HOW TO COMPARE NUMBERS USING ‘GREATER THAN’ AND ‘LESS THAN’:

• Comparing numbers is what you do when you’re given two numbers and asked to figure out which one is bigger.
• When you compare two numbers you’ll use one of the following three symbols:
  • > means “greater than”
  • < means “less than”
  • = means “equal to”
• To make things simple, imagine that > and < are alligator mouths. The alligator always wants to eat the bigger number.
• EXAMPLE: Compare the following numbers using >, <, or =.

1. 1. 114 _ 132
   2. 984 _ 984
   3. 260 _ 146

• • SOLUTIONS:

1. 1. 1. 132 is bigger than 114, so the alligator wants to eat 132. Use the symbol that looks like an alligator mouth trying to eat 132.
         • 114 < 132
      2. 984 and 984 are the same number, so we use =, which means “equal to” or “the same as.”
         • 984 = 984
      3. 260 is bigger than 146, so the alligator wants to eat 260. Use the symbol that looks like an alligator mouth trying to eat 260.
         • 260 > 146

ARE THERE ANY TRICKS FOR REMEMBERING GREATER THAN AND LESS THAN SIGNS?

• When first learning about inequality symbols (< and >) it’s not hugely important to remember what they’re called. It’s most important to understand what they mean (i.e. that the open side always points to what’s bigger).
• However, if you want/need to know how to read the symbols, here’s a trick:
  • Remember that in math, just like in English, we read from left to right.
    • To read 114 < 132:
      • Start from the left and move right. Say “114 is” and pause.
      • Is 114 greater than or less than 132? 114 is less than 132, so we read 114 < 132 as “114 is less than 132.”
      • That means that < is the sign for “less than.”
    • To read 260 > 146:
      • Start from the left and move right. Say “260 is” and pause.
      • Is 260 greater than or less than 146? 260 is greater than 146, so we read 260 > 146 as “260 is greater than 146.”
      • That means that > is the sign for “greater than.”

HOW TO ORDER NUMBERS:

• Ordering numbers is kind of like putting words in alphabetical order.
  • If you need to put numbers in order from least to greatest, that’s like putting words in alphabetical order – starting from ‘a’ and going to ‘z.’
  • If you need to put numbers in order from greatest to least, that’s like putting words in reverse alphabetical order – starting from ‘z’ and working toward ‘a.’
• To properly order numbers you have to understand their value (what they’re worth).
  • The number 141 means 1 hundred, 4 tens, and 1 one.
  • The number 241 means 2 hundreds, 4 tens, and 1 one.
  • The number 173 means 1 hundred, 7 tens, and 3 ones.
  • To order those three numbers from least to greatest, you begin with the smallest number (141), end with the biggest (241), and put the other one (173) in between. Written in order from least to greatest we have 141, 173, 241.
  • To order those numbers from greatest to least, just write the list above backward: 241, 173, 141.

COMMON MISTAKES WHEN ORDERING NUMBERS:

• • FOR SMALL NUMBERS:
    • Given the following set of numbers (7, 10, 15, 1) it’s common for students to order them as 1, 10, 15, 7. Since 1 is smaller than 7, students who make this mistake assume that any number that begins with a 1 should come before any number that begins with a 7.
      • If your student is making this mistake, use objects to show them what each number represents.
        • 7 means 🐸🐸🐸🐸🐸🐸🐸
        • 10 means 🐸🐸🐸🐸🐸🐸🐸🐸🐸🐸
        • 15 means 🐸🐸🐸🐸🐸🐸🐸🐸🐸🐸🐸🐸🐸🐸🐸
        • 1 means 🐸
      • When students can see what numbers represent it’s much easier for them to pick out the smallest group (1). Once the smallest group is removed, ask them what is the new smallest group (7). Move that off to the side and again ask what is the smaller group (10). They’ll be left with the largest group (15) and they will have successfully ordered the numbers.
  • FOR LARGER NUMBERS:
    • A common mistake is to focus on the largest place value and ignore the others.
    • When ordering 141, 241, and 173 it’s easy to tell that 241 is the largest because it has two hundreds, while the other two numbers only have one hundred. If you’re not careful you’ll misorder the other two numbers.
    • Just like when putting words in alphabetical order, if two numbers begin with the same digit you have to move to the second digit to determine which is smaller and which is larger. If the second digits are also the same, continue moving to lower digits until you find a difference.