Homeschool Math Blog

I have recently had the pleasure to add Make It Real Learning workbooks to my site. These books contain real-life math activities with real-life data, companies, and situations. They are written by Frank Wilson. Arithmetic I Fractions, Percents, and Decimals I Linear Functions I Calculus I Periodic and Piecewise Functions I Some examples of the topics included in these activities are: cell phone plans, autism, population growth, cooking, borrowing money, credit cards, life spans, population growth, and music downloads. But there are many more, more than I can list here. As students work through the problems, they can use the math skills and concepts they have learned in their math curriculum (such as the concept of average or graphing), and apply those to a situation from real life. Each activity-lesson in the book contains several questions about the situation, starting with basics and going into more in-depth evaluations, and should be adequate for one-two complete class periods. W...

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...

The word "percent" means "per hundred", as if dividing by hundred — a hundredth part of something. We treat some quantity (say 65 or $489 or 1.392 or anything) as "one whole". This "one whole" is then divided to hundred equal parts in our minds, and each such part is one percent of the whole. If the "one whole" is 650 people, then 1% of it would be 6.5 people (if you have a practical application, you'd need to round such an answer to whole peoples of course). If the "one whole" is $42, then 1% of it is $0.42. Also, 2% of it would be $0.84. So to find 1% of something, divide by 100. To find 24% or 8% or any other percentage, you can technically first find the 1%, then take that times 24 or 8 or whatever is your percentage. For example: To find 7% of $41.50, first go $41.50/100 to find 1% or 1/100 of $41.50, then multiply that by 7. But this is the same as (7/100) x $41.50, and 7/100 is 0.07 as a decimal. ...

Updated with an answer... see below I'm continuing to catch up after vacation, and spotted a good discussion about problems with percent, at MathNotations . (via Let's Play Math blog). Here's a problem to solve, first of all: There are 20% more girls than boys in the senior class. What percent of the seniors are girls? The answer is NOT that 40% are boys and 60% are girls... You see, let's say there were 40 boys and 60 girls, 100 students total. If there are 40 boys, then 20% more than that would be 40 + 4 + 4 = 48 girls and not 60! Try solve it. I'll let you think a little before answering it myself. Don't just rush over to the Mathnotations blog either! Use your thinking caps! I've already given you a big hint! Update: You can easily solve this problem by taking any example number for the number of boys. Like I did above, if you have 40 boys, you'd need 48 girls and there'd be 88 students total. What percent of the seniors are girls then? It'...

Someone asked, how can you use models to multiply decimals? Learning to multiply decimals, I feel, is built on students' previous understanding of multiplying whole numbers and fractions. So models wouldn't necessarily be the focus, but instead relating decimals to fractions first, and learning from that. Multiply a decimal by a whole number Of course, when multiplying a decimal by a whole number, you could use the same models as for fractions: say you have a problem 2 × 0.34 You can use little hundredths cubes, or draw something that's divided to 100 parts. BUT you can also just use fractions, and justify the calculation that way: 2 × 0.34 = 2 × 34/100 = 68/100 = 0.68. OR you can explain it as repeated addition: 2 × 0.34 = 0.34 + 0.34 = 0.68. I employ that idea in these lessons: Multiply mentally decimals that have tenths and Multiply decimals that have hundredths Multiply a decimal by a decimal When students are learning to multiply a decimal by a decimal, th...

Just as of today, I got online and available the new Math Mammoth Grade 7-A and 7-B worksheets collections . These pre-algebra sheets contain problems for beginning algebra topics such as expressions, linear equations, and slope - plus your typical 7th grade math topics such as integers, fractions, decimals, geometry, statistics, and probability. You will find the problems are very varying as these worksheets have been created one by one (not script made). Go download and enjoy the free sample sheets! - including a Percent Fact Sheet .

I'm just going to solve here on the blog another math problem that was sent in to me... Hopefully it helps some of you to learn how to solve problems (you can let me know !) A man travelled 8 miles in the second hour. This is 1/7 times more than during the first hour, and 1/4 times more than he travelled during the third hour. What is the total miles he covered in three hours? In this problem, it is easy to get "deceived" and think that you'd just go 1/7 × 8 miles or something like that. But think first; did the man cover MORE miles during the first hour than during the second hour? Yes; it says plainly that the 8 miles was 1/7 times MORE than what he covered during the first hour. Is that 8 miles a LOT more, or a LITTLE BIT more than what he traveled during the first hour? It's 1/7 times more, so it's a little bit more. So simply mark as x the miles covered during the first hour. Then, 8 miles = 1 1/7 x It's not 1/7 x, but 1 1/7 x, or 8/7x. If you put dow...

