Divisibility Rules

Common Core Strand: 6.EE.1 Student Friendly: Students will be able to use the divisibility rules for 2, 3, 4, 5, 6, 9, and 10 to determine whether numbers with up to eight digits are prime or composite with 80% accuracy. Essential Question: What are divisibility rules and how can I use them to solve math problems?

Vocabulary:  Divisible – a whole number is said to be divisible by another number if the remainder is zero when the first number is divided by the second.  Even – a whole number that is divisible by 2.  Odd – a whole number that is not divisible by 2.  Prime Number – a whole number that has exactly two unique factors, 1 and the number itself.  Composite Number – a number greater than 1 with more than two factors. Divisibility Rules

Why would we need to know the divisibility rules? We should understand the divisibility rules because they can help simplify more complex mathematical computations. Case & Point: Student Work Groups Teams Divisibility Rules

What is I wanted to break the class down into groups for an assignment? Groups of 2, 3, 4, 5, 6, 9 or 10? Divisibility Rules

Real World Example County Fair Problem Example 1: The number of tickets needed to ride certain rides at the county fair is shown. If Jacquez has 51 tickets, can he use all of the tickets by riding only the bumper cars? Divisibility Rules Ferris Wheel2 Roller Coaster5 Scrambler4 Bumper Cars3

Real World Example County Fair Problem Example 1: The number of tickets needed to ride certain rides at the county fair is shown. If Jacquez has 51 tickets, can he use all of the tickets by riding only the bumper cars? We could divide the total number of tickets (51) by the number of tickers it takes to ride the bumper cars (3). But might there be an easier way? Divisibility Rules Ferris Wheel2 Roller Coaster5 Scrambler4 Bumper Cars3

Real World Example County Fair Problem Example: The number of tickets needed to ride certain rides at the county fair is shown. If Jacquez has 51 tickets, can he use all of the tickets by riding only the bumper cars? YES…We could use the divisibility rules. 51 → = 6 and 6 is divisible by 3. SO WE KNOW 51 is divisible by 3. Divisibility Rules Ferris Wheel2 Roller Coaster5 Scrambler4 Bumper Cars3

The Divisibility Rules A whole number is divisible by: RuleExamples 2 if the ones digit is even.2, 4, 6, 8, 10, 12, …2 if the ones digit is even.2, 4, 6, 8, 10, 12, … 3 if the sum of the digits is3 if the sum of the digits is divisible by 3.3, 6, 9, 12, 15, … 5 if the ones digit is a 0 or 5.5, 10, 15, 20, 25, …5 if the ones digit is a 0 or 5.5, 10, 15, 20, 25, … 10 if the ones digit is a 0.10, 20, 30, 40, …10 if the ones digit is a 0.10, 20, 30, 40, … Divisibility Rules

Using the Divisibility Rules Example 1: Is 2,320 divisible by 2, 3, 5, or 10? Divisibility Rules

Using the Divisibility Rules Example 1: Is 2,320 divisible by 2, 3, 5, or 10? 2: Yes, because the digit in the ones place is even. 3: No, because the sum of the digits is 7, which is not divisible by 3. 5: Yes, because the ones digit is 0. 10: Yes, because the ones digit is 0. Divisibility Rules

Using the Divisibility Rules Example 2: A bakery requires 3 pounds of sugar for a large batch of cookies. If they have 38 pounds of sugar left, can they use all the sugar for large batches of cookies? Divisibility Rules

Using the Divisibility Rules Example 2: A bakery requires 3 pounds of sugar for a large batch of cookies. If they have 38 pounds of sugar left, can they use all the sugar for large batches of cookies? No, the bakery cannot use all of the sugar for large batches of cookies because 38 is not divisible by 3. (3 + 8 = 11 and 11 is not divisible by 3) Divisibility Rules

We also have Divisibility Rules for 4, 6, and 9 which are related to the rules for 2, 3, 5, and 10. Divisibility Rules

The Divisibility Rules A whole number is divisible by: RuleExamples 4 if the number formed by the4 if the number formed by the last two digits is divisible by 4.4, 8, 12,…, 104, … 6 if the number is divisible by6 if the number is divisible by both 2 and 3.6, 12, 18, 24, 30, … 9 if the sum of the digits is9 if the sum of the digits is divisible by 9.9, 18, 27, 36, 45, … Divisibility Rules

Using the Divisibility Rules Example 2: Is 684 divisible by 4, 6, or 9? Divisibility Rules

Using the Divisibility Rules Example 2: Is 684 divisible by 4, 6, or 9? 4: Yes, because the number formed by the last numbers is 84, is divisible by 4. 6: Yes, because 684 is divisible by both 2 (ones digit is even) and 3 (sum of digits divisible by 3). 9: Yes, because the sum of the digits is 18, which is divisible by 9. Divisibility Rules

Using the Divisibility Rules Example 4: Hannah is helping her mother put eggs into egg cartons to sell at the local farmer’s market. Their chickens have produced a total of 108 eggs for market. Can Anthony package the eggs into groups 6 so that each carton has the same number of eggs? Divisibility Rules

Using the Divisibility Rules Example 4: Hannah is helping her mother put eggs into egg cartons to sell at the local farmer’s market. Their chickens have produced a total of 108 eggs for market. Can Anthony package the eggs into groups 6 so that each carton has the same number of eggs? NO, because 108 is not divisible by 6. Divisibility Rules

Independent Practice: Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. 1) 72 2) 3,225 3) 480 4) 126 Divisibility Rules

Independent Practice: Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10. 1) 72 → 2, 3, 4, 6, and 9 2) 3,225 → 3 and 5 3) 480 → 2, 3, 4, 5, 6, and 10 4) 123 → 3 Divisibility Rules

Using the Divisibility Rules Extension Problem Tristan has 2 dozen roses. He wants to plant the flowers in rows so that each row has the same number of flowers. Can he plant the flowers in 3 equal rows? Explain. Divisibility Rules

Using the Divisibility Rules Extension Problem Tristan has 2 dozen roses. He wants to plant the flowers in rows so that each row has the same number of flowers. Can he plant the flowers in 3 equal rows? Explain. Yes, he can plant them in rows of 3 because he has a total of 24 roses (24 is divisible by 3). Divisibility Rules

The Divisibility Rules A whole number is divisible by: 2 if the ones digit is even2 if the ones digit is even 3 if the sum of the digits is divisible by 3.3 if the sum of the digits is divisible by 3. 4 if number formed by the last two digits is divisible by 4.4 if number formed by the last two digits is divisible by 4. 5 if the ones digit is a 0 or 5.5 if the ones digit is a 0 or 5. 6 if the number is divisible by both 2 and 3.6 if the number is divisible by both 2 and 3. 9 if the sum of the digits is divisible by 9.9 if the sum of the digits is divisible by if the ones digit is a 0.10 if the ones digit is a 0. Divisibility Rules

Homework p.154 #9-16, 29-32, all Divisibility Rules