Homeschool Math Blog

I just updated my article on resources and courses for algebra 1 ... you will find algebra textbooks, video websites, and online courses -- and several of them are completely free. :) In that sense, it's wonderful the times we're living in! No one with Internet access is left without the opportunity to learn this subject.

I stumbled upon a site that has a complete ALGEBRA 1 curriculum with interactive online exercises - all free! I also added that link to my page that lists video websites and online curricula for algebra 1 . I highly recommend you take a look at some of the sites with VIDEOS for your high school students! In today's world, ANYONE can learn math by using videos - and there are lots of them, so if one teacher's explanations don't quite click, then watch some more from other people -  getting a bit wider perspective usually helps. :)

I've had several people ask me if I'm planning to write algebra 1, algebra 2 and other high school math courses. The answer is no. I'm planning to stop at pre-algebra. The main reason is, I've seen some fantastic high school math books other people have written -- people with lots of teaching experience etc. -- and I feel I could not surpass what those people have done. Especially when I don't have lots of experience teaching high school math to students. You see, with elementary math, there exist numerous homeschool math curricula. I've seen most of them and I can tell many of them  are not written by someone who has a good background in math. To write a math text, it really helps to know what concepts the students encounter later on. But beyond that, math is strange in the fact that many of the FOUNDATIONS of math are only taught at university level. For example, the axiomatic foundation of real numbers; logic and the different proof techniques; the whole idea...

I've made a worksheet generator for simplifying expressions , meant for pre-algebra and algebra 1. The expressions include ones where you need to combine like terms (such as 2t − 9 − 6t + 2), use the distributive property (such as 9 − 2(x + 7)), and to multiply and divide monomials, such as 2x 2 · (−5x 3 ) and −4x 2 · y 2 / 3x 5 . To customize the worksheets, you can control the number of problems, difficulty level, range of numbers used as coefficients and constants, the usage of decimals, the amount of workspace, a border around the problems, and additional instructions.

There is a new worksheet generator at HomeschoolMath.net: Free equation worksheets You can make customizable worksheets for linear equations (first-degree equations) for pre-algebra and algebra 1 courses (grades 6-9). You can choose from SEVEN basic types of equations, including one-step equations, variable on both sides, or having to use the distributive property. Please use the quick links below to generate some common types of equation worksheets. One-step equations, whole numbers, with no negative numbers involved One-step equations, whole numbers, the root may be a negative number One-step equations; involves negative integers Two-step equations Variable on both sides and includes parenthesis Challenges; includes rational expressions, such as (x - 5)/6, within the equations I don't claim it is perfect... though I hope I got it working right. Let me know if you see something you'd like changed, and I can try work it in if it is not too big of a chan...

I have just finished making another worksheet generator, this time for evaluating simple expressions (finding the value of an expression) when the value(s) for the variable(s) are given. This is a skill practiced in grades 6-8, and specifically in pre-algebra and algebra 1 courses. The worksheets look kind of like this: Here are some quick links. Refresh the worksheet page to get another of the same kind, until you are happy with the problems & layout. Level 1: usually one operation, no negative numbers in the expressions Level 1: usually one operation, variable may be negative/positive integer Level 1: usually one operation, variables and the constant may be negative/positive integers Levels 1 & 2: variables have positive integer values Levels 1 & 2: variables and constants are negative or positive integers Levels 1 & 2: variables and constant are positive and may have one decimal digit Levels 2 & 3: variables and constants are positive intege...

I have created yet one more free worksheet generator. This one makes problems that give the student an expression in words , such as the quotient of 7t and 5 , the difference of x and 8, divided by 2 , or the quantity 8 plus 2t, cubed , and ask the student to write a mathematical expression to match that. These worksheets suit best grades 6, 7, and 8, including pre-algebra and algebra 1 courses. They specifically address the Common Core Standard 6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers. However, this skill is also practiced in grades 7 and 8, or in pre-algebra and algebra 1 courses. When using the actual generator , you can control the number of problems, workspace, border around the problems, and additional instructions. Here are some quick links for ready worksheets. Refresh the worksheet page to get another of the same kind, until you are happy with the problems and layout. One operation; 12 problems per sheet Two operations...

