Fraction Wheels Foster Intuitive Learning

My five-year-old is not ready to add mixed fractions. But, by using a fraction wheel, he is already beginning to grasp, intuitively, how fractions work.

Just today, I got out the fraction wheel pieces, and he said he wanted to “build them” himself. He put a half-piece together with a third-piece, then tried to complete the circle. He tried a fourth-piece—too big. Then an eighth-piece—too small. He could see right away, once he tried it, that a sixth-piece added to a third-piece equals a half. He didn’t need to know how to formally convert one-third to two-sixths for this, but he could see visually that one-third equals two-sixths. He also immediately saw that three sixth-pieces are a half and six of them are a whole.

Obviously I’m not going to try to teach him formal fraction conversions until he has a better handle on the four basic operations (addition, subtraction, multiplication, and division). But I think this early work with the fraction wheel set will put him in good shape to grasp adding and subtracting complex fractions later on.

I know there are some really well-crafted fraction wheels with little handles on the pieces; the disadvantage of these is that you can’t stack pieces on top of each other.

My wife and I created a simple fraction wheel set that you’re free to download. For best results, print these out using different colors of paper and then glue them to card stock or cardboard, or just print them out on cardstock if your printer can handle that. Or, as I discuss in my post about triangles, you can use foam sheets, although you probably won’t be able to print the patterns directly onto the foam sheets.

Or you can just buy a set from Amazon (paid link), which is what I did.

Core Knowledge Free Materials for Grades 1 to 8

As discussed in my posts on preschool and kindergarten materials, Core Knowledge offers an enormous amount of educational materials for preschool through eighth grade.

I’m going to provide fewer links for the material for grades 1–8 than I did for preschool and kindergarten. I’ll still walk you through the material and link to the student readers that I find valuable.

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Core Knowledge Free Kindergarten Materials

I’m a big fan of Core Knowledge’s dozens of student readers, free as pdf downloads. But the materials are harder to use (at least for homeschoolers) at the preschool and kindergarten levels. Earlier I compiled relevant preschool materials; see my related post. Here I’ll walk you through the kindergarten materials and include relevant links to Core Knowledge. See also my most on materials for grades 1–8.

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Core Knowledge Free Preschool Activities

You may be aware of Core Knowledge, the educational program started by E. D. Hirsch Jr. Various charter schools, for example, base their programs on Core Knowledge (not to be confused with Common Core). And you may be aware that Core Knowledge offers an enormous amount of K-8 learning materials online at no cost to the user.

Last year I started downloading the student readers in pdf form. Volumes cover history (such as Ancient Greece and Rome), science, and literature. These are amazing resources especially for homeschooling families on a budget. I have an old Kindle reader (the kind with the button keyboard) dedicated to such educational books.

What I didn’t realize until recently is that the preschool level offer a lot of great material presented as “activity pages” rather than as “readers.” These offer content for parents to read with their children as well as simple activities.

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The Place for Bob Books

Great literature Bob Books are not. But that’s not their purpose. Their purpose is to hold children’s hands during their first journeys into reading. And for that they’re great.

These very-short books turn simple words into simple sentences with just enough story and humor to hold a child’s interest for the few minutes it takes to read one of them.

I picked up Sets 1–3, plus a kindergarten set, used via eBay. For months they sat on a shelf. Several times I tried but failed to interest my four-year-old in them. I think their usefulness is all about timing.

My child, now five, has learned the alphabet and can recognize and write lower and upper case letters. Most of the time he associates the correct sound with a letter, although he still sometimes mixes up the similar-looking letters d, b, and g. He is just now gaining the ability to string together the sounds of letters into words. I am reminded of how hard this can be in English (as opposed to, say, Spanish), what with all the different possible letter sounds—we pronounce (for example) “one” the same as “won.” Bizarre.

I tried again to interest my child in a Bob Book—and this time he was receptive. In two days he’s read the first four books. I figure we’ll aim to read two or three per day until we finish. Then if he wants to start over, great; if he wants to be done, also great. I consider the Bob Books as a transition to him reading for himself his first “real books.” Once the Bob Books have served that purpose I’ll pass them along to the next child.

So, to summarize my advice: Get a a few Bob Books (paid link) (or something comparable) when your child is learning the alphabet and the letter sounds. Check in with your child every week or so to see if the books seem interesting. When and if they do, go for it. But don’t overdo it; I’ve found that reading through a single book in one sitting is actually fairly taxing for the child, though it takes but a few minutes. When the books no longer hold the child’s interests, move on to something more substantive.

Learning about Human Progress

I’m a big fan of Jason Crawford’s work for “The Roots of Progress.” Crawford’s main theme is that people have improved their lot dramatically through science, technology, and the underlying causes of those developments. So why not make more of an effort to teach children about human progress? In a July 27 Interintellect discussion that Crawford hosts, several educators weigh in on the topic.

I agree with Lisa VanDamme, founder of VanDamme Academy and one of the presenters, that the project of teaching children about human progress quickly can run into problems. First, she notes, “progress” is not a primary field unto itself, at least in terms of K-12 education, although aspects of it properly integrate with history and science (which are both major fields of study). Second, the proper aim of education is to enable children to ably pursue their own values and live their own lives, not to convince children to embrace certain conclusions (such as “progress is good”). That said, as VanDamme also notes, well-educated children typically will turn out to be the sort of people who do appreciate human progress (among many other things).

Kyle Steele (one of VanDamme’s associates) adds a great point: Properly, children have lots of room to explore their interests outside of their core education. For example (as several speakers discuss), a child keenly interested in music might want to limit time spent learning core subjects and maximize time spent practicing a musical instrument. Similarly, a student keenly interested in science, technology, or entrepreneurship might want to spend disproportionate time in those areas. So, for example, Crawford organized “Progress Studies for Aspiring Young Scholars.” This fits perfectly well as an extension or special-interest program with the sort of core education that VanDamme has in mind.

The entire discussion is fascinating. (Those interested in learning more about Crawford’s project also can check out my podcast discussion with him.)