Operations & Algebraic Thinking
Odd & Even Numbers
Deciding whether a group of up to 20 objects has an odd or even number of members.
Can Everyone Find a Partner?
Take a group of objects and try to pair every object up with exactly one partner. Sometimes every single object gets a partner, and sometimes one object is left over with no partner. That single difference sorts every whole number into one of two families.
Definition — Odd and Even Numbers
Even numbers are also exactly what you get by adding a number to itself (doubling): 2, 4, 6, 8. Every even number can be split into two equal groups. Odd numbers always leave one object by itself, no matter how the pairing is arranged.
Worked Example — Testing a Group for Even
Worked Example — Testing a Group for Odd
Tip
Common Mistakes
Deciding a number is odd or even just by guessing or by how the objects happen to be arranged, rather than actually pairing them up.
Physically or mentally pair the objects two at a time and check whether exactly one is left unpaired at the end.
Assuming a larger number is more likely to be odd or even than a smaller one.
Odd and even alternate one after another no matter how large the number is — every number is exactly one or the other, regardless of size.
Key Takeaways
- An even number of objects can be split into pairs with none left over.
- An odd number of objects always leaves exactly one object without a partner.
- Checking the last digit of a number is a fast way to tell odd from even.
Summary
Sorting numbers into odd and even is about whether objects can be perfectly paired up. The next lesson uses a related idea — arranging objects in neat rows and columns — to take a first step toward multiplication.
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