VIRTUAL Arithmetickles Presents:

Mental Math 

This episode brings us a new challenge –
Here is an analog clock with the numbers 1 through 12 on it.

Using 2 pencils, try to divide the clock into 3 parts so that the numbers add up to equal sums in each part.

In your class, students can try to find the solution by trial and error, however, with a simple clue they will be able to solve the problem with addition and division.


The Solution


After trying to set the pencils randomly on the clock, give your students the clue: first, add all of the hours on the clock together.


Then, when you divide it by 3, you’ll get the sum of each part (26) and that will determine where you’ll place the pencils!


Since 12 is the biggest number,
let’s start with 12.

12+1+2+3+4=22;    22+5=27
which is more than 26



Going back to 12:  let’s add 12+11=23;
23+10=33…that’s way too much!


So let’s try 11+12+1+2=26!! 

Now we know that one pencil must be placed between 10 and 11 and also 2 and 3.


Adding 10+9=19, so it’s clear that 8 will be too much, so instead you add 10+9+3+4=26! Now we know that the second pencil must be placed between 9 and 8 and also 4 and 5.

Finally, check it out: 5+6+7+8= 26!  
 This is the only way to split the clock into 3 equal parts!!


Addition, division and logical thinking


The Clock segment can be viewed by all ages, however, the math level is for grades 3-6.




We would love to hear from you. Your thoughts will help us develop and produce future videos. Please let us know how it worked in class, your students’ reactions, and the level of difficulty.


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