Do You Have a Dance Partner?

When my daughter Janelle was 4 years old, she came home and told us she knew how to tell if a number is even or odd. Take a second to pause here and think about how YOU would explain how you know if a number is even or odd.

She explained: 

"Because 1 is odd, it doesn’t have a dance partner. (she shows us one finger). 2 is even, it has a dance partner." She shows me two fingers, one on each hand, and matches them together.

"Oh, I see!  What about 7?" I asked her.

Janelle counted out seven fingers, going back and forth between her two hands.  She had 4 fingers on one hand, and 3 on the other.  She looked at them, quickly matched up 3 fingers and 3 fingers, leaving the thumb she had counted on the 4 hand out, and said “even.”

“Look at your hands again.”  She proceeded to reexamine her hands, looking at 8 fingers, now with both thumbs hidden.  

“How many fingers do you have up now?”  She then put one down, again leaving 3 on one hand and 4 on the other, but this time no thumbs were involved.  She then tried to match them up, saw one finger with no match, and said “it’s odd.”

"How do you know?"

"It doesn’t have a dance partner."

That’s where we left things for the day. What stuck with me was how Janelle used something familiar (dance partners) and the tools she had (her fingers) to make sense of an important number concept.

You can see the whole interaction in this two-minute video!

Post-Game Analysis

Take a moment to return to your idea of how you would explain whether a number is odd or even. Maybe you think of even numbers as “divisible by 2,” or use the digit rule: “numbers ending in 0, 2, 4, 6, or 8 are even.” Those are useful generalizations—but they’re the result of lots of experience and internalized patterns.

Now think about Janelle’s approach. She’s reasoning through the concept by visualizing pairs. That’s big! Despite her mix-up, she’s grasping that even numbers can be split into equal groups with no leftovers, and odd numbers always leave one out. Her "dance partner" idea may only work with small numbers and fingers for now, but it's rooted in the conceptual understanding that odd and even are about grouping and remainders. That’s something even many older kids haven’t yet internalized. Eventually I imagine her experiences with numbers will lead her to make generalizations like the digit rules above.

Try It This Week

Curious what your child knows about odd and even numbers? Ask!

• “Have you ever heard of odd or even numbers?”
  
  
• “What makes a number odd or even?”
  
  
• “Can you show me what you mean?”
  

If this idea is new to them, introduce Janelle’s "dance partner" metaphor: “Let’s try some numbers—can we find a partner for each one?”

Try using fingers, small toys, or snack items to build groups and look for leftovers.

What you’re really doing is inviting your child into a world of mathematical reasoning, where exploring and explaining matters more than just getting it “right.”