The worksheet "Learning Divisibility Rules With Large Numbers" helps students figure out if large numbers are divisible by single digits with activities that show students the rules they can follow for different digits.

Each page starts by asking a question like "How do you know if a number is divisible by 6?" Then, three sets of activities help students practice a rule to find out how they can tell. In this case, the following activities would ask, "Is the number 454,506 even? If no, it is not a multiple of 6." Different rules and questions are listed according to different numbers. Different worksheets address the rules that go with the divisors 3, 4, 6, and 9.

Additional activities help students practice each rule. For example, students add up all the digits in a large number to get an answer. Then, they add those digits. Based on their final answer, they circle whether it's a multiple of 3 to find out if the bigger number is also a multiple of three. Activities are repeated with different numbers to give students plenty of practice learning each rule.

Learning about multiples can be a handy way for students to expand their thinking about division and tackle more complex math problems, like factoring and simplifying large fractions.

Learning rules can be a fun way for students to make sense of large numbers, and it can help them build confidence. For example, you can teach students to look at the last two digits in a large number. If they are divisible by 4, then the entire number is divisible by 4. You can give them numbers and ask them if they are divisible by 4, or ask them to write a list of 6-digit numbers that are divisible by 4.

Having students complete long division problems and talking about what they notice can help them discover rules on their own. The number 2 can be a good place to start, as students can pick up on the fact that no matter how large the number, if the ones digit is divisible by 2, then the entire number is divisible by 2. They could see if the same rule holds for other numbers, or if other numbers need their own rules.