Wall-to-Wall Trees

Here's your nightly math! Just 5 quick minutes of number fun for kids and parents at home. Read a cool fun fact, followed by math riddles at different levels so everyone can jump in. Your kids will love you for it.

Wall-to-Wall Trees

July 22, 2014

Have you ever played with Lincoln Logs, and as you stacked the little toy sticks, wondered how many trees it takes to build a real house? Well, other people have asked the same question (along with people who build houses, of course). First, it depends on the size of the house: how long, how wide, and how tall. It also depends on how much lumber you can get from one tree. The taller the tree, the longer the boards you can cut from it, and the thicker the trunk, the more boards you can get. Wood is measured in “board feet,” where a board foot is 1 foot long, 1 foot wide, and 1 inch thick. Counting it up that way, a 53-foot-tall pine with a 10-inch wide trunk makes 75 board feet, and it takes more than 5 of those trees to build a normal-sized 3-bedroom house. If you’re looking to build just a treehouse, you’ll need a lot less — but remember to count the tree that’s holding you up!

Wee ones: Which is longer, a 4-foot board or a 6-foot board?

Little kids: If you grab 2 5-foot boards to put a roof on your treehouse, how many board feet is that? (Assume they’re 1 foot wide and 1 inch thick for true “board feet.”)  Bonus: What if you decide you need 3 times as much to keep the rain out – now how many board feet do you need for your roof?

Big kids: If a tree has a 50-foot trunk, how many full 6-foot-long boards can you cut from a 1-foot-wide,1-inch-thck slice that’s the full length?  Bonus: If you’re building a wall that’s 12 feet wide and 8 feet tall, will 100 board feet of wood be enough for the project?

The sky’s the limit: Let’s say all your lumber is in 6-foot or 8-foot pieces (both are 1 foot wide). What’s the least amount of wood you need to cut the necessary pieces to fill a 13-foot-long by 9-foot-tall wall? You can run the boards either side to side, up and down, or a mix of both.

 

 

 

Answers:
Wee ones: The 6-foot board.

Little kids: 10 board feet.  Bonus: 30 board feet.

Big kids: 8 boards, and you’ll have 2 board feet left over.  Bonus: Yes, since you need just 96 board feet.

The sky’s the limit: For the first wall, you can place 13 8-foot pieces vertically, then run a 6-footer and an 8-footer across the top end to end. You’ll need to cut just 1 board foot off the end of the last piece as waste. Alternatively, you could run 9 boards of each length horizontally end to end with each other, but that’s 14 feet of width, so you have to cut 1 foot off each of the 9-foot rows and you waste a lot of wood. The first option is better, using 112 board feet of 8-footers and 6 feet from the 6-footer for a total of 118 board feet. The other option uses up 126 feet.

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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 while still in diapers, 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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