I've written a comprehensive review of Hands-On Equations , a program that lets students solve linear equations using a balance scale - making it like a "play." I was impressed with this program - it teaches them equations that even include negative unknowns and negative numbers and require the usage of the distributive property. For example, in the end of level III of Hands-On Equations, students can do equations such as 4(x + 2) - 3 = 5x + 2(-x) + 3 But even just going through the first level of the program (first seven lessons) enables students to solve equations such as 4(x + 2) = 2x + 10 Read the  review here!

Photo credit: leojmelsrub Ahmed sent me in this kind of word problem: A tea producer want to market mixed green tea leaves at $14 per pound. how many pounds of high mountain green tea leaves worth $20 per pound must be mixed with 90 pounds of regular green tea leaved worth $10 per pound? I have solve many problems like this one on my blog, but it never hurts to solve some more. This can be solved with algebra, using a chart. I've done that before for similar problems... so if you are reading this, and you feel a bit "rusty" in this area, try to make the chart yourself first, before you read further! For the chart, we also need to choose a variable or several. In this case it is easy:  the unknown is obviously what is asked, or the amount of high mountain green tea. Note also that the cost is always the price per pound times the amount. mountain green regular green the mixture tea leaves tea leaves -----------------------------------------------------------...

Here's a word problem that someone sent me recently: The total number of girls in the combined junior and senior classes is equal to the number of boys in those two classes. If the senior class has 400 students and the junior class has 300 students, and if the ratio of boys to girls in the senior class is 5:3, what is the ratio of boys to girls in junior class? This problem gives a lot of information, and it sounds like it can be solved many different ways. But the first task is to notice what we are given and what we are asked . We are asked about a ratio .  We're given one ratio, and all kinds of totals. There are boys and girls , senior and junior classes. In other words, there are four groups: senior boys, senior girls, junior boys and junior boys. This sounds like it can be solved by setting up some equations and using algebra. To start, you could for example notice the two facts given about the senior class: The senior class has 400 students and the ratio of...

Here are two problems for you to solve... OR to learn from me when I solve them. Both problems are for algebra 1, and use a system of 2 linear equations. By the way, the comments have some wonderful ideas for solving these mentally, without using algebra. So please read them too! Problem: John bought red pens for $4 apiece and blue pens for $2.80 apiece. If John purchased a total of 24 pens for $84, how many red pens did he purchase? Solution: This is a typical problem that will have two variables and two equations. Let r be the amount of red pens he buys, and b be the amount of blue pens he buys. We get our first equation from this sentence: "He bought a total of 24 pens." So, r + b = 24. We get the second equation from the fact that his total purchases were worth $84, and red pens cost $4, and blue pens cost $2.80 4r + 2.8b = 84 Now, just solve this system of two equations using your preferred method. r + b = 24 4r + 2.8b = 84 I will multiply the top e...

I have just finished writing a LONG article on homeschool algebra 1 recommendations and advice . It took me quite many hours to write and research. Questions about what to do for algebra 1 have become one of the "frequently asked questions", so I decided to write down something that I can refer people to, from now on. I realize you may have different opinions and even suggestions for algebra curriculum in homeschool, so if you let me know, I'm willing to look into other possibilities not mentioned in the article.

Photo courtesy of Ben Cooper The speed of a freight train is 14km/h slower than the speed of a passenger train. The freight train travels 330 km, in the same time that it takes a passenger train to travel 360 km. Find the speed of each train. Again, an algebra problem about speeds. Again, we will make a simple table about the two trains. The table will have columns for speed, distance, and time. | distance | speed | time ----------------------------------------------- Freight train | 330 | v | ------------------------------------------------- Passenger train| 360 | v + 14 | Notice the problem says "in the same time". Let's call that t. | distance | speed | time ----------------------------------------------- Freight train | 330 | v | t ------------------------------------------------- Passenger train| 360 | v + 14 | t Of course, the goal is to have an equation in a single variable, not in two varia...

Photo by Caribb Someone sent me this algebra problem: An airplane flew for 6 hours with a tail wind of 60km/hr. The return flight against the same wind took 8 hours. Find the speed of the boat in still water. Initially, this sounds like a trick problem, because you can't know the speed of the boat when all the information given is about an airplane! But, let's assume they meant to ask the speed of the AIRPLANE in still air. This problem has to do with constant speed. Constant speed ALWAYS involves TIME & DISTANCE. And here we have two situations with two different speeds: First the airplane flies over there, with the wind helping. Then it flies back, and the wind is contrary of course. It helps to organize our information in a table, once again. We'll need time, distance, and speed. And remember, speed = distance/time, or distance = speed * time. This time, time is known for both situations. Distance is not, but it is the same distance that way and back (call it d ). ...

