Quick Easy Way to Untangle Confusion re: “Greater” and “Less”

Whenever I can find a memory trick that helps students get something straight, I use it. Students needs to remember so many things in algebra, so whatever help we can give them is well appreciated.

So recently I stumbled upon a memory trick that helps students tell which of two numbers is greater and which is less.

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You might be thinking:  greater and less?! Why would any student have trouble with that? Well, before students hit negative numbers and absolute value, there is generally little trouble. The greater numbers are the larger numbers, the lesser numbers are the smaller numbers. And kids basically know what we mean by larger and smaller whole numbers, when they are dealing with positive numbers and zero.

But when students encounter negative numbers, some things change.
While 10 > 5,   – 10 IS not > – 5. Instead:  – 10 < – 5.

As if that were not enough, absolute vale comes along and makes things still more confusing, since it takes the value of any number and makes it positive. So now:

abs. value of – 10 > abs. value of – 5

With the concepts of negatives and absolute value “muddying” the once clear water, students do get confused, especially with the negative numbers.

If you want proof, try this. Talk to three students in Algebra 1. First ask them what is larger:  10 or 5. Talk to a few kids, and you’re likely to get either a straight correct answer or that classic teen look of :  “What, you think I’m stupid?”

But then ask the same kids what is LARGER:  – 10 or – 5. Do this a few times, and you’ll observe a discernible pause before you get an answer; not infrequently, the answer will be – 10!

The trick that helps students straighten this out deals with the number line. Fortunately, on the number line, things are actually still simple when it comes to greater and less. If you are looking at any two numbers, the number that is to the right is greater, the number to the left is less.

This holds true whether both numbers are positive, both are negative, or one is positive and the other negative. And it holds true if either number is zero. That pretty much covers all cases!

So what is my big trick? It is right there, in the words greater and less.

The word “LESS” share the letters “LE”  in the word “LEFT.”

The word “GREATER” share the letters “RT”  in the word “RIGHT.

So the greater number is to the right; the lesser number is to the left.

When I point this out to students, they generally nod their head and say, “Oh …. yeah … ”

I point out that whenever they need to figure out which of two numbers is greater or less, they just need to visualize the two numbers on the number line (some students need to make a “thumbnail” sketch of the two numbers, along with zero). Then all they do is visually check and see which number is to the left, and that number is LESS. Check and see which number is to the right, and that number is GREATER. No more pondering over the impact of negative signs or absolute value symbols. As in elementary school, the answer could not be more plain.

A simple trick, but an easy, helpful one.

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