Honeybees and Hexagons

"Honeybees are some of nature’s finest mathematicians. Not only can they calculate angles and comprehend the roundness of the earth, these smart insects build and live in one of the most mathematically efficient architectural designs around: the beehive."

Learn more by viewing the complete Ted Ed lesson by Zack Patterson and Andy Peterson.

After viewing this you may want to check out this book on patterns and shapes in nature.

Bees, Snails, & Peacock Tails: Patterns & Shapes . . . Naturally (2008), written by Betsy Franco and illustrated by Steve Jenkins explores surprising and hidden shapes and patterns in nature. Poetic text and cut paper collage illustrations serve as a beautiful vehicle for introducing young readers to these concepts. On a page depicting a snake, a spider hanging from a thread, a snail shell, a bee in flight, an ant, and goose silhouetted against the moon, the text begins this way.

In the day
and the night,
on the land
and in flight

tucked in hollows
of trees,
in the tide pools
and seas,

you'll find patterns and shapes—
from the snakes to the bees!

The next page reveals the genius behind a beehive. This is one of my favorite spreads in the book—not only do I love the text, but I could spend hours staring at the bees on the hive. The layers upon layers of paper used to create the illustration are stunning. The text that accompanies it reads:

Study a beehive
and you will see
the mathematical genius of the bee.

The hexagons
you'll find inside
fit side
by side
by side
by side.

This math is passed
mysteriously
from worker bee
to worker bee!

*Swoon* Beautiful images and beautiful words—what better tools are there to introduce nonfiction to young readers? None that I can think of. 

Franco and Jenkins next explore moths, the stunning symmetry of a spider's web, the dazzling feathers of the male peacock, the familiar V of migrating geese, the teamwork and formation of members of an ant colony, the geometry of animal tracks (a mouse in the snow), the shapes on diamondback snakes, the radial symmetry of sea stars, the shape of a puffed-up puffer fish, and the spirals of a snail shell. The text/poem on the shell page is written in the same spiral form displayed by the shell.

The text ends with the same background as the opening spread, though presented at nightfall with some different animals on the page. There are eyes inside a hole in the tree, sea stars on a rock, a moth flitting in the moonlight, and a spider now resting on a completed web. The text reads:

So there you have it . . . .
I think you'll agree

that creatures
on land,
in the air,
in the sea

make patterns and shapes
quite naturally!

Text ©Betsy Franco. All rights reserved. 

The end matter of the book is titled New Angles on Animals and provides a brief bit of information on each of the animals highlighted in the pages of the text.

While I plan on using this book for math to talk about shapes and patterns, I can also see it being used in science to discuss camouflage and other animal adaptations. This is a gorgeous book in both writing and illustration. I highly recommend it.

Monday Math Freebie - Geometry Vocabulary Puzzle

I've been playing around with Formulator Tarsia, "a tool for creating activities in a form of jigsaws or dominos for later use in a class." Sadly, this free software only works on a PC, so I used Wineskin to convert the program to an app that would run on a Mac. It's a bit glitchy (at times), but now I have VMware Fusion, a program that allows you to run Windows on a Mac. I don't use it often, but it's been great for playing around with Tarsia.

This is a very long introduction to say that I am working on a series of puzzles for math. The first is a triangle shaped puzzle to review geometry vocabulary. Simply laminate and cut the large triangles apart. Students try to assemble the 16 pieces into a large triangle. Students should notice that the three corner pieces have writing on only 1 edge. The side pieces have writing along 2 edges, while the interior pieces have writing along all three edges.

Here's what the pieces and completed puzzle look like.

Download Geometry Vocabulary Puzzle

I hope you get a chance to use this puzzle in your home or classroom. Please let me know if you try it and how you like it! 

**BTW, as of this writing I am only 12 followers away from 20,000 on Pinterest! Check out this post to learn more about my boards (all 230 devoted to teaching) and to enter a giveaway for some free books!

Monday Math Freebie - Pattern Block Builder

This week I'm sharing an assortment of activities with pattern blocks. using a game board, students roll dice and take different numbers of blocks depending on where they land and the number they roll. Once they reach the finish they build a shape from their pieces. Then they answer some questions using their pattern blocks.

You'll find two different worksheets in this packet. One focuses on basic counting, graphing, and coin counting skills. The other focuses on fractions and symmetry.

Here's a sneak peak at the contents.

 Download Pattern Block Builder.

I hope you get a chance to use these in your home or classroom. Please let me know if you try these and how you like them! 

A Visual for Pi Day

Visualizing Pi Infographic

Pi Day is Today!

Photo © Mykl Roventine.

Today, March 14th, is Pi Day. No, that's not a typo. It is Pi day, as in 3.14159... you get the idea. The first Pi Day celebration was held at the San Francisco Exploratorium in 1988.

What is pi anyway? I'm sure you remember it from math in some formula you memorized, but do you really know what it is? Pi represents the relationship between a circle’s diameter (its width) and its circumference (the distance around the circle). Pi is always the same number, no matter the circle you use to compute it. In school we generally approximate pi to 3.14 in school, but professionals often use more decimal places and extend the number to 3.14159.

One activity I loved doing with students was to ask them to bring in a can and lid that would soon be recycled. I always brought in a few extras so that there would be a variety of sizes. Each student was given a lid and directed to measure the diameter and circumference. Students then divided the circumference by the diameter. We recorded the results on the overhead and discussed them. Most were amazed to find that the results were nearly the same, allowing for some margin of error in measurement. This is a quick and fun and provides a meaningful way to introduce the concept of pi.

Are you doing anything special for Pi Day? Perhaps you could make a pi necklace or a pi bracelet. Can you find your birthday in pi? My birthday begins with digit number 7669! Since any day is a good day for poetry, you could try reading some pi poems. If you're looking for more ideas, visit the Exploratorium pi site or try this middle school math newsletter.

Learn more about pi at Ask Dr. Math FAQ: About Pi.

Not a fan of pi? Check out my post entitled Pi Day is Tomorrow! But Should We Celebrate It? for a bit of information on the pi/tau wars.

Friday Freebie! - Exploring Quadrilaterals

After two weeks without my computer, I finally have it back! Here's an activity I adapted for my class to compare and analyze attributes of quadrilaterals. This file includes 12 quadrilateral sorting cards, a chart for analyzing attributes, a page to draw in lines of symmetry, and an answer key.

This activity meets the following Common Core Standards for Mathematics:

• 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.
• 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

• 5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
• 5.G.4 Classify two-dimensional figures in a hierarchy based on properties.

Download Exploring Quadrilaterals. Enjoy!

Monday Math Freebies - Geometry Fortune Teller

This week's freebie is a fortune teller for reviewing geometry concepts. The file includes a pre-made fortune teller, a blank template, and directions for assembly.

Download Geometry Fortune Teller. If you like this activity, leave me a note and let me know. I'd like to make some that are a bit more focused, with specific topics like triangles, quadrilaterals, polygons, and 3-D shapes. I also think these would be fun for working with concepts related to measurement.