My five-year-old had fun playing with foam sheet triangles I cut out—and we even introduced Pythagoras’s theorem for right triangles.
I was inspired by some sample materials offered by Math Expressions (start on page 14 of this pdf). One thing this source recommends is to discuss the difference between “turning” a triangle piece and “flipping” the piece.
Like many parents, I have struggled with how much screen time to allow my child. What I’ve settled on is tightly limiting “junk” TV and videos but allowing moderate amounts of quality videos. At this point I do not merely tolerate screen time; I actively welcome it as an important contribution to my child’s education. Here I want to briefly review several high-quality science series that my five-year-old absolutely loves.
Mystery Doug is a series of over a hundred science videos produced by Doug Peltz and the team at Mystery Science. The videos are available at no charge through YouTube and Mystery Science’s web site. When viewed through the web site, which (I think) requires free registration, the core videos accompany supplementary materials.
Raising a child helps you remember just how hard it was to learn certain things. Most kids pick up counting to ten without much problem (after they learn to talk). But grasping double-digit numbers (and beyond) is a greater conceptual challenge. Now you have to be able to count groups of ten (and then groups of a hundred, and so on) and represent them with digit placement. Later on, multiplication (and then exponents) build on a child’s earlier conceptual knowledge.
I’ve found that a pack of wooden cubes can help illustrate the relevant concepts nicely. When a child can see, for example, two sets of ten blocks, plus three extra blocks, the child can more-readily grasp the number 23. One issue I’ve seen is confusion about the number 23 versus the addition of 2 and 3; the difference is very easy to show with blocks. Of course the blocks are also really good for practicing simple addition and subtraction.
I absolutely love DragonBox math game apps. They make math concepts intuitive and fun. My brother used them for his kids and sang their praises, so I got them too. Here I review the four apps aimed at children ages 4 to 9: Numbers, Big Numbers, Algebra 5+, and Magnus’ Kingdom of Chess. The company also has apps for advanced algebra and for geometry; I’ll buy those down the road when my child is ready for them. The app is available for various devices; here I provide links to Amazon for those with suitable Amazon devices.
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.
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.
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.
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.