Probability, Adding Complements and Divisibility Rules

What do the following things have in common: probability, adding complements and divisibility rules? These are all new math worksheets at Math-Drills.com!

Probability

Probability is actually a new section on the Data Management and Probability Worksheets page even though it has had "probability" in its name for quite some time. We decided to start with some probabilities with dice and spinners and included several options for both. For the sum of two dice probabilities worksheets, you can choose between a version without a helpful table or with a helpful table. For the spinners, we've included worksheets with between 4 and 12 sections. Instead of using colors, we used numbers on the spinner as we know many people have black and white printers and it also helps to distinguish between the sections, especially if there are 12 sections on a spinner.

Since it is Halloween season, we thought a Halloween probability math worksheet would be a good idea, so we made a set of them asking students what the probabilities are of getting certain candies while trick-or-treating. We also added a slightly more difficult version where students have to predict how many candies of each type they would get based on how many houses they visited.

Adding Complements

Adding Complements is an interesting skill as it challenges students to find or know what numbers add together to make certain complements. The most common ones are powers of ten (e.g. 10, 100, 1000) and powers of ten minus one (e.g. 9, 99, 999). This has all sorts of wonderful benefits in a student's repertoire of math skills. For example, in subtraction, using a counting up strategy is so much easier if students are familiar with complements of powers of ten. In the question, 1532 - 437, a student can find the 1000 complement of 437 and add it to 532 to find the answer. They could find the difference in other ways too, but knowing the 1000 complements makes this a two-step problem and can be done mentally. In money management, giving change for, say a 10 dollar bill, is made much easier knowing complements because it is simply a matter of finding the 1000 complement for the money amount without the decimal. For example, what change would you get from a 10 Pound note if the total bill was £4.54? Since the 1000 complement of 454 is 546, the change would be £5.46.

Divisibility Rules

Divisibility rules are sometimes overlooked as some people don't see much value in them, but they certainly do help students to understand numbers and patterns much better. Is there not some little joy or fascination in being able to tell whether a 10 digit number is divisible by 4 just by looking at the last two digits? In practice, divisibility rules are quite useful in things like prime factorization, finding factors of a number, long division, and fractions (e.g. simplifying fractions).

To help you break up this skill a little, we've grouped the divisibility rules into several sets. First, we put 2, 5 and 10 together. For the uninitiated, we've included the divisibility rules below where you will see that 2, 5 and 10 are quite straight-forward and only require looking at the last digit of the number. 3, 6 and 9 is our second group where you have to do a little more work to figure out whether a number is divisible by one of these.... but not too much work. The final group is 4, 7 and 8. We included 4 here only because it needed a place to go and we thought we would keep each set with three numbers. The 7 and 8 are normally the difficult ones, and these can be assessed with a calculator too if your students have great difficulty with the rules.

You might also notice we made some versions with random divisibility rules from 2 to 10 on each page. Just find the ones that work for your lesson.

Divisibility of 2, 5 and 10

A number is divisible by 2 if the final digit (the digit in the ones place) is even. Numbers ending in 0, 2, 4, 6, or 8 therefore are divisible by 2.

A number is divisible by 5 if the final digit is a 0 or a 5.

A number is divisible by 10 if the final digit is a 0.

Divisibility of 3, 6 and 9

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 285 is divisible by 3 because 2 + 8 + 5 = 15 is divisible by 3.

A number is divisible by 6 if it is divisible by both 3 and 2 (see above rules).

A number is divisible by 9 if the sum of its digits is divisible by 9. For examples, 285 is not divisible by 9 because 2 + 8 + 5 = 15 is not divisible by 9.

Divisibility of 4, 7 and 8

A number is divisible by 4 if the last two digits of the number is divisible by 4. For larger two digit numbers, you can also take the 100 complement to make it a little easier. For example 694 is not divisible by 4 since the 100 complement of 94 is 6 and 6 is not divisible by 4. (Look at that, we found a great use for 100 complements!)

For 7, there are a couple of strategies to use, but since we don't know one off the top of our heads, we're going to send you to Divisibility Math Tricks to Learn the Facts instead of just copying someone else's work.

A number is divisible by 8 if the last three digits are divisible by 8. This is the standard rule which can be a little sketchy for larger numbers, like who knows if 680 is divisible by 8? Because of this, we offer our Math-Drills.com solution which requires a little arithmetic, but can be accomplished quite easily with a little practice. As you know 8 is 2 to the third power, so we thought if you could divide the last three digits of a number by 2 three times, it would be divisible by 8. 680 ÷ 2 ÷ 2 ÷ 2 = 340 ÷ 2 ÷ 2 = 170 ÷ 2 = 85. We have a winner! 680 is indeed divisible by 8.

We hope you enjoy our latest math worksheets and encourage you to send us a request if there is something that you would like to see on the website.

