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Using the State Curriculum: Mathematics, Grade 4

Algebra | Geometry | Measurement | Statistics | Probability | Number | Processes
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic

Topic B. Number Theory

Indicator 1. Apply number relationships

Objective a. Identify and use divisibility rules

  • Use the rules for 2, 5, or 10 with whole numbers (0 – 1000)

Clarification

Number theory is the study of the properties of numbers and the relationship between the numbers. A number (the dividend) is divisible by another number (the divisor), if when the first number is divided by the second number, the answer (the quotient) has no remainder. In this case, the second number is said to be a factor of the first number. Also, the first number is a multiple of the second number. Divisibility rules are generalizations that state which numbers are divisible by a given factor.

For example, 24 is divisible by 4, because 4 divides 24 evenly with no remainder. 4 is a factor of 24 and 24 is a multiple of 4. The following table shows the most commonly used divisibility rules.

Factor Divisibility Rule
2 A number is divisible by 2, if the last digit of the number is even (ends in 0, 2, 4, 6, 8).
5 A number is divisible by 5, if the last digit of the number is 0 or 5.
10 A number is divisible by 10, if the last digit of the number is 0.
3 A number is divisible by 3, if the sum of the digits of the number is divisible by 3.
6 A number is divisible by 6, if the number is divisible by both 2 and 3.
9 A number is divisible by 9, if the sum of the digits of the number is divisible by 9.
4 A number is divisible by 4, if the number formed by the last two digits of the number is divisible by 4.

How can knowing your divisibility rules help you? They can help you determine the factors of numbers and they can help you decide whether numbers can be put into equal groups.

Classroom Example 1

The fourth grade from Public School #9 is going on a field trip. There are 261 students in the fourth grade. Can an equal number of students be put on 5 buses? 9 buses?

Answer: The students will not be evenly distributed on 5 buses because 261 is not divisible by 5. The divisibility rule for 5 says that only whole numbers ending with a 0 or a 5 are divisible by 5. However, an equal number of students can be put on 9 buses because 261 is divisible by 9. 2 + 6 + 1 is 9. The sum of the digits is 9 and 9 is divisible by 9.

Classroom Example 2

If you have 50 prizes and you want to share them equally with friends. How many friends can you share with?

  1. 2 friends
  2. 5 friends
  3. 10 friends
  4. all the above

Answer: All of the above.  50 is divisible by 2, 5, and 10.  50 is divisible by 2 because 50 ends in 0, 2, 4, 6, or 8.  50 is divisible by 5 because 50 ends in a 0 or 5.  Numbers divisible by 10 end in 0.  50 ends in 0, thus it is divisible by 10. So 50 prizes can be equally shared with 2, 5 or 10 friends.

Can the 50 prizes be shared by 3 friends? No.  50 is not divisible by 3.  5 + 0 is 5 and 5 is not divisible by 3.

Classroom Example 3

Parker baked 4 dozen cupcakes. He has 10 boxes. Will he be able to evenly distribute the cakes among 10 boxes? 6 boxes?

Answer: No, Parker will not be able to evenly distribute the cakes amongst 10 boxes because 4 dozen (48) is not divisible by 10. Parker can distribute the cupcakes among 6 boxes because 48 is divisible by 6.

Classroom Example 4

Of the numbers 2, 5, 10, 3, 6, 9, and 4, which are factors of 324?

5 and 10 are not factors because 324 does not end in 5 or 10.
All the rest are factors.

  • 324 ends in 0, 2, 4, 6, or 8. 324 is divisible by 2. 2 is a factor of 324.
  • The sum of the digits of 324 is 3 + 2 + 4 which is 9.  9 is divisible by 3, so 324 is divisible by 3.  3 is a factor 324.
  • Since 324 is divisible by 2 and divisible by 3, it is also divisible by 6.  Therefore 6 is a factor of 324.
  • The sum of the digits of 324 is 3 + 2 + 4 which is 9.  9 is divisible by 9, so 324 is divisible by 9.  9 is a factor of 324.
  • The number formed by the last two digits of 324 is 24.  24 is divisible by 4, so 324 is divisible by 4.  4 is a factor of 324.

Classroom Example 5

In the multiplication table;

  • Shade the numbers divisible by 2 in yellow.
  • Shade the numbers divisible by 5 in blue.
  • Which numbers are shaded twice (in green)? What is true about these numbers? [They end in 0; they are divisible by 10.]

    geometric image

  • Is there another way of stating a divisibility rule for 10? [A number is divisible by 10 if it is divisible by 5 and 2.]
/toolkit/vsc/clarification/mathematics/grade4/6B1a.xml
Resources for Objective 6.B.1.a:
CLARIFICATIONS | Lesson Seeds |