## Dynamic Divisibility

### Tina Davis

#### Description

Students learn the rules of divisibility for the numbers 2,3,5,6,9 and 10. Students use these rules to check large numbers for their divisibility.

#### Objectives

The student uses divisibility rules.

#### Materials

-Transparency of Divisibility Rules (See Associated File)
-Divisibility Practice worksheet (See Associated File)

#### Preparations

1. Make transparency of the Divisibility Rules. (See Associated File)
2. Make copies of the Divisibility Practice worksheet for the students. (See Associated File)
3. Check the overhead projector for usability.

#### Procedures

1. Pretend to be a mind reader from the Jay Leno show. Ask a student to give you a two-digit number, and you tell the students (without working on it), the number(s) that it is divisible by. Ask the students to check your answers to see if you are correct. Try again with another number. Tell the students it is “magic,” the “magic” of divisibility, that enables you do such wonderful things without actually doing long division.

2. Explain the topic for the day - divisibility: the ability to determine what numbers a larger number is divisible by.

3. Review quickly the concepts of divide and divisibility. Let the students know that with divisibility rules, long division isn't required.

4. Display the Divisibility Rules transparency for the numbers 2,3,5,6,9 and 10. (See Associated File) Read the steps out loud, stopping at each one to ensure the rule is understood.

5. Using an overhead marker, write a larger two- or three-digit number on the overhead. Model the procedure for using the rules to check the number for its divisibility. Do several examples with the students, continuing with larger and larger numbers until students seem comfortable.

6. Ask students to discuss with a partner why this skill is useful. Discuss with the class as a whole.

7. Have students complete the Divisibility Practice worksheet. (See Associated File) Students check large divisors to see if they are divisible by 2,3,5,6,9 or 10. They list the numbers as the answer.

#### Assessments

Students use the divisibility rules to check larger numbers for divisibility by 2,3,5,6,9 or 10. Students correctly list all the divisible numbers for each problem on the Divisibility Practice worksheet. (See Associated File)

Students should correctly list the numbers in 7 out of 10 problems from the Divisibility Practice worksheet. Those students who have difficulty should receive feedback, more modeling and additional practice.

#### Extensions

1. For students with modality issues, list the numbers 2,3,5,6,9 and 10 underneath each problem on the Divisibility Practice worksheet. (See Associated File) Students circle the numbers that the larger ones are divisible by.
2. For students with short-term memory deficits, have a hard copy of the rules for the students to use.
3. Extension Lesson. Supplies needed: blank drawing paper, coloring supplies, rulers for making straight edges, notebook paper.
Task: Create a calendar for an imaginary place that has 450 days in a year (make the number larger or smaller depending on students' skill levels). The students determine how many months are in the year, and how many days are in each month.
Criteria: Each month must have an equal number of days. (Divisibility rules can be applied here to determine what numbers can be divided evenly.) The calendar should be neatly drawn, and months and days labeled.
Written Explanation: Each calendar must be accompanied by a written explanation of how the months/days were determined for the calendar year. Thoughts and descriptions about the creation of the names for the months and days should also be included.
Assessment: See associated file for rubric to score the calendar.