Flip-Flopping Flag

Flip-Flopping Flag

June 14, 2020

It’s Flag Day here in America, so it’s a great time to talk about all the crazy math our nation’s flag has done. Each time our country added a new state, we added a star to that blue box. We also tried adding a stripe for each new state. But after adding Vermont and Kentucky (#14 and #15), we realized the flag would turn into a pink blur of teeny stripes! So we went back to 13 stripes and used stars for states after that. Sometimes a bunch of states joined at once, sothe number of stars made some big jumps, like from 38 to 43 when we added the Dakotas, Idaho, Montana, and Washington. Thankfully, today’s 50-star flag has lasted the longest, so we can remember what it looks like!

Wee ones: If the flag has 7 red stripes and 6 white stripes, which color has more stripes?

Little kids: Since the stripes on our flag are red, then white, then red, then white…what color is the 8th stripe? (Don’t peek!)  Bonus: When the flag jumped from 48 stars to 50, how many states had we added?

Big kids: One flag in 1818 had the stars laid out in a star shape: 1 star in the middle, 10 more around it to make a pentagon, and then 3 in each of the 5 points. How many states did we have at that time?  Bonus: How many more states would we need today to double that number of stars?

The sky’s the limit: What number of states would allow the stars to make a perfect square (same number of rows across and down), and where the digits of the number add up to 9?










Wee ones: More red stripes.

Little kids: White.  Bonus: 2 more states – Alaska and Hawaii, in 1959.

Big kids: 26 states, since it’s 1+10+15 stars.  Bonus: Double would be 52, so we’d need 2 more states.

The sky’s the limit: 36. The only perfect square numbers between 13 and 50 are 16, 25, 36, and 49. 36 is the only one where the digits add to 9 — because it’s the only one divisible by 9!

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About the Author

Laura Overdeck

Laura Overdeck

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.

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