Homeschool Math Blog

As many of you are preparing for school work again, please take note (and bookmark!) these comprehensive worksheet lists that include most math topics for any given grade: Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Best of all, the worksheets are free! They are dynamically generated so you get a different one every time you click on the link. You can also save them to your device and edit them in your favorite word processor. Also, I recently formatted the above pages so they look good on mobile devices.

(This is an older post that I have revised plus added a video to it. ) In this article I want to explore some ideas for using MENTAL math in calculating percent s or percentages. I have also made a video about this topic: And here are the ideas: Find 10% of some example numbers (by dividing by 10). Find 1% of some example numbers (by dividing by 100). Find 20%, 30%, 40% etc. of these numbers. FIRST find 10% of the number, then multiply by 2, 3, 4, etc. For example, find 20% of 18. Find 40% of $44. Find 80% of 120. I know you can teach the student to go 0.2 × 18, 0.4 × 0.44, and 0.8 × 120 - however when using mental math , the above method seems to me to be more natural. Find 3%, 4%, 6% etc. of these numbers. FIRST find 1% of the number, then multiply. Find 15% of some numbers. First find 10%, halve that to find 5%, and add the two results. Find 25% and then 75% of some numbers. 25% of a number is 1/4 of it, so you find it by dividing by 4. For example, 25% of 16 is 4. ...

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 ...

Problem: If a:b = 1:3 and b:c = 3:4, find a:c. Two ratios are given, third is to be found. This is very very simple. The picture shows the two given ratios as blocks. We can see that a is one block and c is four blocks, so the ratio a:c is 1:4. You don't need an image for that, of course, since the original ratios are so easy. If a:b=1:3 and b:c=3:4, b being the same in both cases, we can write the ratio a:b:c as 1:3:4 right off. But what if the numbers weren't so friendly? What if it said this way: If a:b = 1:3 and b:c = 5:7, find a:c. This is solvable in various ways. I'll use equivalent ratios, in other words change the given ratios to equivalent ratios until we find ones where the b 's are the same. In the first ratio, 1:3, b is 3. In the other ratio, 5:7, it is 5. We can make those to be 15 by changing the ratios to equivalent ratios - which is done in an identical manner as changing fractions to equivalent fractions. 1:3 = 5:15 and 5:7 = 15:21. Now the ratio o...

Updated with solutions! Today I want to highlight a square problem I saw at MathNotations . I hope Dave Marain doesn't mind me showing this picture and problem on my blog... I have no problem acknowledging it's from his blog. I COULD just tell you all to "go read it at Dave's blog.... BUT I don't feel that's the best way, IF I want you to think about this. I can just guess that most of the folks would feel too lazy to click on the link and go read it there (would you?). So I want to show it here. Figures not drawn to scale! And this is important! Now here's the question: Does the given information in each diagram guarantee that each is a square? If you don't think so, your mission is to draw a quadrilateral with the given information but that clearly does NOT look like a square. The IDEA is to make our students THINK LOGICALLY, or practice their deductive reasoning skills. A great little problem. The answers: Figure 1 is not necessarily a square. The u...

Dave at MathNotations had an interesting ratio problem : In Virtual HS, the ratio of the number of juniors to seniors is 7:5. The ratio of (the number of) junior males to junior females is 3:2. The ratio of senior males to senior females is 4:3. What is the ratio of junior males to senior females? He asked if it can be solved using "Singapore" style bar model. I'm not sure if this is exactly how they'd do it, but this is how I'd do it... so here goes. After I made the diagrams, I soon saw that Dave's numbers are two awkward; the bar diagram drawing would get too messy because we'd need to divide it into too tiny parts to see anything. BUT... you probably know about the PROBLEM SOLVING STRATEGY called "solve an easier problem". My agenda is therefore: show how to solve a few related simple ratio problems using the bar diagram solve a variant of the original problem (with friendly numbers) solve the original problem. 1. Here's a bar diagram re...

I failed to publish this the other day since Blogger was acting up. I'll try it now. A rectangular kitchen table is three times as long as it is wide. If it were 3 m shorter and 3 m wider it would be a square. What are the dimensions of the rectangular table? 1) You can solve this using algebra: set width to be x, the length is then 3x. We know these two will be equal if the former is increased by 3, and the latter is decreased by 3: x + 3 = 3x - 3 2x = 6 x = 3. The dimensions are 3 and 9. But since this is supposed to be a 6th grade problem, surely we can find another way to solve it, as well. 2) Think of the two quantities length and width as just numbers. If you reduce one by 3, and increase the other by 3, they will "meet" or be the same. Below, I've drawn the two numbers as lines; you could use bars. length |---------------------------------| width |----------| If I decrease the length by 3 and increase the width by 3, they'll be equal: length |----------...

The main struggle with integers comes, not with the numbers themselves, but with some of the operations. There seem to be so many little rules to remember (though less than with fractions). Some good real-life MODELS for integers are: - temperature in a thermometer - altitude vs. sea depth - earning money vs. being in debt. When first teaching integer operations, tie them in with one of these models. I'll take for example the temperature. Assuming n is a positive integer, the simple rules governing this situation are: * x + n   means the temperature is x° and RISES by n degrees. * x − n   means the temperature is x° and DROPS by n degrees. It's all about MOVEMENT — moving either "up" or "down" the thermometer n degrees. For example: 6 − 7 means: temperature is first 6° and drops 7 degrees. (-6) − 7 means: temperature is first -6° and drops 7 degrees (it's even colder!). (-2) + 5 means: temperature is first -2° and rises 5 degrees. 4...

This is what I've been working on behing the scenes so to speak... and now some of it is finally come to the fruition and is available to the public: (now comes the sales pitch as was made up by my dear husband) Meet Mrs. Maria Miller's Most Marvellous & Magnificent Math Mammoth Modified Modern Mathematics Meticulous Multiplication Methodology Major Madness - It's Mmm Mighty Majestic! Ok, back to normal... I have been making worksheets for SpiderSmart, Inc. tutoring company and the 6th grade ones are now available as two downloadable ebooks at: Math Mammoth Grade 6 Worksheets These aren't your run-of-the-mill worksheets, but more like carefully hand-crafted quality problem sheets, with varying problems that both emphasize understanding of concepts and computation. The worksheets do NOT have explanations and therefore best suit math teachers or others who can explain the mathematical subject matter to the student(s). I will later on (next year) be making more workte...

I was going to write about Euclid but this came up. Someone submitted a review of a math program called RightStart mathematics to my site. While browsing that site, I found out they offer a separate geometry program which looked really good: See, many students have great problems with high school geometry. I've written an article Why is high school geometry so difficult? about that already. One of the remedies for that is to do things right BEFORE high school: teach true geometry and DRAW - don't spend all your time calculating areas and volumes from grades 3 till 8. So now I have stumbled upon a geometry program for middle grades that seems to be just that: emphasis is on drawing. Check it out: RightStart Geometry program . I haven't seen all of it, but based on the example pages , it looked good. It's $57 for the whole package. Categories: geometry