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...

When dividing decimals by decimals, such as 45.89 ÷ 0.006, we are told to move the decimal point in both the dividend and the divisor so many steps that the divisor becomes a whole number. Then, you use long division. But why? Schoolbooks often don't tell us the "why", just the "how". This video explores this concept. Divide decimals - why do we move the decimal point? It has to do with the fact that when we move the decimal point, we are multiplying both numbers by 10, 100, 1000, or some other power of ten. When the dividend and the divisor are multiplied by the same number, the quotient does not change. This principle makes sense: 0.344 ÷ 0.004 can be thought of, "How many times does four thousandths fit into 344 thousandths?" The same number of times as what four fits into 344! So, 0.344 ÷ 0.004 can be changed into the division problem 344 ÷ 4 without changing the answer. Both 0.344 and 0.004 got multiplied by 1000. When we simplify fractions or wr...

In this video I show, first of all, the common shortcut: you move the decimal point in the number as many steps as there are zeros in the number 10, 100, 1000 etc. For example: 2.16 × 10,000 = 21,600.0 It is as if the point moved four steps from between 2 and 1 to between zeros. You can see better examples of this in my lesson Multiply and Divide Decimals by 10, 100, and 100 at HomeschoolMath.net. Then, I also show where this shortcut originates , using PLACE VALUE charts. In reality, it's not the decimal point moving (it's sort of an illusion), but the digits of the number move within the place value chart (to the opposite direction from the way the decimal point seems to "move"). This explanation can really help students to understand the reason behind the "trick" of moving the decimal point. Multiply & Divide Decimals by powers of ten

Denise has made a good post on the concept of division , which I heartily recommend. She deals with a study where Finnish researchers gave this problem about division and remainders to high school students and pre-service teachers: We know that: 498 ÷ 6 = 83. How could you use this relationship (without using long-division) to discover the answer to: 491 ÷ 6 = ? [No calculators allowed!] I really like the question. To solve it, you need to TRULY understand what DIVISION and remainders are all about! Now, let's think about it. Have you ever seen a pattern in division and remainders , like the one below? 20 ÷ 4 = 5 21 ÷ 4 = 5 R1, or 5 1/4 22 ÷ 4 = 5 R2, or 5 2/4 23 ÷ 4 = 5 R3, or 5 3/4 24 ÷ 4 = 6 25 ÷ 4 = 6 R1, or 6 1/4 26 ÷ 4 = 6 R2, or 6 2/4 27 ÷ 4 = 6 R3, or 6 3/4 28 ÷ 4 = 7 29 ÷ 4 = 7 R1, or 7 1/4 30 ÷ 4 = 7 R2, or 7 2/4 31 ÷ 4 = 7 R3, or 7 3/4 Students need to see and do such patterns when they are first learning basic division. The pattern shows that every fourth number ...

I've made two videos on a very important topic (I feel) of fraction division. The two videos show a step-by-step approach for teaching division of fractions conceptually: Start with sharing divisions that divide evenly. For example, 4/7 ÷ 2 can be thought of as "Two people share 4/7 of a pie evenly. How much of the pie does each person get?" Children can figure these out mentally without using any rule. Continue to measurement divisions where we think, "How many times does the divisor fit into the dividend?". Again, the problems should first be designed so that the divisions are even. For example, 4 ÷ (1/2) means "How many times does 1/2 fit into 4?" Or, 3 1/5 ÷ 2/5 means "How many times does 2/5 fit into 3 1/5?" Again, no rule is necessary to solve these - just logical thinking. Next, study measurement divisions with the dividend of one. This leads to the concept of reciprocal numbers . For example, 1 ÷ 3/4 is thought of as ...

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 ...

