Word (.docx)
Acrobat (.pdf)
Examples
Example: The product of 5 and 6 is 30.Example: The quotient of 27 and 9 is 3.
Clarifications
Clarification 1: Instruction focuses on helping a student choose a method they can use reliably.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Expression
- Equation
- Factor
- Dividend
- Divisor
- Commutative property of multiplication
- Associative property of multiplication
- Distributive property of multiplication
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to utilize skills from the exploration stage of multiplication and division (MA.3.NSO.2.2) to develop an accurate, reliable method that aligns with the student’s understanding and learning style. Procedural fluency of multiplication facts with factors up to 12 and their related division facts is not expected until Grade 4 (MTR.2.1, MTR.3.1).- This benchmark provides the opportunity for students to generalize patterns they see within the tools used during the exploration stage (e.g., rectangular arrays, equal groups) to then identify multiplication and related division facts (MTR.4.1).
- Instruction that builds procedural reliability should connect multiplication understanding with the properties of multiplication (commutative, associative and distributive). The patterns students recognize help them relate facts to one another, and to use the related facts to find the products and quotients of unknown facts. In this benchmark, students should be able to explain how they know facts and how they can find products of unknown facts (MTR.5.1). For example, students should recognize that 4 x 6 and 6 x 4 have the same product of 24 and identify this pattern as evidence of the commutative property of multiplication. This can also be discovered through arrays for multiplication using objects or drawings, where students can observe that the arrays contain the same total number of squares, but the orientation of the array has just rotated so the rows and columns are switched as shown below (MTR.5.1).
Common Misconceptions or Errors
- This benchmark does not support students’ memorization of multiplication and division facts. Memorization does not indicate work toward multiplication and division fact fluency. Students should be able to explain how they know multiplication and division facts, and how they can find products and quotients of unknown facts.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to experience the properties of multiplication and division. Students use and apply properties to build procedural fluency. Students should understand that multiplication and division both involve grouping equal sets of numbers or objects.
- For example, the teacher shows students an array of 8 × 6 = 48 and has them describe what they see with rows and columns. This learning can be connected to the concept of “groups of” objects, 8 groups of 6 is the same as 8 jumps of 6 on the number line.
- Teacher provides opportunities to build and manipulate what a multiplication fact looks like and then relates how it looks as division.
- For example, students model 3 x 4 as 3 rows of 4 with counters.
- The teacher then relates the multiplication model to division by separating the rows into groups. 12 = 4 groups of 3 counters, or 12 divided by 4 = 3.
Instructional Tasks
Instructional Task 1
- Part A. Show how to find the product of 6 × 7 in two different ways.
- Part B. Identify the related division facts from your equation in Part A.
Instructional Items
Instructional Item 1
- What is the product of 11 and 4?
Instructional Item 2
- Provide two division facts that have a quotient of 8.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Educational Game
Educational Software / Tool
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Expert
Perspectives Video: Teaching Idea
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will be required to rank musical instrument lesson packages based on the price, the number of minutes of practice each week, and the quality of the instructor.
Part of the task involves students figuring out the elapsed time of the lessons based on their start and stop times. They will also need to figure out the total weekly cost of the lessons based on the number of lessons offered per week and the cost of each lesson based on its length.
The twist will require students to determine whether or not to revise their ranking based on new information about the cost of instrument rentals per lesson and the class size of each package.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this pool of floating rafts, students will divide to find the cost of each flotation device. They must then determine which raft is the best for public use based on cost, warranty, and assembly. Students will submit a letter to the client explaining their procedure for ranking the flotation devices.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are assessed on their fluency with multiplication facts for the products of two one-digit numbers.
Students are asked to describe two different ways to find the product of two numbers.
Students are given a context for a multiplication problem and asked to determine how to solve it and what the product means.
Students are given division word problem and asked to determine how it might have been solved and what the quotient means.
Original Student Tutorials Mathematics - Grades K-5
Learn how Maritza uses multiplication to stuff school supplies into backpacks with this interactive tutorial.
Student Resources
Original Student Tutorial
Learn how Maritza uses multiplication to stuff school supplies into backpacks with this interactive tutorial.
Type: Original Student Tutorial
Educational Game
This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.
Type: Educational Game
Educational Software / Tool
In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Educational Software / Tool
