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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 c. Identify multiples

  • Use the first 5 multiples of any single digit whole number

Clarification

Number theory is the study of the properties of numbers and the relationship between the numbers. A number is divisible by another number if when the first number (the dividend) is divided by the second number (the divisor), there is no remainder. The first number is divisible by second number then the first number is a multiple of the second number. Also, the second number is said to be a factor of the first number. Multiples are the products of a whole number greater than 0 and any other whole number. Products are the result of multiplication. For example, 8 is a multiple of 4, because 4 × 2 = 8.  24 is also a multiple of 4 because 4 × 6 = 24.

To find the first five multiples of a number:

  • Every number is a multiple of itself because the identity property of multiplication says any number times 1 is equal to the number. n × 1 = n. So the first multiple of any number is the number itself.
  • Multiply the number by 2. This product is the next multiple.
  • Multiply the number by 3. This product is the next multiple.
  • Continue until you have multiplied the number by 1, 2, 3, 4, and 5. These products will be the first five multiples of 5.

Example:
Find the first five multiples of 5.

5 × 1 = 5, so 5 is the first multiple
5 × 2 = 10, so 10 is the second multiple
5 × 3 = 15, so 15 is the third multiple
5 × 4 = 20, so 20 is the fourth multiple
5 × 5 = 25, so 25 is the fifth multiple

5, 10, 15, 20, and 25 are the first five multiples of 5.

Classroom Example 1

List the first five multiples of 4.

  1. 0, 1, 2, 4
  2. 1, 4, 8, 12, 16, 20
  3. 4, 6, 8, 10, 12
  4. 4, 8, 12, 16, 20

Answer:
D is the correct answer, because 4 × 1 = 4, 4 × 2 = 8, 4 × 3 = 12, 4 × 4 = 16, 4 × 5 = 20.

Classroom Example 2

Which number is the smallest multiple of 4 and 6?

Answer:
A list of the first four multiples of 4 are: 4, 8, 12, and 16
A list of the first four multiples of 6 are: 6, 12, 18, and 24
The smallest multiple they share is 12.
This is called the 'least common multiple.

Classroom Example 3

Martha needed to buy cups for a party. 35 people will be at the party. The cups come in packs of 8. How many packs should she buy?

Correct Answer:
The first six multiples of 8 are: 8, 16, 24, 32, 40, 48
So that everyone has a cup, she should buy 5 packs, since 40 is the 5th multiple of 8.

/toolkit/vsc/clarification/mathematics/grade4/6B1c.xml
Resources for Objective 6.B.1.c:
CLARIFICATIONS | Sample Assessments |