Recently I answered a question about teaching integers on an email list, and decided to post all that on my site as well. Also, I spent a few hours making downloadable fact sheets about all integer operations - these are free. The sheets try to include quite a bit about "why" the rules for adding, subtracting, multiplying, dividing integers work. Teaching integers Enjoy! Also I will answer here a question left on my site... there was no email address left so I couldn't answer via email. how do you do this problems: elizabeth bought 3 1/3 pounds of tomatoes for $2.50. how much did she pay per pound? Prices per pound are always given in [dollars per pound] or [dollars / pounds ]. This gives you the idea: you need to take the dollar amount and DIVIDE it by the pounds. $2.50 ÷ 3 1/3 lb = $2.50 ÷ 10/3 lb = $2.50 × 3/10 = $7.50/10 = $0.75 per lb.

It's very good to know something about the most common misconceptions students might have. The website CountOn.org has 22 examples of them at http://www.counton.org/resources/misconceptions/ . Here are some examples: #2. Multiplication always increases a number... is that really so? Well, to small kids it appears to be so - but only if you just try whole numbers. Take 10 for example. If you multiply it by 2, 3, 4, 5, etc., it does get bigger. But all you have to do is multiply it by a fraction less than 1, or by a negative number, and 10 does not get bigger... 1/2 x 10 is 5. 1/4 x 10 is 2.5. -3 x 10 is -30. We must remember that repeated addition is not the only meaning or definition for multiplication . That's what it is for whole numbers. For fractions, 1/3 x 12 is better understood as 1/3 of 12. #3. As 1 x 1 = 1, then 0.1 x 0.1 = 0.1. This one was new to me. Quite curious. A child might think of 0.1 as some kind of "unit" like 1. But seriously, 0.1 is one tenth....

Resources These are some of the links I've added to my site recently. Maybe there's some that interest you. Mathopenref.com Free online textbook for high school geometry; not finished. GapMinder Visualizing human development trends (such as poverty, health, gaps, income on a global scale) via stunning, interactive statistical graphs. This is an interactive, dynamic tool and not just static graphs. Download the software or the reports for free. How to write proofs A 12-part tutorial on proof writing. Includes direct proof, proof by contradiction, proof by contrapositive, mathematical induction, if and only if, and proof strategies. Money Math Crystal clear tutorial on interest. Graph Mole A fun game about plotting points in coordinate plane. Plot points before the mole eats the vegetables. All sorts of sites to explore! But if those didn't fit your bill, if you're in need of a game or tutorial about specific math topic, check my link lists of online math resources; they...

I get lots of questions, seemingly, about sine. It's because one of my pages with that topic ranks well in search engines and has the comment box in the end. Here's another one: how to measure right triangle sine? Well, you don't measure the sine per se. You measure certain sides of the triangle, and then calculate the sine. For example, in this picture, if we want to find the sine of the angle α, we measure the opposite side and the hypotenuse. They are already given as 2.6 and 6 units. Then just take their ratio: 2.6/6 and that's your sin α. You might also enjoy reading my lesson about sine in a right triangle . Tags: math , trigonometry

A little bit of math for you today. Usually kids encounter these words in algebra or maybe pre-algebra. But, they use the principle long before that, say in 2nd or 3rd grade. Did you know where? The distributive property says (as it's stated in algebra class) that a (b + c) = ab + ac. It's true for all real numbers - including negative ones, so it follows it's true for subtraction too: a (b - c) = ab - ac. We use this principle often when multiplying numbers. For example, do in your head 7 × 21. Most people take 7 × 20 and 7 × 1 and add those. In other words, you 'broke down' 21 to two parts and multiplied the parts by 7 separately: 7 × (20 + 1) = 7 × 20 + 7 × 1. How about 8 &times 98? Aren't you tempted to go 8 &times 100 and subtract 16? 8 × (100 - 2) = 8 × 100 - 8 × 2. Studying multiplying 2-digit numbers is THE time to talk about this idea in detail. 37 ×   4 Here, you should explain that this algorithm (or procedure) ...

I've finally posted the review of RightStart Geometry course on the site. I think you will want to check it out - this course is excellent, absolutely great! It teaches geometry with a "hands-on" method, in other words, the course includes A LOT of drawing. And you're using a drawing board, a T-square, and triangle rulers to do your drawing on the worksheets. It teaches geometry in a way I think geometry should be taught and learned. You see, many school books sort of reduce geometry to a) learning vocabulary (what is obtuse angle or parallel lines or vertical angles or diameter etc. etc.) b) learning how to calculate perimeter, area, and volume... ...but there's not much reasoning. RightStart Geometry has that reasoning part in it - plus much more, such as proofS of Pythagorean theorem, drawing all sorts of interesting designs and figures, midpoint theorems, tessellations, fractals... I've tried to do something similar in a small scale in my own geometry ebo...

Since we've been talking about coherent & focused curriculum lately, and someone asked about scope and sequence, I decided to make a chart. It's just a rough GUIDELINE and it only includes the major topics. The idea is to show the major focus on each grade and how it changes over the years. And I don't mean that you wouldn't teach a first grader about 1/2. The chart only deals with the major focus for the topic. And here you can find more details: Scope and sequence suggestion (grades 1-7) Tags: curriculum , math