Homeschool Math Blog

I know the following piece is a bit long, but I REALLY hope you will take the time to read and try to understand the thoughts (if you don't know them already). This is one of the areas where YOU can show your students something about mathematics that is FASCINATING, AMAZING, awesome, mind-boggling!!! ... show them that mathematics is NOT just mundane, mind-numbing manipulation of numbers in calculations. This topic is not extra-curricular; it IS taught in pre-algebra / algebra 1 (real numbers), BUT you can explain some parts of it even to 4-6th graders. This sounds really strange. How could there be different kinds or sizes of infinities? I first encountered this idea in my university studies, and I thought it was absolutely FASCINATING! The video below goes through the basics and explains them well, though really fast. I recommend you pause the video at those points where it goes too fast for you, and "rewind" or rewatch those parts. I will explain some of the ...

I recently created a worksheet generator for Roman numerals . Feel free to use it. Roman numerals is not any major topic in the math curriculum. They are still used in clocks, to number chapters of a book, write year numbers, and such, so students need to study them, even if just briefly. Fortunately it isn't that difficult a topic. Many youngsters might, in fact, be interested in learning about different number systems that have been used in various civilizations over the centuries. I just posted about writing in math class , and this topic would make for an excellent writing project that connects math, writing, and history. Then you wouldn't be doing it just for the sake of learning the math, or the historical facts, but also to practice writing a report or an essay. It's probably the easiest to work into the curriculum if you're homeschooling, because classroom teachers may have to just kind of scurry by the Roman numerals on into the next topic. But even if you'...

Many times students just accept what they are told in math class without much questions; it's perhaps boring, they don't want to take time to investigate and delve deeper, or whatever the reasons. The teacher feeds them with knowledge and they take it in: "Oh, okay, there's such a thing as Pi. Oh, okay, some numbers are irrational." But a question such as this shows that the person is wondering, wanting to understand the material more. So it's a good question! I will divide the 'division' question to two parts. 1) When exact answer is desirable, often we do cannot technically divide. For example, let's take Pi ÷ 2. Well, we just write it as Pi/2 or π/2 and leave it at that. If we can simplify the answer, we do that. For example, √ 15 /√ 5 can be simplified to √ 3 . We could simplify √ 2 /2 this way: since 2 = √ 2 √ 2 , then √ 2 /2 = √ 2 /(√ 2 √ 2 ) = 1/√ 2 . But often the expression √ 2 /2 is left as i...