Does Banapples make sense? Lets learn about the Importance of the Law of Sameness!

Feb 17, 2022 | Red Deer


When we learn math, we tend not to make a connection that one math knowledge actually has the same foundation with another. We didn’t realize that ½ + 1/3 has the same concept as 12+3.7 or 1 dime + 1 quarter.  This principle is called The Law of Sameness: You can only add and subtract things of the same kind, things that have the same name.

  • What are 3 apples plus 2 apples? 5 apples.
  • Three bananas plus 2 bananas? 5 bananas.
  • Three bananas plus 2 apples? Not 5 banapples – but either 5 pieces of fruits or 3 bananas and 2 apples.

It is not uncommon to see kids, even middle school and high school students, think that ½ plus 1/3 is 2/5. They just add both numerators and also both denominators; They have not been taught that you cannot combine things with different names.


The Importance of NAME and SAMEness

At Mathnasium, we teach using the rich mathematics vocabulary, including a deep understanding of the importance of NAME and SAMEness; finding the common name (nom in Latin) or the common denominator is the key in various contexts. When more than one thing is involved, the Law of SAMEness comes into play.

  • ½ + 1/3 = 1 half + 1 third = 3 sixths + 2 sixths = 5 sixths = 5/6
  • 1 dime + 1 nickel = 10 cents + 5 cents = 15 cents
  • 1 foot + 6 inches = 12 inches + 6 inches = 18 inches or 1 foot + ½ foot = 1 ½ feet
  • 3x + 2y is not 5xy
  • 12 + 3.7 = 1 ten & 2 ones plus 3 ones & 7 tenths = 1 ten & 5 ones & 7 tenths = 15.7 (too many kids are confused with Place Value and add numbers that do not have a common name).

When the idea of sameness becomes a part of a child’s experience base, they begin to develop the vision necessary for a deeper understanding of mathematics. Taught since early, it would be easier for them to connect Counting to Proportional Thinking, and they wouldn’t feel that they are learning a brand-new concept when they meet fractions or algebra down the road.



Mathnasium of Red Deer is your neighbourhood’s math-only learning centre, and we are here to help your child. Our centre director, Riwan, would be happy to meet you! We are conveniently located in the shopping destination area in Red Deer: 5250 22nd St, Unit 30 B – at the Gaetz Avenue Crossing shopping centre, in the same area as Chapters Indigo/Starbucks, Michael Arts, Petland and Ashley, and the phone number is 403-872 MATH (6284). 

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