A Multiplication Based Logic Puzzle

Posts tagged ‘Multiplication Rhymes’

How Lucky Can 777 Be?

  • 777 is a composite number.
  • Prime factorization: 777 = 3 x 7 x 37
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 777 has exactly 8 factors.
  • Factors of 777: 1, 3, 7, 21, 37, 111, 259, 777
  • Factor pairs: 777 = 1 x 777, 3 x 259, 7 x 111, or 21 x 37
  • 777 has no square factors that allow its square root to be simplified. 77727.8747197.

777-factor-pairs

Some people think that 7 is a lucky number. If that is true, then 777 should be even luckier.

Some numbers are lucky enough to be included in Multiplication Rhymes.ppt – mathval, a fun power point that helps students learn 12 multiplication facts, including these three that use Lucky Numbers:

  • 3 & 7 are always lucky numbers; 3 x 3 = 9 lives of a cat.
  • 3 & 7 are always lucky numbers; 3 x 7 = 21 lucky age.
  • 3 & 7 are always lucky numbers; 7 x 7 = 49er Gold Miner.

In Number Theory Lucky Numbers are actually defined and can be generated using a sieve somewhat similar to the prime number generating Sieve of Eratosthenes. There is an infinite number of Lucky Numbers, and yes, 3, 7, 9, 21, 49, and 777 all make the list.

Oeis.org’s wiki, Lucky numbers, includes several lucky number lists including the first 33 composite Lucky Numbers thus defined because ALL of their factors are also Lucky Numbers. 777 was the 19th number on that particular list because ALL of its factors, 1, 3, 7, 21, 37, 111, 259, 777 are Lucky Numbers, too!

If that isn’t lucky enough, 777 is a repdigit in three different bases.

  • 3333 BASE 6; note that 3(6^3) + 3(6^2) + 3(6^1) + 3(6^0) = 777
  • 777 BASE 10; note that 7(100) + 7(10) + 7(1) = 777
  • LL BASE 36 (L is 21 base 10); note that 21(36) + 21(1) = 777

Did you notice that lucky numbers 3, 7, and 21 showed  up again? I liked that coincidence so much that I made this graphic:

777 Repdigit

777 is also the sum of three squares four different ways:

  • 26² + 10² + 1² = 777
  • 22² + 17² + 2² = 777
  • 20² + 19² + 4² = 777
  • 20² + 16² + 11² = 777

 

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194 and Are Multiplication Rhymes Able to Help Kids Learn the Multiplication Table?

194 is a composite number. Factor pairs: 194 = 1 x 194 or 2 x 97. Factors of 194: 1, 2, 97, 194. Prime factorization: 194 = 2 x 97.

Are multiplication rhymes able to help kids learn the multiplication table? The obvious answer is, of course, YES! Duh!

Little Pigs Multiplication Rhymes

However, sometimes this obvious answer may not be correct. I recently read a researched article on the effectiveness of certain teaching practices in helping first grade children learn mathematics. The points made in the article would likely apply to third and fourth grade students learning multiplication as well. The article states that alternative techniques (music, movement, m&m’s, other manipulatives, etc.) do reinforce concepts for students who already understand what is being taught, but students who struggle actually make no gains when unproven techniques are used. The researcher hypothesized that when students struggle learning mathematical concepts “alternative techniques tend to demand more, cognitively, from [these] students.” Demanding more cognitively can backfire: Requiring a student to memorize a rhyme and the math fact could put that student’s brain on overload with even less facts learned.

I have now modified my opinion of multiplication rhymes. If rhyme-and-rhythm is helpful, use it, if not, don’t. What is good for some of the class, may not be good for all of the class. If a student doesn’t make progress using the rhymes, it may be better to stick with more direct instruction to learn the math facts. Additionally, each rhyme should be examined individually and its own pros and cons considered.

Here are two of my FAVORITE sources of multiplication rhymes: American Academy’s MULTIPLICATION-RHYMES.pdf now requires registration to view, but it has rhymes printed in pretty colors and contains a few of my favorite multiplication rhymes. Kids would probably like looking at this pdf multiple times.

Multiplication Rhymes 1 is an entertaining You-tube video made by Mrs. Rice that children would probably enjoy watching over and over again, and it also has a few very memorable rhymes.

Mrs. Rice shares 4 x 4 = 16 rhyme.

Although these two sources are great, I think some of the rhymes are too similar:

  • From the pdf we have “8 and 4 were sad and blue, 8 x 4 = 32” while the video recites “6 and 7 are sad and blue, they make number 42.” If students learned either of those rhymes, they may have difficulty remembering the product or which two numbers were sad and blue several weeks later.
  • The video also gave two other rhymes that were too similar to each other: “9 and 8 what do they do? They go play (tag) with 72.” and  “9 and 9 are having fun. They play tag with 81.” “Tag” is in parentheses because it wasn’t on the note card that was shown, but it was spoken on the video. Again weeks later, groups or individuals may not remember which numbers were playing tag or what the product was when they were multiplied together.

I compiled my own List of Multiplication Rhymes which focus on the multiplication facts highlighted in the multiplication table below. I included some rhymes from the above pdf and the video and added some from the song Five Pennies Make a Nickel. All of those rhymes are in italics. The rhymes that I wrote myself are in regular print. If I modified an existing rhyme, the modifications are in regular print while the rest of the rhyme is in italics. I also ordered the rhymes in a way that should make finding the rhyme for any particular fact much easier. I hope there will be many rhymes on this list that you enjoy as well, and that they get used to help many students learn the very important multiplication facts highlighted in the table below.

Multiplication Rhymes Table

 Multiplication Rhymes

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