Using the State Curriculum: Mathematics, Grade 4

Multiplication charts

Although the assessment limit for this objective indicates that students should identify and use divisibility rules for 2, 5, and 10, all or parts of this lesson seed can be used to develop additional divisibility rules, such as 3, 6, 9 and 4. The rules should be generalized by the student as they look for patterns in the products. Ample wait time should be given so that all students have an opportunity to make these generalizations. Divisibility rules can be easily developed by students using a multiplication chart

Divisibility Rule for 2

To develop a divisibility rule for 2 as a factor, on the multiplication chart:

• Find 1 × 2 and shade the product (by moving either vertically, horizontally, or both).
• Then calculate 2 × 2 and shade the product.
• Continue with whole numbers 1-10. Look for a pattern. What do you notice? [All the shaded numbers have a 0, 2, 4, 6 or a 8 in the ones place.]

What generalization could you make? [A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.]

Divisibility Rule for 5

To develop a divisibility rule for 5 as a factor, on the multiplication chart:

• Find 1 × 5 and shade the product (by moving either vertically, horizontally, or both).
• Then calculate 2 × 5 and shade the product.
• Continue with whole numbers 1-10. Look for a pattern. What do you notice? [All the products end in either 0 or 5.]

What generalization could you make? [A number is divisible by 5 if it ends in 0 or 5.]

Divisibility Rule for 10

To develop a divisibility rule for 10 as a factor, on the multiplication chart:

• Find 1 × 10 and shade the product (by moving either vertically, horizontally, or both).
• Then calculate 2 × 10 and shade the product.
• Continue with whole numbers 1-10. Look for a pattern. What do you notice? [All the shaded numbers have a 0 in the ones place.]

What generalization could you make? [A number is divisible by 10 if it ends in 0.]

Divisibility Rule for 3

To develop a divisibility rule for 3 as a factor, on the multiplication chart:

• Find 1 × 3 and shade the product (by moving either vertically, horizontally, or both).
• Then calculate 2 × 3 and shade the product.
• Continue with whole numbers 1-10. Add the digits of each product. What do you notice? [They can all be divided by 3 evenly.]

What generalization could you make? [A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
For example, 231 is divisible by 3 because 2 + 3 + 1 is 6 and 6 is divisible by 3.]

Divisibility Rule for 6

To develop a divisibility rule for 6 as a factor, on the multiplication chart, shade numbers divisible by 2 in red and then shade numbers divisible by 3 in blue.

What do you notice about the numbers shaded by both colors? [Those numbers are divisible by both 2 and 3. Therefore they are also divisible by 6.]

In general, a number is divisible by 6 if it is divisible by both 2 and 3.

Divisibility Rule for 9

To develop a divisibility rule for 9 as a factor, on the multiplication chart:

• Find 1 × 9 and shade the product (by moving either vertically, horizontally, or both).
• Then calculate 2 × 9 and shade the product.
• Continue with whole numbers 1-10. Add the digits of each product. What do you notice? [They can all be divided by 9 evenly.]

In general, a number is divisible by 9 if the sum of the digits of the number is divisible by 9.
For example, 342 is divisible by 9 because 3 + 4 + 2 is 9 and 9 is divisible by 9.

Divisibility Rule for 4

Below is a list of numbers divisible by 4.

1,236     144     728     23,508     5,724     1,234,512

Look at only the last two digits of the numbers.

1,236     144     728     23,508     5,724     1,234,512

What do you notice? Do you see a pattern? The number formed by the last two digits is divisible by 4.

In general, a number is divisible by 4, if the last two digits of the number form a number divisible by 4.