Let's be reminded first of all that there are two basic "interpretations" of division: 1) Sharing division. In it, you think that 16 / 2 means "If there are 16 beads divided between 2 people, how many does each one get? 2) Quotative division. In it, you think how many groups of the same size you can form. Or, "how many times does the divisor fit into the dividend?" For example, 16 / 2 is interpreted as: "If you have 16 beads, how many groups of 2 beads can you make?" Sharing division is easy to understand as a concept, but it's hard to do without the knowledge of multiplication tables. Just imagine, if a child who doesn't know their times tables is trying to find the answer to the question, "If there are 56 strawberries and 8 people, how many will each one get?" It'll take some guesswork, trying and checking. But quotative division is easy for children to do with the help of manipulatives (or by drawing pictures). Just make...

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

Some recent additions to Math Mammoth Blue Series books: Math mammoth Multiplication 2 This book concentrates on multi-digit multiplication, first explaining what it is based on (multiplying in parts), then practicing the algorithm. also included: order of operations, multiplying with money, and lots of word problems. See sample pages here: (PDF) Contents & Introduction Multiply by Whole Tens and Hundreds Multiply in Parts Multiplying in Columns, Standard Way Error of Estimation Order of Operations Money and Change Multiplying 3-digit by 2-digit Math Mammoth Division 2 This book includes lessons on division, long division, the remainder, part problems, average, and problem solving. See samples: Contents and Introduction Division Terms, Zero and One Finding Parts with Division Long Division 1 Long Division with 4-Digit Numbers Average Divisibility Rules NOTE: Multiplication 2 and Division 2 now replace the earlier book called Multiplication Division 2. Math Mammoth Place Val...

Well today I hopefully have something for everybody. The site DoubleDivision.org shows you an alternative long division algorithm, which takes the guessing away from estimating how many times the divisor goes into what needs divided. Also called 1-2-4-8 division. This is a pretty cool way of dividing! The interactive tool shows you the steps right there for any problem you might come up with. At MathLogarithms.com you can download an ebook by Dan Umbarger explaining logarithm how's, why's, and wherefore's in all detail for students. Great resource for precalculus students. You might also enjoy an alternative way to multiply called lattice multiplication . I did! It seems pretty simple. And lastly, if the math topics didn't interest you, how about my hubby's newest website called Laser-TVs.net ... It's about a totally new way of making TVs using lasers.

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 =...

is 9/56 rational? when converted to a decimal it seems to be never ending and it seems like there's no pattern (at least as far as the calculator shows) Well, relying on a calculator is leading this person astray. Obviously the number is rational - it's a fraction (!); it fits the definition of a rational number. The calculator gives 0.160714286 (to nine decimal digits), but if you use long division and continue it till you get just a few digits more, you get 0.16071428571428..., or 0.160 714285 .

I was updating my Division 1 ebook and thought I'd share a lesson idea. Have you ever tried this kind of exercise when studying remainder in division? 1 ÷ 3 = 0, R 1 2 ÷ 3 = 0, R 2 3 ÷ 3 = __, R __ 4 ÷ 3 = __, R __ 5 ÷ 3 = __, R __ 6 ÷ 3 = __, R __ 7 ÷ 3 = __, R __ 8 ÷ 3 = __, R __ 9 ÷ 3 = __, R __ 10 ÷ 3 = __, R __ 11 ÷ 3 = __, R __ 12 ÷ 3 = __, R __ 13 ÷ 3 = __, R __ 14 ÷ 3 = __, R __ 15 ÷ 3 = __, R __ 16 ÷ 3 = __, R __ 17 ÷ 3 = __, R __ 18 ÷ 3 = __, R __ 19 ÷ 3 = __, R __ 20 ÷ 3 = __, R __ 21 ÷ 3 = __, R __ 22 ÷ 3 = __, R __ 23 ÷ 3 = __, R __ 24 ÷ 3 = __, R __ 25 ÷ 3 = __, R __ 26 ÷ 3 = __, R __ 27 ÷ 3 = __, R __ You should do it with different divisors, and ask the student(s) to find a pattern. Do you know it? Tags: math , elementary , lesson