# Homeschooling Corner: Summer Fun

Hello, everyone. I hope you have had a lovely summer. We ended up scaling back a bit on our regular schedule, doing about half as much formal “schoolwork” as usual and twice as much riding bikes and going to the playground.

Here are some of the books we found particularly useful/enjoyable this summer:

String, Straightedge, and Shadow: The Story of Geometry, by Julia E Diggins

This is my favorite book we read this summer.

I was looking for a book to introduce simple geometry and shape construction. Instead, I found this delightful history of geometry. It is appropriate for children who understand simple fractions, ratios, and the Pythagorean theorem, but it is not a mathematics textbook and only contains a few equations. (I’m still looking for an introduction to geometry, if anyone has any recommendations.)

This is a new edition of a book originally published in 1965, but its age isn’t really important because geometry hasn’t changed much in the intervening years.

The story begins with geometry in nature–the shapes of trees and flowers, spiderwebs and honeycombs–then develops a speculative account of how early stoneage humans might have become increasingly aware of and attuned to these shapes. Men saw the shapes of the sun and moon in the sky, and might have observed that an ox tied to a pole traced out a similar shape in the dirt.

Then Egyptian surveyors developed right triangles, used for measuring the corner of fields and pyramids. The Mesopotamians developed astronomy, and divided the circle into 360 degrees. Then came the Greeks–clever Thales, mystical Pythagoras, and practical Archimedes. And finally, at the end, Eratosthenes (who used geometry–literally, earth measuring–to measure the circumference of the Earth,) and a few paragraphs about Euclid.

Writing with Ease, by Susan Wise Bauer

There are many books and workbooks in this series, so you can pick the ones that best suit your child’s ability level. (The “look inside the book” feature is great for judging which level of textbook you want.)

I am sure these books are not everyone’s cup of tea. They may not be yours. But they were what we needed.

My eldest children are fairly different in writing needs, but I do not have time for separate curricula. One is a good speller, the other bad. One has acceptable handwriting, the other awful. One will write independently, the other hates writing and plays dead if I try to get them to write. These books have worked well for everyone. Spelling, handwriting, and general willingness to write have all improved.

Even if you aren’t homeschooling, this book might make a good supplement to your kids’ regular curriculum.

In science, we have been growing bacteria in petri dishes and looking at them under the microscope, with the help of Usborne Science and Experiments: The World of the Microscope (I think this is the same book, but cheaper.)

Petri dishes are cheap, agar is easy to make at home (it’s just like making jello,) and kids can learn things like “doorknobs are dirty” and “that’s why mom makes me wash my hands before dinner.”

Just be careful when handling large quantities of bacteria. Even if it’s normal household bacteria that you’re exposed to regularly, you’re not used to it in these quantities. The instructions recommend wearing gloves and safety goggles while handling bacteria and making slides out of them–and besides, kids like dressing up “like scientists” anyway.

Our pattern blocks have been in the family for decades–passed down to me by my grandmother–but the geoboards are a new acquisition. I remember geoboards in elementary school–they sat behind the teacher’s desk and we never actually used them. I didn’t know what, exactly, geoboards were for, so I went ahead and got new workbooks for both them and the pattern blocks.

We are only a few lessons in, but so far I am very pleased with these. We have been talking about angles and measuring the degrees in different shapes with the pattern blocks–360 in a circle, 180 in a triangle, 720 in a hexagon, etc–which dovetails nicely with the geometry reading. The geoboards let us construct and examine a variety of different shapes, like right and equilateral triangles. The lesson plans are easy to use and the kids really enjoy them. Just watch out for rubber bands flying across the room.

Super Source makes workbooks for different grade levels, from K through 6th.

Learn to Program with Minecraft, by Craig Richardson

This book introduces Python, and is a nice step up from the Scratch workbooks. You may have to install a couple of programs, like Python and the API spigot, but the book walks you through this and it is not bad at all. There are then step-by-step instructions for making simple programs, along with bonus challenges to work out on your (or your kid’s) own.

The book covers strings, booleans, if statements, loops, etc, in kid-friendly ways. Best for people who already love Minecraft and can type.

# Homeschooling Corner: Erdos, Fibonacci, and some Really Big Numbers

One of the nice things about homeschooling is that it is very forgiving of scheduling difficulties and emergencies. Everyone exhausted after a move or sickness? It’s fine to sleep in for a couple of days. Exercises can be moved around, schedules sped up or slowed down as needed.

