Patterns and Rules of Divisibility
October time to think about sailing ships and jack-o-lanterns. And it’s also time to be thinking about helping students to master their basic facts. This month’s little teaching tip involves the patterns of divisibility (or multiples). Students enjoy finding patterns, and become quite proficient once they begin to open their minds to mathematics making sense!
Begin with a hundreds chart. I’ve provided a copy for you with this newsletter. Have students draw a ring around all of the multiples of 2, and then ask, “How do you know when a number is a multiple of 2?” Depending on the age of the students (beginning of the year 3rd graders up, or end of the year 2nd graders), you might get answer such as, “They are even numbers.” “The numbers end in - 2, 4, 6, or 8.” “It’s every other number.” (Accept this, but ask the students to explain their thinking. Ask if 3,5,7,9 are even because they too show every other number.)
Once you have exhausted their patterns, have them do the same for 3s. Some sample answers are: “They go odd, even, odd, even, odd.” Ask: “Can you tell that a number is a multiple of 3 if that is the only pattern it follows?” Can you give me an example where numbers continue in a sequence odd, even, odd, even, and are NOT all multiples of 3? (5, 6, 7, 8… for one). Then there must be a different type of pattern.” Have students work together to find the pattern (the sum of the digits is a multiple of 3:3, 6, 9, 12 (1 + 2 = 3), 15 (1 + 5 = 6) and so forth.
Continue for 4, 5, 6, 9, and 10. Here are the rules.
- 4 No matter how large the number, the last 2 digits for a number that is a multiple of 4. This may not become evident until you give students larger numbers. A calculator is an excellent tool for finding this pattern. 12,467,812 IS a multiple of 4 because 12 is a multiple of 4
- 5 All multiples end in 5 or 0.
- 6 If students are using the hundreds chart, it will be very evident that the multiples of 6 are also multiple of 2 and of 3.
- 10 All multiples of 10 end in 10.
- 9 For this table, you will want to write the multiplication facts as I demonstrate on the blackline master. There are SO MANY patterns of 9s. Once you’ve found a few, you might like to send this one for homework and have other family members see what they can find.
Knowing the patterns of divisibility can help students master their multiplication facts. Once they know these patterns, it’s time to practice, practice, practice. L&M Instructional Resources, Inc. has a great little program, FASTFacts that will help your students master even the most unfriendly fact. Check out the special offer for a fundraiser for your school. Not only will you be helping students learn their multiplication facts, you’ll also be helping your school in these tough-budget times!
SEE YOU NEXT MONTH!
Ms Fritzie!
