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Clarifications
Clarification 1: Instruction includes determining if a number is a multiple of a given number by using multiplication or division.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to determine whether a whole number is a multiple of a given one-digit number (e.g., Is 45 a multiple of 5?). Understanding of multiples extends what students learned in Grade 2 about skip-counting (e.g., skip-counting by 2s results in multiples of 2). Building a strong foundational understanding of multiples prepares students for relating multiples and factors to prime and composite numbers in Grade 4 (MA.4.AR.3.1).- Understanding of multiples extends from multiplication by expecting students to understand that the products of the given one-digit number and other factors create multiples of that one-digit number. For example, the products of 5 1, 5 2, 5 3,... are multiples of 5 (5, 10, 15,...). Understanding of multiples extends from division by expecting students to understand if a given whole number from 1 to 144 is divisible by a given-one- digit number, then that dividend is a multiple of it (e.g., 45 is divisible by 5, so 45 is a multiple of 5) (MTR.5.1).
- The focus of instruction should be on the vocabulary of multiples as it relates to multiplication and division. Students should first have a strong understanding of how multiplication and division work before developing their knowledge of multiples. Instruction can include real-world applications (e.g., Can 45 cookies be placed into 5 bags with an equal number in each bag?) (MTR.4.1, MTR.5.1).
Common Misconceptions or Errors
- When listing multiples of numbers, students may not list the number itself. It is important to emphasize that the smallest multiple is the number itself. Having students write multiples of a number by consecutive factors beginning with one.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to write multiples of a number by consecutive factors beginning with factor 1.
- Instruction includes opportunities to connect finding multiples to skip counting.
- For example, to find the multiples of 8, students can generate lists of multiples beginning with 1 × 8. Their generated list should include each of the counting numbers through 12 × 8. Students model generating multiples with counters. The teacher asks students to make one group of 8, having them record how many counters there are in an equation (1 × 8 = 8). Next, students add another group of 8, recording the number of counters in an equation (2 × 8 = 16). Students add more groups of 8 while recording the number of counters they have in an equation. Students should make all multiples of 8 through 12 × 8 = 96. When students have created their multiples, they record the products in a horizontal list in order from 1 × 8 = 8 to 12 × 8 = 96 and explain the connection between the products in their equations and the multiples in their list.
Instructional Tasks
Instructional Task 1
Use a visual model or write an equation to show whether 27 is a multiple of 3.Instructional Task 2
Use a visual model or write an equation to show whether 36 is a multiple of 8.Penelope says that when she counts by 6s, the numbers are also multiples of 3.
- 6, 12, 18, 24,…
Is she correct or incorrect? Explain.
Instructional Items
Instructional Item 1
Select all the numbers below that are multiples of 8.- a. 28
- b. 56
- c. 18
- d. 24
- e. 30
Instructional Item 2
Which number is NOT a multiple of 3?
- a. 30
- b. 32
- c. 33
- d. 36
Related Courses
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Related Resources
Formative Assessment
Original Student Tutorial
Problem-Solving Task
MFAS Formative Assessments
Students determine if a given number is a multiple of six, both with and without context.
Original Student Tutorials Mathematics - Grades K-5
Learn how to determine whether a whole number is a multiple of another whole number by using multiplication facts and skip-counting. You will be able to help Detective Barker in solving this mystery of which multiples belong to which whole numbers.
Student Resources
Original Student Tutorial
Learn how to determine whether a whole number is a multiple of another whole number by using multiplication facts and skip-counting. You will be able to help Detective Barker in solving this mystery of which multiples belong to which whole numbers.
Type: Original Student Tutorial
Problem-Solving Task
The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference. The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Task
The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference. The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.
Type: Problem-Solving Task