This week we finished some great books (note: I always try to borrow books from the library before considering buying them. Most of these are fun, but not books you’d want to read over and over):

The Boy who Loved Math: The Improbable Life of Paul Erdos, by Deborah Heligman, was a surprise hit. I’ve read a bunch of children’s biographies and been consistently disappointed; the kids loved this one. Improbable, I know.

I suppose the moral of the story is that kids are likely to enjoy a biography if they identify with the subject. The story starts with Erdos as a rambunctious little boy who likes math but ends up homeschooled because he can’t stand regular school. My kids identified with this pretty strongly.

The illustrations are nice and each page contains some kind of hidden math, like a list of primes.

Professor Astro Cat’s Frontiers of Space, by Dominic Walliman. This is a lovely book appropriate for kids about 6-11, depending on attention span and reading level. We’ve been reading a few pages a week and recently reached the end.

Minecraft Math with Steve, by Steve Math. This book contains 30 Minecraft-themed math problems (with three sub-problems each, for 90 total.) They’re fairly simple multiplication, subtraction, division, and multiplication problems, probably appropriate for kids about second grade or third grade. A couple of sample problems:

Steve wants to collect 20+20 blocks of sand. how much is that total?

Steve ends up with 42 blocks of sand in his inventory. He decides that is too much so drops out 12 blocks. How many blocks remain?

A bed requires 3 wood plank and 3 wools. If Steve has 12 wood planks and 12 wools, how many beds can he build?

This is not a serious math book and I doubt it’s “Common Core Compliant” or whatever, but it’s cute and if your kids like Minecraft, they might enjoy it.

We are partway into Why Pi? by Johnny Ball. It’s an illustrated look at the history of mathematics with a ton of interesting material. Did you know the ancient Greeks used math to calculate the size of the Earth and distance between the Earth and the moon? And why are there 360 degrees in a circle? This one I’m probably going to buy.

Really Big Numbers, by Richard Evan Schwartz. Previous books on “big numbers” contained, unfortunately, not enough big numbers, maxing out around a million. A million might have seemed really good to kids of my generation, but to today’s children, reared on Numberphile videos about Googols and Graham’s number, a million is positively paltry. Really Big Numbers delivers with some really big numbers.

Let’s Estimate: A book about Estimating and Rounding Numbers, by David A. Adler. A cute, brightly illustrated introduction. I grabbed notebooks and pens and made up sample problems to help the kids explore and reinforce the concepts as we went.

How Big is Big? How Far is Far? by Jen Metcalf. This is like a coffee table book for 6 yr olds. The illustrations are very striking and it is full of fascinating information. The book focuses both on relative and absolute measurement. For example,  5’9″ person is tall compared to a cat, but short compared to a giraffe. The cat is large compared to a fly, and the giraffe is small compared to a T-rex. My kids were especially fascinated by the idea that clouds are actually extremely heavy.

Blockhead: The Life of Fibonacci, by Joseph D’Agnes. If your kids like Fibonacci numbers (or they enjoyed the biography of Erdos,) they might enjoy this book. It also takes a look at the culture of Medieval Pisa and the adoption of Arabic numerals (clunkily referred to in the text as “Hindu-Arabic numerals,” a phrase I am certain Fibonacci never used.) Fibonacci numbers are indeed found all over in nature, so if you have any sunflowers or pine cones on hand that you can use to demonstrate Fibonacci spirals, they’d be a great addition to the lesson. Otherwise, you can practice drawing boxes with spirals in them or Pascal’s triangles. (This book has more kid-friendly math in it than Erdos’s)

Pythagoras and the Ratios, by Julie Ellis. Pythagoras and his cousins need to cut their panpipes and weight the strings on their lyres in certain ratios to make them produce pleasant sounds. It’s a fun little lesson about ratios, and if you can combine it with actual pipes the kids can cut or recorders they could measure, glasses with different amounts of water in them or even strings with rock hanging from them, that would probably be even better.

Older than Dirt: A Wild but True History of Earth, by Don Brown. I was disappointed with this book. It is primarily an overview of Earth’s history before the dinosaurs, which was interesting, but the emphasis on mass extinctions and volcanoes (eg, Pompeii) dampened the mood. I ended up leaving out the last few pages (“Book’s over. Bedtime!”) to avoid the part about the sun swallowing up the earth and all life dying at the end of our planet’s existence, which is fine for older readers but not for my kids.

Hope you received some great games and books last month!