Even or Odd Numbers of Objects

When you look at a small pile of buttons, blocks, or apples, you can tell whether there is an even or an odd amount of them without even counting to a big number. All you have to do is try to put the objects into pairs. If every object finds a partner, the group is even. If one object is left standing alone, the group is odd.

An even number of objects can always be arranged into pairs with nothing left over. An odd number of objects always has exactly one object that cannot find a partner once every other object has been paired up. This is the most basic, hands-on way to understand even and odd, before ever looking at written numbers or digits.

Follow these steps whenever you are given a picture or a pile of real objects and asked whether the total is even or odd.

1. Look at all the objects in the group.
2. Draw a loop, line, or bracket connecting two objects at a time to make a pair.
3. Keep pairing objects until you run out.
4. Check what happens at the end: if every object belongs to a pair, the group is even; if one object is left alone, the group is odd.

This method works no matter how the objects are arranged, whether they are lined up in a row, scattered on a page, or organized in a picture like a number grid. The order of the objects does not change whether the total is even or odd, only the total count matters.

Example 1: A basket has 9 apples. Pairing them up gives 4 full pairs and 1 apple left over, since \(9 = 4 \times 2 + 1\). Because one apple has no partner, 9 is odd.

Example 2: A jar has 12 marbles. Pairing them up gives exactly 6 pairs with none left over, since \(12 = 6 \times 2\). Because every marble has a partner, 12 is even.

Example 3: You are shown a picture of 15 dots. Counting the dots and grouping them two at a time leaves 1 dot without a match, so 15 is odd.

Once you get comfortable pairing real objects, you can move on to deciding whether a written number is even or odd just by looking at its last digit, which is covered in identifying a number as even or odd. You can also picture even and odd numbers as positions along a number line, which is explored in even or odd numbers in number lines. Both of these build on the exact same pairing idea you practice with real objects here.

• Do not count the total first and stop paying attention to the objects; always check by physically pairing or circling them, especially with larger totals.
• Do not skip an object by accident when drawing pairs; miscounting can make an even group look odd or an odd group look even.
• Remember that zero objects is considered even, since there are simply no objects left unpaired.

Related lessons

• Math 1