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MathBait™ Multiplication


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Understanding how numbers are built is a superpower and sure-fire way to build fluency quickly. In this activity, students explore the patterns within multiples using Napier's Bones.


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Primary Topic

Playing with Napier's Bones







This activity is recommended for younger students just learning multiplication or for older students to build number sense.

The goal of this activity is for students to examine their rods to find patterns. You may structure this activity more by directing students to examine certain areas, such as the diagonals or the ones place. It is fun to allow students to at least play detective on their own for 5-10 minutes before providing some guidance.

Here are some fun patterns to explore and discuss:

  • What do you notice about the ones place on all the even rods? (They all cycle between the even digits 2, 4, 6, 8, 0).

  • Can you find a rod that contains every digit in the ones place? (1, 3, 7, and 9 which are our odds, with 5 removed as multiples of 5 always end with a 0 or 5).

  • What is the pattern of the ones place on the 3, 7, and 9 rods? Will this continue if we extend the rods? (For 3's we have 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 and for 7's we have 7, 4, 1, 8, 5, 2, 9, 6, 3. The 9's are fun to look at as they follow the pattern 9, 8, 7, 6, 5, 4, 3, 2, 1 which can lead to a great discussion on how adding 9 is the same as adding 10 then subtracting 1. This means the multiples of 9 will always have a tens place that is 1 more and a ones place that is 1 less).

  • Examine the diagonals. What do you notice? (The diagonals also form fun patterns; the first diagonal is 0 followed by 010, 02020, 0304030, 040606040, 05181918150, and so on. The symmetry is the same symmetry we know from the table as a result of the commutative property.)

  • Add the digits of each multiple. What do you notice? (In this case, multiples of 3 and 9 always sum to their multiple. We do not recommend going deeply into this unless your students are mathematically advanced enough to understand why this happens. If so, you may wish to explore our video on Instagram or Facebook explaining this useful result).

Teachers may determine how deep to explore each pattern. We want students to see that numbers have a clear structure. The better we understand this structure, the easier it will be to multiply (as well as other more advanced topics). We also want to encourage making sense of patterns and identifying patterns we notice.

The material on this page is copyrighted by MathBait™. Please use and enjoy it! MathBait™ provides a temporary license for Non-Commercial purposes. You are not permitted to copy, distribute, sell, or make derivative work without written permission from MathBait™. 

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