Treegonometry- Christmas Tree Math

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.

Treegonometry- Christmas Tree Math

December 20, 2013

My kids say their favorite Christmas tradition is decorating our Christmas tree. There’s Christmas music and pretty lights. The whole family pitches in and we enjoy hot cocoa afterwards as a reward–what’s not to like? The kids don’t realize it, but there’s also math all along the way.

First, we need to buy a tree. The kids get to choose a tree from our local lot. We give them free rein in terms of species of tree and shape but there is a size limit to make sure it fits. How tall is the ceiling in our living room? They will give the tree a fresh cut before loading it on our car, but if it’s going to fit we also need to factor in the tree stand and the 6-inch star on top!

Find out what variety of evergreen you chose and how fast it grows. About how long did it take for your tree to reach its height? If you chose a 6-8 foot tree, it probably took about 5-7 years to grow. At Rockefeller Center this year there is a 76 foot Norway Spruce. The Spruce was a “living Christmas tree” planted by a family in their front yard in 1953. It was probably at least 5 years old at that time. How many inches did this tree grow, on average, per year, to reach its 76-foot height in 2013?

We get our much smaller tree home and wrestle it into the base and anchor it. We want our tree to last through the season so we have to make sure we water it! According to the National Christmas Tree Association, a tree needs one quart of water is required for each inch of the trunk’s diameter. An average tree is 4 inches in diameter and needs about gallon (4 quarts) each day.

Once the tree is safely ensconced in our living room, my husband drags big boxes of ornaments out from storage.

Inside the boxes are ornaments friends and family gave us at tree-trimming parties, strange and mangled ornaments (like bald birds or a sponge-bunny) my mother-in-law snuck over in an attempt to prune her own huge collection, and the most special ones…handmade ornaments from the kids.

We have a lot of ornaments! How many will your family hang on the tree?

As a young adult, I always imagined a lovely Victorian-style tree with small white lights and perfectly spaced, coordinated ornaments in red and gold. My husband, on the other hand comes from a tradition of multicolored lights with a few bubble lights thrown in for good measure. Our ornaments are eclectic and quirky and definitely not coordinated.

Let’s say for a minute that the family wanted to humor me, however. How many ornaments would we need to achieve a perfect density on our tree? A group of students in the UK came up with a series of formulas to calculate the right amount of tinsel, baubles, and lights, and even the length of your tree topper, based on the height of your tree. We don’t use tinsel because of our cats but we make up for it in lights and ornaments! Check out their Treegonometry calculator and see if you agree. In the United States, you’ll have to convert their metric results to standard measurement.

We could argue as to whether there is a standard or it’s a matter of taste. Do you like more or fewer decorations on your tree? Do you hang all of your decorations or just some? You can quantify that amount with your child. What percentage of your collection will you hang?

Even if my family agreed to go with my elegant and balanced decoration plan, there’s still the matter of our two-year-old. My oldest two children did such a good job, placing breakable ornaments at the top, hooking the heaviest ones on sturdier branches closer to the trunk, and putting only lightweight, non-breakable ornaments at the bottom. Within a week, however, our little one had pulled all the ornaments off the bottom, which leads to another math question: how high can a 36-inch child reach?

Treegonometry, meet the tree-terrorizing toddler.


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About the Author

Candace Lindemann

Candace Lindemann, of Naturally Educational, is a nationally recognized and quoted educational expert and published children's writer who holds a B.A. from Yale University and an M.Ed. from the Harvard Graduate School of Education,

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