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💡 Even & Odd — The Dot-Pair Way
An even number can have all its dots paired up with nothing left over.
An odd number always has exactly 1 dot left over after pairing.
We can use this idea to PROVE rules about adding even and odd numbers!
Proof 1: Even + Even = Even
Both numbers have all dots in pairs. When you combine them, every dot still has a partner.
Nothing left over → the result is always even! This works for ANY two even numbers.
Proof 2: Odd + Odd = Even
Each odd number has 1 leftover dot. The two leftovers pair up together!
No dots left over → the result is always even!
Proof 3: Even + Odd = Odd
The even number has no leftovers. The odd number has 1 leftover.
That 1 leftover stays → the result is always odd!
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1 Draw Your Own Dot Proof ✏️
Use dots to prove each statement. Draw paired dots and mark any leftover.
Prove: 8 + 6 is even
Draw dots for 8:
Draw dots for 6:
Combined: — left over?
Prove: 7 + 5 is even
Draw dots for 7:
Draw dots for 5:
Combined: — left over?
Prove: 6 + 3 is odd
Draw dots for 6:
Draw dots for 3:
Combined: — left over?
Prove: 9 + 9 is even
Draw dots for 9:
Draw dots for 9:
Combined: — left over?
2 Predict: Even or Odd? ⚡
Use the rules you proved to predict the answer WITHOUT calculating!
Even + Even
=
Odd + Odd
=
Even + Odd
=
Odd + Even
=
124 + 336
=
457 + 891
=
200 + 77
=
13 + 13 + 13
=
3 Explain It! 💬
In your own words, explain why odd + odd = even.
Answer Key:
2) Even, Even, Odd, Odd, Even (E+E), Even (O+O), Odd (E+O), Odd (O+O+O → O+O=E, E+O=O)