MA.3.A.1.3Archived Standard

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Identify, describe, and apply division and multiplication as inverse operations.

Remarks

Example: Twenty-four children are going to the circus in 6 cars. How many children can ride in each car, with the same number of children in each car? Which of the following number sentences can be used to solve this problem?

 

a) 24 - 6 = __ b) 24 + 6 = __ c) __ ÷ 6 = 24 d) 6 x __ = 24
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 3
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 1 - Develop understandings of multiplication and division and strategies for basic multiplication facts and related division facts.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC item(s)

  • Clarification :
    Students will identify the inverse of a multiplication or division equation. 

    Students will apply the inverse property to solve real-world problems and to check the solution of a problem involving multiplication or division.

  • Content Limits :
    Items may include whole-number multiplication facts from 0 X 0 through 9 X 9 and the related division facts. 

    Items will not include identifying the inverse property by name.

  • Stimulus Attributes :
    Blank spaces (4 X _ = 36), geometric shapes (e.g.,Δ ), or letters may be used to represent variables. 

    Items may be set in either a real-world or mathematical context.

  • Response Attributes :
    Responses should be multiplication or division expressions or equations.
Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question: A group of 24 people is getting on a roller coaster. Each car of the roller coaster can hold 4 people. Which equation could be used to find the number of roller coaster cars needed to hold all 24 people?
  • Difficulty: N/A
  • Type: MC: Multiple Choice

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Unit/Lesson Sequences

All About Multiplication:

This four-lesson unit from NCTM's Illuminations has students explore several meaning and representations of multiplication (number line, equal sets, arrays, and balanced equations). Other multiplication topics covered include: the commutative (order) property, the results of multiplying by 1 and 0, and the inverse property. Students will write and solve multiplication story problems, and convert word problems into equations. A bibliography of children's literature with a focus on multiplication is provided, which can be integrated so that students can connect through literature.

Individual Lessons

    • Students are shown how to generate products on a number line, highlighting the measurement aspect of addition. After some practice, they are asked to predict and then verify sums, and are also introduced to the commutative property.
  • Lesson 2: Exploring Equal Sets
    • Students explore the set model for multiplication. They find products using equal sets and present their results in a table. Next students apply their knowledge about multiplication in the creation of pictographs.
  • Lesson 3: Modeling Multiplication With Streets and Avenues
    • The array model of multiplication lays the foundation for the later study of area, and in this lesson, students will create arrays of the factors of 4 and 6 using toothpicks as representations of streets and avenues. The teacher will ask how many stoplights would be needed to fill each intersection. Zero and one will also be used as factors. Finally they will write their results as multiplication problems.
  • Lesson 4: Balance Beam Discoveries
    • The balance beam model of multiplication is examined in this lesson, along with another important relationship, the inverse of multiplication. This will lead naturally into the representation of multiplication facts as equations. Students will also practice multiplication facts by playing the Product Game.

Type: Unit/Lesson Sequence

Computation Through Literature :

This collection of 10 lessons uses children's literature to engage students in addition, subtraction, multiplication, and division. The lesson arrangement is flexible and adaptable for any scope and sequence.

Type: Unit/Lesson Sequence

Student Resources

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Parent Resources

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