Homeschool Math Blog

How about some practical tips for mental math ? Please share this article on your FB page or other social media (assuming you like it), because I feel it can benefit all kinds of people, not just moms and dads and teachers. :)

This is a pretty amazing performance of "mathemagic" – calculating things in one's head by Arthur Benjamin. He not only can calculate but also ENTERTAIN, so this video is sure to captivate you! I enjoyed it a lot, and my children watched it multiple times in a row. :) I also posted the video on my website with some more commentary: Mental math "mathemagic" with Arthur Benjamin

Number talks are short discussions among a teacher and students about how to solve a particular mental math problem. The focus is not on the correct answer, but on all the possible methods of finding the answer. Each student has a chance to explain their method, and everyone else will learn from other people's methods! To start a number talk, the teacher gives the students a SHORT math problem to solve — but the students are not allowed to use a calculator or paper & pencil. The idea is to solve it in one's head! For example, you could ask students to solve 5 × 18 using mental math. Read more here - and see a great video by Jo Boaler. This is a "tool" you can't afford to miss as a math teacher!

Can you help me solve this question? Jayne is given £5 for her birthday. She spends 30% of it. How much of her birthday money does she spend? And... Is my method correct for this question? 100-30=70 70/5=14 1.40 No, the asker's method is not correct. In fact, it looks to me like she is randomly doing operations with numbers... To find 30% of something, one MENTAL MATH method that I like is to first find 10% of that something. Now, 10% of something is of course 1/10 of it. And to find 1/10 of it, just divide that by 10. So, we divide £5 by 10 to find 1/10 of £5. It is £0.50. That's 10% of the total. And 30% of the total is three times as much, or £1.50. So Jayne spent £1.50. See also this video that explains how to find percentages using mental math:

(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. ...

Someone asked me, How many times does 3/4 fit into 15 6/8? Here are two ways to solve this: 1) These numbers look awkward, but if I changed them to easier ones, for example "How many times does 2 fit into 834", then we'd all soon realize that we need to use DIVISION. So the original problem is solved by fraction division: 15 6/8 ÷ 3/4 Are you ready? Remember how to divide fractions? 2) But wait a minute! These numbers aren't so difficult after all... because 6/8 equals 3/4. Let's use this thinking cap of ours - mental math. 3/4 goes into 1 1/2 two times. Doubling that, we find 3/4 goes into 3 four times. And so to 15... fives times that: 3/4 goes into 15 4 × 5 or 20 times! And, of course 3/4 goes into 6/8 exactly one time. So all total 3/4 goes into 15 6/8 exactly 21 times. No leftovers. And that was easy! On another note, Denise in Illinois has made up a mnemonic poem for kids to remember better the "invert and multiply" rule .

Some children might be delighted to learn math 'tricks' - curious ways to do calculations such as multiplying 2-digit numbers. The 'tricks' do not contain any magic but are based on solid mathematical principles. For example, to subtract any number from 1000 or 10,000 or any power of ten... just subtract from 999 or 9999 etc. and add 1. Subtracting 10,000 - 2,596 with the usual method in columns, you will get into lots of borrowing over zeros... and end up having a row of nines to subtract from - except in the ones column where you have 10. So 10,000 - 2,596 is quickly done by looking at each digit's difference to 9 - except in the case of one's digit, when you will subtract from 10. The result: 7,404. Another 'trick' is called vertically and crosswise and applies to multiplication. It can easily be proven to work using simple algebra. But it is a nice little mental math method that can impress kids. Read more about that trick here . You can also practic...

Would you say that students' understanding of percent is sometimes - or often - hazy? Find the number of which 79.5% is 101. Often, solving these kinds of problems is taught with the idea that you "translate" certain words in the problem into certain symbols, and thus build an equation. Solving that way, the unknown number would be Y, "of" would be multiplication, and "is" corresponds to '='. We'd get: Y × 79.5% = 101. 0.795 Y = 101 Y = 101/0.795 = 127.044025157 I'm a bit leery of this method, as it's so mechanical. What if a question comes that is not worded exactly as the ones in the book, and the student just gets stuck? Or it is worded so that the student gets misled and calculates it wrong? So while this idea is great and works, it is also necessary for students to understand the concept of percent well. In the above problem, we are to find a number so that 79.5% of that number is 101. ( Obviously, then, the number itself is ...

The example of decimal division I found recently made me think some more about how we teach our students the use of mental math. For example, how would you want your (current or future) high schooler to find the answer to 5 × 24 or maybe 6 × 71 and such like? a) I wish he'll use pencil and paper, put 5 under 24 and use the algorithm. b) I wish he will go 5 × 20 and 5 × 4 in his head and add those. c) I wish he grabs the calculator. d) I wish he asks me. Also think WHICH of the four options is the most efficient 'tool' for finding the answer? After all, just like a carpenter, a good problem solver knows which tools are available and which one is the best to use for a particular task. Now let's back up in time when the student is in third grade. How are we encouraging third graders to do the same problem? As you may realize, kids usually spend lots of time mastering the multiplication algorithm (the pencil & paper method) and go thru tons of practice probl...

Recently I saw this kind of problem used as an example; it went something like this: We're in the grocery store. We're going to buy 6 watermelons, and divide each of them into fourths. How many slices will we get? I want you to think hard :) ... and find the answer to that question. Also note HOW you found it... Got it? Now listen how it was solved in this particular mathematics tutorial: They changed a fourth into its decimal equivalent, 0.25, and proceeded to divide 6 by 0.25 - going thru the motions of multiplying both dividend and divisor by 100 before getting to the long division of 600 ÷ 25, and then finally onto the answer!!! And this was for 7th grade math. Sad! What happened to mental math? What happened to solving problems with the most efficient and quickest way? Well here's a suggestion for an example instead of that one: You are considering buying notebooks for your school which are $0.42 each. Your budget is $200. How many notebooks can you buy? You can solve ...

Math in your life- I'm not talking about schoolwork or teaching now, but everyday situations where you've used math. I'd like to encourage you to share those 'math' moments with your child. It shows him/her that math is NOT a 'hateful' activity done in school, but something useful and normal ! For example, cooking is an excellent example. Kids will be enthusiastic to do all kinds of measuring while cookies are in the works! (Now I hope you aren't one of those who will rather find another recipe than figure out the half or 3/4 or 1 1/2 of the recipe). My hubby said he uses math when designing a website layout. He has to figure out what should the table column widths be, if the screen resolution is 600x800, and he wants this wide cell-padding, this wide borders, this wide cell-spacing. Another example: A few years back I was interested in the essential omega-3 fat alpha-linolenic acid (ALA), and figured out how many ounces of flaxseed would one need to g...