There is more than one way to get the answer.
Everyone agrees on the importance of Mathematics. We also agree that children are unique and learn differently. When my children encounter a difficult problem, I try and show them different ways to solve that problem. I aim to instill confidence that a problem can be solved. I utilize include reinforcement, tricks for counting on hands, Left to Right approach, and Vedic mathematics tricks, among others. Alternative ways of solving addition, subtraction, multiplication, and division problems expand their viewpoint and engages their creativity.
Addition Techniques
“One friend from Sesame Street, plus one friend from Sesame Street, equals two friends from Sesame Street! Ah, ha, ha!”
— Count von Count, Sesame Street
Counting
Counting is essential, and something to start as early as possible. How many stuffies, crayons, or socks are on the bed? Count the number of trees, bridges, or houses as we walk or drive by. The moment of epiphany when a child realizes the increment of home or street numbers is priceless.
Count by 2s. Count by 3s. Count by 19s. Count by 106s. I love to encourage them, and then challenge them.
Reinforcing
If 1 + 1 =2, what is 1 hundred + 1 hundred? Correct, 2 hundred. What about 1 thousand plus 1 thousand? Or 1 million +1 million.
What is that number plus 1?
What is the biggest number? Tens, Hundreds, Thousands, Millions, Billions, Trillions, Quadrillions, … there is no bazillion, but there are a Googol and Googolplex (google it to see how many digits those are).
Counting on Hands
My kids love using their hands and fingers to perform math. They also enjoy making the “L” sign behind each other’s backs. Using 2 hands they can count to 10. Using the finger indents, we can count to 30. Using their hands and mine, we can reach 60. Tactile learning!
Circle of Ten
The Circle of Ten comes from Vedic Mathematics. The circle shows that the numbers 1–9 have compliments which sum to 10. Keeping these compliments in mind, we can create associations to calculate easier and faster. For example, what is 2 + 3 + 7+ 8? Seeing the compliments of 8 + 2, and 7 + 3 we easily have 10 + 10 = 20.
Left to Right
Addition from Left to Right may seem longer with more steps however, it is more logical. This method promotes an understanding of the whole problem by saying the entire number. What is 123 + 789? 100 + 700 = 800. 800 + 20 = 820. 820 + 80 = 900. 900 + 3 = 903. 903 +9 = 912. In the Left to Right approach, the hundred’s and ten’s places are enforced, and the full scope of the problem is calculated.
Subtraction
“I got them subtraction blues! Take it away, take it away!”
— Count von Count, Sesame Street
My kids love Halloween. I would be remiss if I did not use candy to reinforce math skills. How many will you have left, if you eat 2? I am taking 5, how many remain?
Counting on Hands
What is 5 minus 2? On one hand, just close 2 fingers and viola. What is 18 minus 12? Use your finger indents.
Counting Backwards
Counting in reverse order solidifies the number sequence. Counting backward by 2s or 3s enforces subtraction skills. It is a great bedtime routine for the “I’m not tired” excuse.
Left to Right
Subtraction from Left to Right again may seem to have more steps. However, it emphasizes the entire problem. What is 211–123? 200–100= 100. 100 + 10 = 110. 110–20 = 90. 90 + 1 = 91. Finally, 91–3 = 88. When my kids struggled with carrying and borrowing, this method aided them.
Multiplication
Counting on Hands.
You probably can multiply by 5s with your hands and feet. Using finger indents, we can multiply by 3s.
What about multiplying by nine? Young kids love this trick. Label your fingers 1–10 from left thumb (1) to right thumb (10). What is 9 x 5? Hold down the left-hand pinky finger and now you have 4 on one side and 5 on the other = 45.
Here is another method of labeling your fingers, which allows for multiplying 6s through 10s. Label your fingers from 10–6 on each hand from the thumb to the pinky. Connect fingers you want to multiply, for example, 9 x 7; connect the left index finger with the right ring finger. The joined fingers and those below each represent a 10, there are 6 such fingers and hence a sum of 60. The left-hand fingers above the join are multiplied by the right-hand fingers above the join, 1 x 3 = 3. 60 + 3 = 63.
Alternative Technique
Once they are open to it, math provides many ways to calculate a problem; for example, multiplying by 19.
An alternative approach is considering that 19 = 20–1, and 20 is 2 x 10. Therefore, to multiply by 19 we can take a number, double it, add a zero at the end, and subtract the number. For example, to calculate 18 * 19; we take 18 double it to reach 36, add a zero and it becomes 360, and subtract 18 to arrive at 342.
- Multiply by 4 — Double the number and double that number
- Multiply by 19 — Double the number, add a zero at the end and subtract the original number
- Multiply by 21 — Double the number, add a zero at the end and add the original number
I plan on showing them the crosswise multiplication technique, and multiplication by base numbers in due time.
Line Method
The Line method of multiplication is fun and sure to amaze when first shown. What is 22 * 22? Draw horizontal lines equal to the individual digits of the first number, leaving space in between. Next, draw vertical lines over the first set, equal to the individual digits of the second number, leaving space in between. Create Arcs to separate the sections. Count the intersections between the lines, to arrive at the calculated amount.
Division
“Divide means to separate things into different groups or sections.”
— Nia Long, Sesame Street.
Pizza Pie
There are 8 slices in this pizza and 4 of us, how much does each person receive? I apply this analogy all the time for division problems; I convert the problem into slices and people.
Multiplication
Division is multiplication written differently. What is 27 divided by 9? An alternative way of asking the same question is, What times 9 equal 27?
Subtraction
What is 343 divided by 97? Employing subtraction is a good technique for problems such as these. Subtract 97 from 343 to get 246. Subtract 97 again to calculate 149. Subtract 97 once more to get 52. As 52 is less than 97 we halt. Counting the number of subtractions, and minding the remainder of 52, we arrive at our answer 3R52.
Alternative Technique
In an alternative approach for solving division problems, the remainder is written alongside the next number. For example, what is 243 divided by 9? 2 is less than 9, so we write it next to the 4. 24 is divided by 9, 2 times with a remainder of 6. We write the 6, next to the 3. 63 divided by 9 is 7.
Math is a universal subject that all children should feel comfortable with. Children are unique and learn differently. Using alternative techniques such as the Left to Rich approach or via tricks with fingers and hands, all children can gain confidence and excel at mathematics.
