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Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position.
Clarifications
Clarification 1: Instruction extends the development of algebraic thinking skills where the symbolic representation of the unknown uses any symbol or a letter.Clarification 2: Problems include the unknown on either side of the equal sign.
Clarification 3: Multiplication is limited to factors within 12 and related division facts. Refer to Situations Involving Operations with Numbers (Appendix A).
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Equation
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to find an unknown value represented by a symbol or letter in a multiplication or division equation, continuing the work from Grade 2, where students found unknown values in addition and subtraction equations.- Instruction that emphasizes the relationship between related facts in a fact family helps students use known values to solve for unknown values. For example, a fact family could be used to help students determine the unknown value in the equation 72 ÷ ? = 9 (MTR.5.1).
72 ÷ ? = 9
72 ÷ 9 =?
9 × ? = 72
? × 9 = 72
- Students can use any of these related facts to determine that the unknown value is 8. Teachers should encourage students to use such equations to justify their solutions (MTR.6.1).
- In the primary grades, students used fact families to find missing addends and understand the relationship between addition and subtraction.
- Understanding and using related facts to solve for unknown values is an important algebraic understanding for using inverse operations to solve equations in future mathematics courses (MTR.5.1).
Common Misconceptions or Errors
- By Grade 3, many students expect the solutions of equations to be an expression on the right side of the equal sign. When students determine unknown values in multiplication or division equations, give examples with the product or quotient on the left side.
Strategies to Support Tiered Instruction
-
Instruction includes opportunities to explore the meaning of the equal sign within the context of multiplication and division. The teacher provides clarification that the equal sign means “the same as” rather than “the answer is,” supporting the understanding that the product and quotient can be on either the left or the right side of the equal sign. Multiple examples are provided for students to solve for the unknown with the product or quotient on both the left and right sides of the equation. The teacher uses the same equations written in different ways to reinforce the concept.
- For example, the teacher shows the following equations, asking students to solve for the unknown. Students explain why each equation is true after solving, repeating with additional examples.
- Teacher provides opportunities to explore the meaning of the equal sign within the context of multiplication and division using visual representations (e.g., counters, drawings, base-ten blocks) to represent the equations. The teacher provides clarification that the equal sign means “the same as” rather than “the answer is,” supporting the understanding that the product and quotient can be on either the left or the right side of the equal sign. Multiple examples are provided for students to solve for the unknown with the product or quotient on both the left and right sides of the equation, using the same equations written in different ways to reinforce the concept.
- For example, the teacher shows the following equations, asking students to solve for the unknown and explain why each equation is true after solving. Students use counters, drawings, or base-ten blocks to represent the equation, repeating with additional operations.
Instructional Tasks
Instructional Task 1
Sam is having trouble deciding whether the value of n that makes the equation below true is 4 or 36. Which number is correct? Show your thinking using an equation or visual model.3 = ÷ 12
Instructional Task 2
- How could Wendy use 6×7=42 to help her find the value of the unknown number in the equation below?
7× ?=42
Instructional Items
Instructional Item 1
What value of makes the equation below true? ÷ 6 = 5
Instructional Item 2
What is the value of the unknown number in the equation 7 × = 56?
Instructional Item 3
What is the value of the unknown number in the equation below?
132÷n=11
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
MA.3.AR.2.AP.3: Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the product or quotient unknown (e.g., 2 × 5 = __, 10 ÷ 5 = __). Multiplication may not exceed two single-digit whole numbers and their related division facts.
Related Resources
Vetted resources educators can use to teach the concepts and skills in this benchmark.
Formative Assessments
Lesson Plans
Teaching Idea
MFAS Formative Assessments
Find the Unknown Number:
Students are given multiplication and division equations within 50 and are asked to find missing numbers. The missing numbers are presented in all positions.
Missing Numbers In Division Equations:
Students are given division equations involving numbers within 50 and are asked to find missing numbers. The missing numbers are presented in all positions.
Missing Numbers In Multiplication Equations:
Students are given multiplication equations with products within 50 and are asked to find missing numbers. The missing numbers are presented in all positions.
Multiplication and Division Equations:
Students are given multiplication and division equations within 100 and asked to find the missing numbers. The missing numbers are presented in all positions.
Student Resources
Vetted resources students can use to learn the concepts and skills in this benchmark.
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.
