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.

Hot off the presses! I wanted to share this 7th grade lesson on the distance of two integers that I recently wrote for the upcoming Math Mammoth grade 7. I'd be interested in feedback, as well! It is written specifically to match the Common Core Standard 7.NS.1 (c) Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. In easier terms... the lesson deals mostly with integers, and teaches that the distance of two integers m and n can be found by taking the absolute value of their difference: | m − n |. Download the lesson here (a PDF file). There is no answer key at the moment -- sorry about that!

(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. ...

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...

I have another neat problem for you to solve. This one should be accessible to middle schoolers on up. The sides of triangles A and B measure 5, 5, 8 and 5, 5, 6 respectively. What is the ratio of the area of triangle A to that of triangle B? Express in simplest a:b form. This problem is original to John Morse. He is a local mathematics researcher/ author/tutor/computer programmer in Delmar, NY, and has written this problem to help learners use creative and problem-solving skills in various ways. And I think this problem can indeed help in that - it can be solved in many different ways. [update - solution follows] I like this problem because there are many ways to solve it and to use it with different grade-level students - such as is already mentioned in the comments. 1) You could use this as a drawing and measuring exercise with 6th or 7th graders who have learned to do compass and ruler constructions. Once they know how to construct a triangle given its three sides (or see here ...

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...

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...

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...

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 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