Connecting Benchmarks/Horizontal Alignment

• MA.3.NSO.2.2 
• MA.3.NSO.2.4

 

Terms from the K-12 Glossary

 

Vertical Alignment

Previous Benchmarks

• MA.2.AR.3.2

 

Next Benchmarks

• MA.4.NSO.2.1 
• MA.4.AR.3.1

 

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 $x$ 1, 5 $x$ 2, 5 $x$ 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.