Homeschool Math Blog

I have been working in a particular section of my HomeschoolMath.net site - the section that has free math lessons. It's been needing some updating for a long time... and finally I got around to it. Websites are like most anything else you own - you have to take care of them. Well, they CAN go on their own (like autopilot) for a while but if you never update them, they will eventually lose traffic and go downhill. I still have lots of work to do... (and I'll do my best to keep cleaning and improving the pages in this section) but here are some updated multiplication and division lessons. They are essentially sample lessons from my books. Enjoy! Multiplication Lessons Grade 3 Multiplication concept as repeated addition Multiplication on a number line Multiplication is commutative Multiply by zero Multiplication word problems Order of operations Grade 4 Multiplying by whole tens & hundreds Distributive property Partial products - the easy way Multiplication...

I feel students need to get grounded conceptually in this topic. So many times, all they learn about decimal division are the rules of how to go about decimal division when using long division, and it becomes an "empty" skill - a skill that lacks the conceptual foundation. So for starters, we can do two different kinds of mental math division problems. Division by a whole number - using mental math Here it is easy to think, "So much is divided between so many persons". 0.9 ÷ 3 is like "You have nine tenths and you divide it between three people. How much does each one get?" The answer is quite easy; each person "gets" 0.3 or three tenths. And... remember ALWAYS that you can check division problems by multiplication. Since 3 × 0.3 = 0.9, we know the answer was right. 0.4 ÷ 100 turns out to be an easy problem if you write 0.4 as 0.400: 0.400 ÷ 100 is like "You have 400 thousandths and you divide it between 100 people; how much does each one ...

This is a tough topic... in a sense. It is not difficult at all, if you just follow the rule given in your math textbook, because the rule is pretty straightforward: To multiply decimal numbers, multiply them as if there were no decimal points, and then put as many decimal digits in the answer as there are total in the factors. The difficulty is only if you try to understand why we have such a rule - where does it come from? Understanding the rule for decimal multiplication is actually fairly simple, because it comes from fraction multiplication. But, I will propose here a little different way of explaining all this. First, look over this decimal multiplication lesson that is taken from Math Mammoth Decimals 2 book. It talks about how 0.4 × 45 is like taking 4/10 part of 45. The same applies if you have 0.4 × 0.9 - you can think of it as taking 4/10 part of 0.9. Can you see now why the answer to 0.4 × 0.9 has to be smaller than 0.9? Or, turn it around: 0.9 × 0.4 is taking 9/10 of 0....

I felt like giving away something again to help all of you who need math lessons... This one is taken from Math Mammoth Division 2 book and is a lesson on the concept of average... meant for initial teaching for 4th-5th graders who have mastered long division. I've written it quite recently, and in fact improved it just last night by adding the bar graph problems into it. (That seems to be the "way of life" with these books: I constantly keep tweaking and improving them as I learn. Which means constant uploading of files here and there... keeping our bandwidth usage large...) The lesson mainly uses word problems, BTW. Please post your comments below; I'm anxious to hear them! Right click and choose save: Average_from_Math_Mammoth_Division_2.pdf

When some quantity changes, such as a price or the amount of students, we can measure either the absolute change ("The price increased by $5" or "There were 93 less students this year"), or the percent change. In percent change, we express WHAT PART of the original quantity the change was. For example, if a gadget costs $44 and the price is increased by $5, we measure the percent change by first considering WHAT PART $5 is of $44. Of course the answer is easy: it is 5/44 or five forty-fourths parts. To make it percent change, however, we need to express that part using hundredths and not 44th parts. this happens to be easy, too. As seen in my previous post, you COULD make a proportion to find out how many hundredths 5/44 is: 5/44 = x/100 To solve this, you simply go 5/44 x 100, which is easy enough to remember in itself. In fact, this is the rule often given: you compare the PART to the WHOLE using division (5/44), and multiply that by 100. There were 568 students o...

This topic is often not understood real well by teachers or students. But we want them to learn, not only the rule, but also the meaning. These ideas can help you to explain and understand division of fractions: 1) The rule of "invert and multiply" applies to division in general - not just to division of fractions. It is a general principle. For example: 20 ÷ 4 I can invert and multiply: 20 × 1/4 = 5. With whole numbers, division can be thought of as making equal parts. When you divide something by 7, you're dividing it into 7 parts, so might as well just take 1/7 part - multiply by 1/7. You can always change division into multiplication with this principle: 18 ÷ 2.51 = 18 × 1/2.51 2) Think of fraction division this way: how many times does the divisor fit into the dividend? You can use this to judge the reasonableness of your answer. For example consider 1 3/5 ÷ 2/3. Clearly 2/3 can fit into 1 3/5 more than two times. 1 3/5 ÷ 2/3 = 8/5 × 2/3 =...