Word (.docx)
Acrobat (.pdf)
Clarifications
Clarification 1: Instruction includes equal groups, arrays, area models and equations.Clarification 2: Within the benchmark, it is the expectation that one problem can be represented in multiple ways and understanding how the different representations are related to each other.
Clarification 3: Factors and divisors are limited to up to 12.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
- MA.3.NSO.2.3
- MA.3.NSO.2.4
- MA.3.AR.1.1
- MA.3.AR.1.2
- MA.3.AR.2.1
- MA.3.AR.2.2
- MA.3.AR.3.2
- MA.3.GR.2.2
- MA.3.GR.2.3
- MA.3.GR.2.4
Terms from the K-12 Glossary
- Area Model
- Commutative Property of Multiplication
- Dividend
- Divisor
- Equal sign
- Equation
- Expression
- Factors
- Rectangular Array
- Whole Number
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
- Instruction should relate multiplication to repeated addition work that began in Grade 2. In Grade 2, students used repeated addition to find the total number of objects using rectangular arrays and equations (MA.2.AR.3.2).
- Students should explore multiplication and division through word problems, writing expressions and drawing models that match the problems’ contexts (MTR.2.1, MTR.3.1).
- In division, students should see examples of sharing, or partitive division (where the number of groups are given and students determine the number in each group), as well as measurement, or quotative division (where the number in each group is given and students determine the number of groups).
- Instruction should relate division facts to known multiplication facts (e.g., fact families). Fact families can be explored through arrays and equal groups (MTR.5.1).
Common Misconceptions or Errors
- Students may have difficulty relating word problems and real-world scenarios to models, expressions, and equations. For example, students may not differentiate the number of groups versus the number in each group in multiplication, which then impacts their models, expressions, and equations.
- Students may be confused by measurement (or quotative) division when the amount in each group is given and the number of equal-sized groups is found.
Strategies to Support Tiered Instruction
- Instruction includes demonstrating the use of counters, arrays, and skip counting to model groups of objects, including the use of real-world scenarios to support students’ understanding of the number of groups versus the size of each group. Students represent their models with equations to reinforce the concept of multiplication.
- For example, a farmer is planting rows of sunflowers. He plants 6 rows with 5 sunflowers in each row. How many sunflowers does he plant?
- For example, there are 3 tables in the library. There are 4 students sitting at each table. How many students are sitting at tables in the library?
- Instruction includes demonstrating the use of counters and arrays to model division problems where the amount in each group is given and the number of equal-sized groups is found. The teacher provides real-world scenarios to represent the number of objects in each group and the number of groups Students form a group based on the context of the problem continuing to form groups of that size until the total is reached. Students can skip counting to keep track of how many counters they have used, representing their models with equations to reinforce the concept of division.
- For example, Renee is setting up chairs in the library. She is placing 24 chairs into rows. If she places 6 chairs in each row, how many rows of chairs will she have?
- For example, there are 15 students working on an art project. The art teacher divides them into groups of 3 students to work on the project. How many groups are there?
Instructional Tasks
Instructional Task 1 (MTR.3.1, MTR.7.1)
- Build 12×9 with place value blocks or counters.
- Part A. How would you solve for the product? What strategy did you use to solve the problem?
- Part B. Now build 9×12with place value block or counters. What is the product of 9×12? How did you see it?
- Part C. Draw a model for 9×12 or solve using a different strategy.
- There are 32 photos that need to be organized into a photo album. What are all the possible ways to display the photos on the pages of the album? Each page must have an equal number of photos. Use manipulatives, models, or equations to help you figure out all the possible combinations.
- Tina has 4 shelves on her bookshelf. Each row has 6 books. How many books are on Tina’s bookshelf in all? Draw a model and write an equation to represent your answer.
- Mateo goes to the grocery store with his dad to buy some fruit. The prices of the fruit are shown above.
- Part A. Mateo’s dad buys 6 bags of grapes. Write an equation that represents how many grapes he bought.
- Part B. Mateo’s dad also buys 4 bags of apples and 5 bags of oranges. Did he spend more money on apples or oranges? Explain how you know.
- Part C. Mateo sees his friend Jeremy at the grocery store. Jeremy’s mom buys 7 bags of grapes and 5 bags of apples. How much more does she spend on apples than grapes? How do you know?
Instructional Items
Instructional Item 1- What expression equals 7 x 6?
a. 6 + 6 + 6 + 6
b. 6 + 6 + 6 + 6 + 6
c. 6 + 6 + 6 + 6 + 6 + 6
d. 6 + 6 + 6 + 6 + 6 + 6 + 6
- Elizabeth has 28 pairs of earrings that she wants to put into her jewelry organizer. Each drawer of the organizer holds 4 pairs of earrings. How many drawers will she need to organize all of her earrings?
