### Clarifications

*Clarification 1:*Instruction includes the connection to the relationship between multiplication and division and patterns with divisibility rules.

*Clarification 2:* The numbers 0 and 1 are neither prime nor composite.

**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

- Composite Number
- Factors
- Prime Number

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to begin understanding factors of whole numbers which sets the foundation for determining prime factorization in grade 6 (MA.6.NSO.3.4).- This benchmark also refers to prime and composite numbers. Prime numbers have exactly two factors, the number one and the number itself (e.g., the number 13 has the factors of 1 and 13 only so it is a prime number). Composite numbers have more than two factors.
- For example, 14 has the factors of 1, 2, 7 and 14. Since this number has more factors than 1 and 14, it is a composite number.

- Instruction may allow students to use divisibility rules to determine the factors of a number.
- All numbers are divisible by 1.
- All even numbers are divisible by 2.
- A number is divisible by 3 if the sum of the digits is divisible by 3.
- A number is divisible by 4 if the 2-digit number in the tens and ones places is divisible by 4.
- A number is divisible by 5 if the number in the ones place is a 0 or 5.
- A number is divisible by 6 if it is an even number and the sum of the digits is divisible by 3.
- A number is divisible by 9 if the sum of the digits is divisible by 9.

- Students should use models (arrays) to determine why a number would be prime or composite.

### Common Misconceptions or Errors

- Students may think of the number 1 as a prime number. It is neither prime nor composite.
- Students may also think that all odd numbers are prime.
- Some students may think that larger numbers have more factors. Have students share all factor pairs and how they found the factors.

### Strategies to Support Tiered Instruction

- Instruction includes opportunities to identify the factor pairs of whole numbers from 0- 144 with teacher guidance. Students also determine if the number is prime, composite or neither. The teacher refers to the divisibility rules shown above in “Purpose and Instructional Strategies” to support students as they determine the factors of the given number. Students use manipulatives and models (e.g., counters and arrays) to identify factors of the given number.
- For example, the teacher displays the following number: 48. Students draw arrays to determine the factors of 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48). Students may use multiplication and skip counting to check factor pairs (e.g., 5 can be ruled out as a factor because 5 × 9 = 45 and 5 × 10 = 50). The teacher asks students if 48 is prime, composite, or neither (composite). This is repeated with additional whole numbers from 0-144.

- For example, the teacher displays the following number: 32. Students are provided 32 counters and use them to create arrays to determine the factors of 32 (1, 2, 4, 8, 16, 32). Students may use multiplication and skip counting to check factor pairs (e.g., 5 can be ruled out as a factor because 5 × 6 = 30 and 5 × 7 = 35). Students may explore using counters to rule out additional numbers as factors (e.g., if you make 6 rows with a total of 32 counters, there will not be an even number in each row). The teacher asks students if 32 is prime, composite, or neither (composite). This is repeated with additional whole numbers from 0- 144.

### Instructional Tasks

*Instructional Task 1* (MTR.3.1)

### Instructional Items

*Instructional Item 1*

- a. 42 is a factor of 84.
- b. 84 is a composite number.
- c. 84 has exactly 4 distinct factor pairs.
- d. The prime factors of 84 are 2, 6 and 7.
- e. 84 can be written as the product 2 × 2 × 3 × 7.

**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 Games

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Task

## Tutorial

## MFAS Formative Assessments

Students are asked to find all the factor pairs of a given number and identify the number as a multiple of the factors.

Students are asked to find all the factor pairs for each of four given numbers.

Students are asked to determine whether each of four given numbers is prime or composite and justify their choices.

## Original Student Tutorials Mathematics - Grades K-5

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem in this interactive tutorial.

## Student Resources

## Original Student Tutorial

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem in this interactive tutorial.

Type: Original Student Tutorial

## Educational Games

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.

Type: Educational Game

This fun and engaging game will test your knowledge of whole numbers as prime or composite. As you shoot the asteroids with a particular factor, the asteroids will break down by that chosen factor. Keep shooting the correct factors to totally eliminate the asteroids. But be careful, shooting the wrong factor has consequences!

Type: Educational Game

## 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

## Tutorial

This Khan Academy tutorial video reviews how to determine if a number is prime or composite.

Type: Tutorial

## 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