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Given a mathematical or real-world context, write an equation involving multiplication or division to determine the unknown whole number with the unknown in any position.
Examples
The equation 96=8×t can be used to determine the cost of each movie ticket at the movie theatre if a total of $96 was spent on 8 equally priced tickets. Then each ticket costs $12.Clarifications
Clarification 1: Instruction extends the development of algebraic thinking skills where the symbolic representation of the unknown uses 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.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
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
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to continue connecting real world situations to multiplication and division by writing equations to represent these situations and using the relationship between multiplication and division to solve problems. This connects the work from grade 3 of determining the value of the unknown number in multiplication and division equations that are given (MA.3.AR.2.3).- Instruction of this benchmark should emphasize helping students to see the relationship between multiplication and division (MA.4.NSO.2.1) when solving for an unknown in any position in an equation.
- Success with this benchmark will facilitate automaticity with multiplication and division facts (MA.4.NSO.2.1).
- Within this benchmark, students may use multiplicative comparison (e.g., 50 is 5 times as many as 10).
- Using a bar or tape diagram can be helpful for students to model the real-world situations presented (see example below).
Common Misconceptions or Errors
- Even though many students know their multiplication and related division facts with automaticity, students without a firm conceptual understanding of multiplication and division may have difficulty problem solving with multiplication and division and writing equations to model situations. Provide opportunities for students to explain their models and justify solutions.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to connect real-world situations to multiplication and division by writing equations to represent these situations and using the relationship between multiplication and division to solve problems. The teacher emphasizes the inverse relationship between multiplication and division, reinforcing conceptual understanding of multiplication and division by having students use drawings, models, and equations to solve real-world problems.
- For example, the teacher displays and reads the following problem aloud: “ Enrique has 63 baseball cards, which is 9 times as many as Damion. How many baseball cards does Damion have?” The teacher guides students to use a drawing, such as a bar model, to solve and write an equation. Through prompting and questioning, students explain their models and justify their solutions. This is repeated with multiple examples of real-world problems.
- The teacher provides opportunities to connect real-world examples to multiplication and division using the relationship between multiplication and division to solve problems using hands-on models and manipulatives. The teacher emphasizes the inverse relationship between multiplication and division, reinforcing conceptual understanding of multiplication and division by having students use manipulatives and equations to solve real-world problems. Through prompting and questioning, students explain their models and justify their solutions.
- For example, the teacher displays and reads the following problem aloud: “Sabrina hiked 48 miles in the month of May. Andre hiked 8 miles in the same month. How many times more miles did Sabrina hike than Andre?” The teacher guides students to use manipulatives, such as counters or base-ten blocks, to model the problem by showing equal groups, reminding students that multiplication and division are inverse operations. Through prompting and questioning, students explain their models justify their solutions, and write an equation. This is repeated with multiple examples of real-world problems.
Instructional Tasks
Instructional Task 1 (MTR.7.1)
A typical Dalmatian weighs 54 pounds and a typical Yorkshire terrier weighs 9 pounds. Write an equation to model this situation. Use your equation to determine how many more times the typical Dalmatian weighs than the typical Yorkshire terrier?
Instructional Items
Instructional Item 1
Shernice has 84 comic books which is 12 times as many as Cindy.Which equation below represents how many comic books, C, Cindy has?
- a. 84=12+C
- b. 84=12×C
- c. C=12+84
- d. C=12×84
*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.
5012060: Grade Four Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712050: Access Mathematics Grade 4 (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.4.AR.2.AP.2: Given a real-world context, identify or generate an equation involving multiplication or division to determine the unknown product or quotient. Multiplication may not exceed two-digit by one-digit and division must be related to one-digit by one-digit multiplication facts.
Related Resources
Vetted resources educators can use to teach the concepts and skills in this benchmark.
Formative Assessments
Lesson Plans
Original Student Tutorials
Teaching Idea
MFAS Formative Assessments
Books and Yarn:
Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.
Dogs as Pets:
Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.
Juice Boxes:
Students are given a two-step word problem and are asked to solve the problem and write an equation with a letter representing the unknown in the equation.
Throwing Footballs:
Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.
Original Student Tutorials Mathematics - Grades K-5
Space: Division as Comparison:
Discover how multiplicative comparison problems, from outer space, can be solved using division in this online tutorial.
Space: Multiplication as Comparison:
Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial.
Student Resources
Vetted resources students can use to learn the concepts and skills in this benchmark.
Original Student Tutorials
Space: Division as Comparison:
Discover how multiplicative comparison problems, from outer space, can be solved using division in this online tutorial.
Type: Original Student Tutorial
Space: Multiplication as Comparison:
Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial.
Type: Original Student Tutorial
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.