- If 72 eggs are packaged twelve eggs to a carton, how many cartons will we need to package all the eggs? Solve using an equation, model or other strategy.
Instructional Item 4
- A total of 56 chairs are in the cafeteria for an assembly. The principal arranges the chairs into 8 rows with the same number of chairs in each. Which equation shows the quotient as the number of chairs that will be in each row?
- a. 56÷8=7
- b. 56÷8=48
- c. 56÷8=64
- d. 56÷8=6
*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
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Experts
Perspectives Video: Teaching Ideas
Problem-Solving Tasks
Student Center Activities
Teaching Idea
STEM Lessons - Model Eliciting Activity
Students will decide which performing arts facility their principal should recommend for group chorus singing lessons. They will apply multiplication, division, and time skills for telling time to the nearest minute and time intervals. Students will work collaboratively as a group to analyze this Model Eliciting Activity (MEA), and engage in collaborative discussion that involves higher level critical thinking. They will write letters on which performing arts facility is the best choice.
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 read a multiplicative comparison word problem and are asked to write an equation that matches the problem.
Students are asked to illustrate a division problem and write a corresponding equation.
Students are asked to explain what 5 x 7 means and to provide a real-world context for 5 x 7.
Students are given a context for a multiplicative comparison and asked to explain the comparison.
Students are asked to explain how to use a number line for multiplying, in the context of a word problem.
Students discuss the relationship between the lengths of two snakes in a multiplicative comparison problem that includes an equation.
Students are asked to explain how to use a number line for dividing, in the context of a word problem.
Students write an equation to match a given word problem.
Students are asked to write multiplication word problems prompted by pictures and then to write both an addition and a multiplication expression that can be used to solve the problem.
Original Student Tutorials Mathematics - Grades K-5
Allie learns to be fair when she shares and she learns more about division in this interactive tutorial.
Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.
This is part 1 of 2-part series, click HERE to view part 2.
Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.
This is part 2 of 2-part series, click HERE to view part 1.
Come play with Marty the monkey as he teaches you how to understand the concept of multiplication in this interactive tutorial.
Student Resources
Original Student Tutorials
Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.
This is part 2 of 2-part series, click HERE to view part 1.
Type: Original Student Tutorial
Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.
This is part 1 of 2-part series, click HERE to view part 2.
Type: Original Student Tutorial
Come play with Marty the monkey as he teaches you how to understand the concept of multiplication in this interactive tutorial.
Type: Original Student Tutorial
Allie learns to be fair when she shares and she learns more about division in this interactive tutorial.
Type: Original Student Tutorial
Problem-Solving Tasks
Both of the questions are solved by the division problem 12÷3 but what happens to the ribbon is different in each case. The problem can be solved with a drawing of a tape diagram or number line. For problem 1, the line must be divided into 3 equal parts. The second problem can be solved by successive subtraction of 3 feet to see how many times it fits in 12.
Type: Problem-Solving Task
The first of these is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"
Type: Problem-Solving Task
In this task, the students are not asked to find an answer, but are asked to analyze the problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.
Type: Problem-Solving Task
Parent Resources
Perspectives Video: Experts
Explore strategies students may use to solve basic multiplication problems and ways to support their understanding by watching this video.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Perspectives Video: Expert
Explore strategies students may use to solve basic division problems and ways to support their understanding in this video.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Perspectives Video: Expert
Problem-Solving Tasks
Both of the questions are solved by the division problem 12÷3 but what happens to the ribbon is different in each case. The problem can be solved with a drawing of a tape diagram or number line. For problem 1, the line must be divided into 3 equal parts. The second problem can be solved by successive subtraction of 3 feet to see how many times it fits in 12.
Type: Problem-Solving Task
The first of these is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"
Type: Problem-Solving Task
In this task, the students are not asked to find an answer, but are asked to analyze the problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.
Type: Problem-Solving Task
Student Center Activities
In this game, students develop fluency with addition or multiplication facts and strengthen number sense through fast-paced problem-solving.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
In this game, students bop balloons into the correct basket by solving math facts and matching them to their answers to strengthen fluency through movement-based play.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
In this game, students develop fluency with counting sequences and number patterns and strengthen number sense through movement, rhythm, and voice modulation while also practicing active participation and listening skills.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
Teaching Idea
This guide offers five practical strategies to help after-school providers support meaningful, low-pressure math experiences that lead to deeper understanding and better long-term outcomes for K-5 students.
Type: Teaching Idea
