Is it IMPOSSIBLE?

​What’s new with SUM OF WHICH?  Well, did you know that now there are a total of FIVE games you can now play with the materials that come with SUM OF WHICH?  SUM OF WHICH is a slower paced, thoughtful kind of game.  You take time to strategize and plan, then you place your tiles.  The other four games; SO YOU THINK YOU CAN ADD, IT’s IMPOSSIBLE, ODDS OR EVENS, and MAKE IT COUNT, are all very fast paced fluency games.  These games get your blood flowing and your hands flying.  Did you know that when you buy SUM OF WHICH you have everything you need to play all these games?  You don’t have the directions to the other 4 games?  Check out the tab called “LEARN” at sumofwhich.com.  You can download the directions to all the games and any others that I come up with in the future.  There is even a video teaching SO YOU THINK YOU CAN ADD and SUM OF WHICH.

I just returned from Buffalo NY where I was able to share SUM OF WHICH and the other games with hundreds of educators. 

​Later this week I will head to Massena NY where more than 300 special educators will have a chance to play the game.

I ​ have to say, the most rewarding part of this venture is the opportunity to help so many students.  So, this month I share the following:  Try this with your students. 

You are going to show students 5 numbers.  Then have them identify the smallest sum (the sum of the 2 smallest numbers) and the largest sum (the sum of all 5 numbers)  Next, have them write all the numbers in between those two numbers.  For Example:  If I have a set of numbers with my smallest sum of 3 and my largest sum of 10, the numbers in between would be 4, 5, 6, 7, 8,and 9. 
​
Finally, the students race to find if they can make those numbers using addition of at least two addends using only the numbers given.  If they cannot make a number, then “IT’s IMPOSSIBLE”.  I am giving you several examples below to use in your classroom.  The sample answers are also given.  Be aware that some sums can be made in more than one way.  I have given you just one of the possible sums for each.

If you have students still practicing addition to 10: 
Show them the following numbers 1    3    2    2    2  

SAMPLE ANSWERS:  Smallest sum is 3, largest is 10. 
4= 3 + 1,     5 = 3 + 2,     6 = 3 + 2 + 1,    7 = 3 + 2 + 2,     8 = 3 + 2 + 2 + 1,      9 = 3 + 2 + 2 + 2. 
They are all possible.

If you have students practicing addition to 20: 
Show them the following numbers 2    3    5    8    2  

SAMPLE ANSWERS:  Smallest sum is 5, largest is 20. 
6 = IMPOSSIBLE,    7 = 3 + 2 + 2,     8 = 3 + 5,     9 = 5 + 2 + 2,    10 = 8 + 2,     11 = 8 + 3,     
12 = 5 + 3+ 2 + 2,         13 = 8 + 5,     14 = IMPOSSIBLE,      15 = 8 + 2 + 5,      16 = 8 + 5 + 3,
17 = 8 + 2 + 5 + 2,      18 = 2 + 3 + 5 + 8,       19 = IMPOSSIBLE

If you have students practicing addition to 100:  Show them the following numbers 10    25    30    20    15   (This time they are looking for all the multiples of 5 between 25 and 100)

SAMPLE ANSWERS:  Smallest sum is 25, largest is 100. 
30 = 20 + 10,     35 = 25 + 10,      40 = 30 + 10,     45 = 25 + 20,     50 = 30 + 20,     55 = 30 + 25,
60 = 25 + 15 + 20,     65 = 30 + 25 + 10,     70 = 25 + 15 + 30,     75 = 30 + 20 + 25,     
80 = 10 + 25 + 30 + 15,      85 = 10 + 25 + 30 + 20,      90 = 25 + 30 + 20 + 15,      95 = IMPOSSIBLE

If you have students practicing addition of fractions to 1: 
Show them the following numbers 1/8, 2/16, 1/4, 3/8, 3/16  
(This time they are looking for all units of 16ths between 3/16 and 1)

SAMPLE ANSWERS:  Smallest sum is 5/16, largest is 1. 
4/16 = 2/16 + 1/8,   5/16 = 3/16 + 2/16,   6/16 = 1/4 + 1/8,   7/16 = 1/4 + 3/16,  
8/16 = 1/8 + 2/16 + 1/4,   9/16 = 1/4 + 3/16 + 1/8,    10/16 = 1/4 + 3/8, 
11/16 = 1/8 + 2/16 + 1/4 + 3/16,   12/16 = 1/4 + 3/8 + 1/8,   13/16 = 1/4 +3/8 + 3/16,
14/16 = 1/8 + 2/16 + 1/4  + 3/8,     15/16 = IMPOSSIBLE

If you have students practicing addition of integers: 
Show them the following numbers. -3    5    -2    6    3  

SAMPLE ANSWERS:  Smallest sum is -5, largest is 14. 
-5 =  -3 + -2,    -4 = IMPOSSIBLE,    -3 = IMPOSSIBLE ,    -2 = -3 + -2 + 3   , -1 = IMPOSSIBLE,
0 =3 + -3,    1 = 3 + -2,    2 = 5 + -3,    3 = 5 + -2,     4 = 6 + -2,    5 =   , 6 = 6 + 5 + -2 + -3,
7 = 6 + 3 + -2,   8 = 5 + 6 + -3,    9 = 6 + 3,    10 = IMPOSSIBLE,   11 = 5 + 6,    12 = 5 + 6 + 3 + -2,
13 =  IMPOSSIBLE,    14 = 5 + 6 + 3
 
You can play IT's IMPOSSIBLE as a race.  The first player to finish must recite the answers to the class.  If they have it perfect, then they have “Done the Impossible”.  If they err on one, then have the person who finished second take over. 

Please try one of these in your class and let me know how it went.  I would love to hear from you. 
​ 
Keep in mind that IT’s IMPOSSIBLE is a game you could play with the materials you get when you purchase SUM OF WHICH.  The full directions for the game are under the “Learn” tab.