Standard: 4.OA.B4 – Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
Grade level: Grade 4
Subject: Mathematics
Domain: Operations & Algebraic Thinking
Teacher Overview
This standard focuses on helping students understand the concepts of factors, multiples, and prime numbers. Mastery of this standard is crucial as it lays the groundwork for more advanced mathematical concepts such as fractions, greatest common factors, and least common multiples. Students should be comfortable with basic multiplication and division, and have a good grasp of even and odd numbers. This foundational knowledge is necessary for students to successfully identify factors and multiples.
Mastering this standard will prepare students for more complex mathematical concepts, such as finding the greatest common factor and least common multiple, and understanding fractions.
Common Misconception 1
Some students may believe that a number can only have one factor pair, which is incorrect. For example, the number 12 has multiple factor pairs: (1, 12), (2, 6), and (3, 4).
Intervention 1
To address this misconception, use visual aids such as factor trees and arrays. These tools can help students see that numbers can have multiple factor pairs.
Common Misconception 2
Another common misconception is that students may confuse prime numbers with odd numbers. While all prime numbers except 2 are odd, not all odd numbers are prime.
Intervention 2
Provide clear definitions and examples of prime and composite numbers. Use sorting activities to help students distinguish between the two.
Prerequisite Knowledge
Students should have a basic understanding of multiplication and division, including the ability to multiply and divide within 100. They should also be familiar with the concepts of even and odd numbers.
Subsequent Knowledge
After mastering this standard, students will be able to apply their understanding of factors and multiples to more complex problems, including finding the greatest common factor (GCF) and least common multiple (LCM) of two numbers. They will also be better prepared to understand and work with fractions.
Instructional Activities
- Create factor trees for numbers between 1 and 100
- Use arrays to visualize factor pairs
- Sort a list of numbers into prime and composite categories
- Solve real-world problems involving factors and multiples