Today I wanted to highlight two companies that both offer lots of free high school level math materials in the form of videos. These are real, commercial companies, yet they have chosen to offer the videos online for free. Both have something else they sell, hoping to make some money obviously from that part of the business. The video content can really be of help for all students, teachers, or parents who need additional help with high school math (algebra, geometry, calculus). And since I'm highlighting these two, if you have a topic you have trouble with (such as polynomials or factoring or inequalities) you can even check out videos for that topic in both places. 1) BrightStorm Math . They currently have over 2,000 videos available for free - a free registration is required though. Algebra through calculus. What they are selling is test preparation courses. 2) MathTV.com MathTV.com has over 6,000 free math videos, including some in Spanish. Prealgebra through calculus. What the...

I guess it is time for some more problem solving, since someone sent this question in. Two numbers are in the ratio of 1:2. If 7 be added to both, their ratio changes to 3:5. What is the greater number? We can model the two original numbers with blocks. 1 block and 2 blocks makes the ratio to be 1:2. |-------| |-------|-------| Now add the same thing to both (the 7): 7 |-------|---| |-------|-------|---| 7 The way I just happened to draw these suggests that I could just split the original block in two, and the problem is solved: 7 |---|---|---| |---|---|---|---|---| 7 Here, each little block is 7. The original larger blocks are 14 each. So the original bigger number, which had two larger blocks, is 28, and the smaller number is 14. Check: Their ratio is 28:14 = 2:1. If you add 7 to both, you have 35 and 21, and their ratio is 35:21 = 5:3. Solving the same problem using algebra The two numbers in the ratio of 1:2 are x and 2x. Once 7...

I am hoping you can help me. I can not remember how to solve mixture problems and how to set them up. Examples are as follows: A merchant made a mixture of 150lb. of tea worth $109.50 by mixing tea worth $1.25 a pound with tea worth $.65 a pound. How many pounds of each kind did he use? Organizing the information in a table or chart is usually very helpful in dealing with mixture problems. Other than that, it helps to study several examples and practice solving them yourself. After a while, it gets easier and patterns begin to emerge. The first problem has two unknowns. Let x be the amount of more expensive tea, and y the amount of the cheaper tea (in pounds). In our table, we will look at the amounts of tea (in pounds), price per pound, AND the amount the tea is worth, which is (the amount) times (the price). amount | price per lb | worth ------------------------------------- x | $1.25 | 1.25x ------------------------------------- y | $0.65 | 0...

I got an advance notice of a new games website called Mangahigh.com . It's more than just simple math games, though. These games are designed extremely well, both from mathematical and "enjoyment" perspective. Mangahigh is led by a team of mathematicians, educationalists, and games designers so the games feature commercial-quality gameplay. I wanted to highlight two of the free games here: Flower Power This is the one that I liked most... it's addictive! Grow flowers and harvest them to make money. Practice ordering decimals, fractions, and percentages. The game starts with ordering decimals (daisies), and proceeds into fractions (tulips or roses) and percents. Each time you get a full stem, you need to decide whether to pick the flowers to sell (earn money) or to let them be pollinated and thus get more flowers to grow. Grades 3-8. Save Our Dumb Planet Defend Earth from deadly meteorites using missiles. A team of dumb scientists are on hand to suggest possible trajec...

I will be hosting the blog carnival Math Teachers at Play next week. (You can send in submissions here .) One submission I got about various multiplication tricks or shortcuts got me inspired to write a proof of the particular trick. You could definitely use this in algebra class. First explain the shortcut or trick itself. Then ask students to prove it, or to explain WHY it works, using algebra. You could also explain this to younger students as an additional "neat trick" and let them explore and play with it. THE "TRICK" If a number ends in 5, then its square can be calculated using this "trick" (I like to call it a shortcut because there's nothing magic about it): Let's say we have 75 × 75 => Go 7 × 8 = 56. Then tag 25 (or 5 × 5) into that. You get 5625. Let's say we have 35 × 35 => Go 3 × 4 = 12. Then tag 25 into that. You get 1225. Let's say we have 115 × 115 => Go 11 × 12 = 132. Then tag 25 into that. You get 13,225. Let...

This review has been moved here .