act it out or by using a picture or diagram in order to understand and solve the problem.

7-5 Sharing and repeated subtraction both involve separating equal groups and are two ways to think about division.

7-6 Information in a problem can often be shown by using objects to act it out or by using a picture or diagram in order to understand and solve the problem.
Resources:

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