Many don’t realize it but Math really is fun. Math was made for exploration and toying with. The way numbers work with one another simply begs for games to be made out of math problems. There are several projects that may appear to be games but are in reality true learning tools.
1) MULTIPLICATION TABLE: You will need ¼ inch ruled graph paper, rulers, and pens or pencils. I used to make these for my kids all the time; they were invaluable and used so much that ultimately I laminated them and even made a couple for other students. To have the student make their own is where the value lies.
Have the student outline a square on their piece of graph paper, 25 grids wide by 25 grids long. Just on the outside of the borderlines have them place a number in each of the little squares, one through 25. Do this on both the left and right hand verticals and on the top and bottom horizontal borders. You should now have a square on the graph paper with numbers all the way around it, one through 25.
Now comes the fun part. Explain “intersection” to the student and show them what an intersection is on their sheet. Have them start on the left hand vertical, find the number one, and travel to the right with their pencil. At every intersection of row number one with a number from the top horizontal have the student enter the multiplication answer. Since the first number we are using is number one, the first row of answers will look exactly like the row of horizontal numbers on the outside of the grid border.
Move the student to number two on the left hand vertical. Have him or her do the same thing only this time they have to enter the answer to the multiplication problem; 2 times 1 is, 2 times 2 is, 2 times 3 is and so on. Their second row of numbers will be as though they were counting by twos; 2, 4, 6, 8 etc.
Go to number three on the left hand vertical and do the same thing. The row of answers will be as though they were counting by threes; 3, 6, 9, 12 etc. Continue doing the same thing all the way through number 25. It will indeed get more difficult; somewhere around number 7 I usually start to lose a few students. Definitely after number 12 it becomes very difficult; it actually requires them to do some math.
I have made tables as small as 12 by 12 and 15 by 15 but the more numbers that can possibly be included the better for future use. The final table can be used for quickly finding answers to difficult multiplication problems, discovering how to count by certain bases; the table even displays some of the natural tricks that numbers give us. For instance, with it right in front of us we can see how counting by nines is no more than adding one digit to the first number while subtracting one from the second; 09, 18, 27, 36 and so on. There are many secrets exposed by a well-constructed multiplication table.
2) DIVISION SPELLING: A math puzzle that has appeared in cross word books for years is one that challenges the student on both spelling and math. Regular long division problems are displayed, fully solved, with answers portrayed. However, all the numbers that should be there have been replaced with letters. The object is to discover which number each letter stands for. The puzzle is generally built around a familiar ten-letter term or phrase. The word or phrase is selected then the letters replaced with numbers and, mathematically, the problem is solved and waiting for the student to discover what letter equals what number.
This is a real test on numbers. It highlights standard behavior of numbers. Students can familiarize themselves with the way numbers react to certain conditions. This is a very trying puzzle but very valuable for math training.
3) CROSS SUMS: One of my favorites is a puzzle called Cross Sums; it too appears in many crossword puzzle books. The presentation is a crossword looking tableau but little numbers have been entered to the outside of every square where you would expect to place a letter. In this version you are using numbers instead. All digits, zero to nine, are used but no individual digit can be used twice in any one answer.
The challenge is to make the numbers used in the crossword squares add up to the value of the little number that appears just outside of the square. There are no clues, its strictly addition and subtraction. The student learns standardized combinations and is exposed to things numbers cannot do. For instance if the student needs to enter a three digit answer that adds up to seven he will quickly learn the combination must be some arrangement of the digits 1 – 2 – 4. There is no other three number combination that adds up to seven.
This puzzle will have the student memorizing many different math tricks simply because they are needed to solve the puzzle. Things like, 1 – 2 – 3 – 4 equals ten, a two digit 16 can only be formed by using 9 and 7, there is no way to make 18 with two different numbers, a two space 17 has to be a combination of only 9 and 8, 4 will always be 1 and 3, it cannot be 2 and 2 because of the rules.
Very rapidly the student will gain a respect for math and a better understanding of the power and versatility of numbers in addition to the demands and limitations.
Math does not have to be a chore. Simple puzzles and games like these three here will give the student a better understanding of math while challenging him or her to figure something out and win the game. These are all easily prepared for the classroom and require no elaborate equipment or supplies. They could even be assigned on a daily basis.