9-Mulitples using Make10 (we continue to wastes MM of hours of student time - plz read)

There is a way to make learning the multiplication table at least 10 percent easier, and I hope that Khan Academy will help share it. This simple, easy-to-implement change to elementary math will save students millions of hours a year - year after year.  It will take you less than one minute to try it.

Learning the math facts is difficult.  Many students decide math is not for them by third grade and learning the multiplication table is one of the reasons.  

The consistent change of the 9-multiples is a gift we should not ignore.  Taking the 9s off the memorization list will make digits 2 - 8 easier to learn because there will be more time between these remaining digits and less interference between digits.

As Graham Fletchy writes, almost every student in the class on this exercise was familiar with the 9-hands calculation: https://gfletchy.com/2015/02/05/take-a-math-trick-and-make-it-bleed/.  Millions of students currently calculate the 9-multiples with their hands when they could have been practicing Make10 and Count Back.  These are skills we want students to practice - not using their fingers to do math.  

This is the fastest method to calculate the 9s (diagram in next email).  It is a ‘trick’ in that it tricks students into practicing Count Back and Make10.

To calculate the 9s, simply Make10 out of the multiplier, but just before you do, name the number that comes before it.  For 9 x 4, the number that comes before 4 is 3 (for 30) and you Make10 out of the 4 with a 6:  36

K/1st graders have memorized the count back order so the first step is not even a calculation.  The second step (Make10) is an almost instant calculation.  This method is fast enough to replace memorization!

About 4 million students (just in the US) need to memorize the multiplication table each year - averaging about 20 hours per student - so at least 2 hours wasted on the 9s (looking up, using their fingers, then finally memorizing).  

Some might suggest the Make10 method to calculate the 9-multiples will result in students not understanding multiplicative skills like scaling.  Please have them address how students do it already with the multiples of 1 and 10.  Students learn the 10 multiples by K/1st grade with zero knowledge of multiplication.  They learn the 1-multiples when they learn the Identity Property.  They do not learn these multiples through multiplicative reasoning.  They use the multiplicative skills they learned from the other digits - which were learned by repetition, building answers, etc….and apply them to 1 and 10.  Now they can do it with the 9s.   All three digits leverage the knowledge gained from learning digits 2 - 8.  

When to teach?  The 9s can be taught as soon as students are proficient at Count Back from 10 and Make10…and every student is adept at both by the end of first grade or already behind in subtraction skills and mental math skills.  K and first-grade teachers do dozens of Make10 exercises.  Add this as a Make10 exercise and improve their mental math skills while they learn to calculate the 9-multiples.  It takes less than a minute to learn to pair this two-step.  The most common mistake is to move to the count-back result rather than doing both steps on the original multiplier.  One number stays in the brain’s ‘register’ for both steps.  It’s one of the reasons the calculation is so fast.

Whether the teacher explains what the student accomplishes with Minus1/Make10 (M&M) is debatable.  If nothing is said, the student learned to calculate the 9-multiples and did another Make10 exercise.  Zero incremental time used.   When the student is introduced to multiplication, review the method again.  It should be almost second nature by the second go around.

I have shared this method with kindergartners and first graders when tutoring in a group setting. There are some negatives associated with sharing something with a student that they won’t fully understand, but I think it energized them. They were able to see how the results they calculated matched up to a multiplication table.  I wrote 9 + 9 + 9 + 9 (in a column, and updated it to match the number of 9s to the multiple)..and explained, that this is how many times you just added 9, instantly, in one step.  Other students gathered around.  They started quizzing one another.  Quizzing me the next day.  I think they felt empowered, and they were able to see one of their new tools (Make10) put to use.

In sum, we currently waste about 8 million hours of student time per year memorizing the 9s, and we leave students no choice but to use their fingers to calculate the 9-multiples until they learn them.  It takes about a minute to teach the Make10 method. Is there a simple change to elementary math with greater impact?