Social Pages and Privacy

Over the years, Math-Drills.com has tried a number of social platforms and we've kind of settled on a few.... for now... until something else comes along. We thought you might like to learn about our efforts to keep you informed through social media, and maybe, just maybe, teach you a thing or two about your online privacy. First of all, here in a particular order (from our most recommended to our least recommended), is what we log into.

Blogger is our preferred venue for a number of reasons. First, you can read our posts in three different ways: by signing up for our email list, by subscribing to our blog feed, or by visiting the actual blog itself. Most of you, will actually be reading this in an email or via a feed rather than on the actual blog website. One huge advantage of blogger, is that we don't have to limit our posts to 140 characters or silly things like that. We can explain, show and discuss our posts thoroughly. We can also post something in 140 characters or less if we choose to. If you read our blog, you will know about all updates and get (hopefully) interesting news and other posts. Reading our blog does not require you to register, have an account or otherwise give out any personal information if you visit the online version at:

http://blog.math-drills.com/

Pinterest was very new to us a few months ago, but we saw the huge potential in this social sharing site that it is now our number two pick for the most useful way to enhance Math-Drills.com. We use it most often to share the useful math resources that we've found online and more importantly, to immediately announce new worksheets that are added to the website. If you are one of our many loyal users, you will probably appreciate the ability to stay up-to-date on new material that we add. By the way, we love it when users request new material, so don't be shy. Pinterest was actually a very good thing for us because it caused us to make improvements to the website that had other benefits such as thumbnail images in searches, better search results, and the ability to share images of our math worksheets on Pinterest and other social websites. Another great advantage to Pinterest is that you also do not need to have an account or register or give out any personal information to view our math worksheet updates or other boards. You do have to register if you would like to pin our content or follow our boards though. Here is a link to our boards:

http://pinterest.com/freemath/

We have a small crowd of Twitter users who follow us, so we usually tweet something when there is a new blog post or a new math worksheet. Once in a while we also tweet or retweet things on Twitter exclusively if we found the item there and thought it might be interesting to our followers. One disadvantage of Twitter is that our tweets can easily get lost in the steady flow of tweets. There is no need to register to see our tweets, just head over to this link:

http://twitter.com/mathdrills

Google+ seemed like it was going to catch on quite nicely since there are so many Google users out there, but we haven't seen the crowds other places have. We are still sticking it out though and posting the occasional Google+ exclusive and always posting links to new blog posts. You don't need to register to see our Google+ page, but you will to interact or put us in your circles. Join us at Google+ at the following link:

https://plus.google.com/111836579110801042148/posts

And finally, we have arrived at Facebook, sadly at the bottom of our list. Facebook used to be our #1 sharing place, but they have unfortunately done a few things to make it very difficult to continue supporting them. Their very questionable privacy issues aside, they are now asking for real money, and a lot of it, to "promote" posts. If you don't pay to promote your post, they only show the post to around 15 to 20 percent of people who have liked the page. As an example, we have 2270 likes as of this blog post, and only 308 people saw our last Facebook post. If we had paid them some money, more people would have seen it. We have chosen not to pay them a cent. Despite their new way of operating, we still post things to Facebook... the occasional Facebook exclusive post and always a link to new blog posts. The good news is that we have made our posts public, so you don't have to log in to see them if you visit our page directly at:

https://www.facebook.com/freemath

Your Privacy

Some of you may be aware of the EU Cookie Law which we think is a wonderful thing especially for people who don't know a great deal about their online privacy. We were inspired by the new law to further protect the privacy of our users, even though our home is in Canada and most of our users are in the United States. We updated our privacy policy to include more information about cookies and changed a few other things, so you would be subjected to even less tracking than ever. For example, our Share/Save link that you can find on all of our pages is a simple image and a simple link. No cookies, no tracking, no privacy issues at all. When you click on the share/save button, though, some information is needed in order to process the request, and this is done through the Lockerz Share service. If you are interested in more information about your privacy, please do read our privacy policy and/or perform a search, but be careful, all those search engines are watching you!

We actually appreciate websites that aren't full of advertisements, videos, pop-ups, fancy social sharing buttons, etc. since they are much easier to navigate through, they load faster and they aren't full of privacy issues. We try to provide you with the same things that we appreciate. We figure if it isn't necessary, why include it.

Whenever we make updates to the Math-Drills.com website, we like to test it out in the four main browsers (IE, FF, Chrome and Safari). We did notice that the most recent Safari browser (5.1.7 for Windows 7) made it really easy to change privacy and security settings. They even tell you about the cookies that are being stored and give you a one button method to remove or block cookies. If you are concerned about your privacy, we think that you might want to check out Safari while the other browsers catch up.

That's it for now. We hope you have discovered a little bit more about how you can stay up-to-date on Math-Drills.com, how we are working to protect your privacy and what you can do to further protect your privacy. Have a great week!

New Halloween Math Worksheets

For some of you, it is the time of year when things get a little more spooky. Luckily, you can always head over to Math-Drills.com for a few Halloween items that will help students with their math skills. This week, a few new Halloween Math Worksheets were added to the website. Here is a quick description of each.

1. A second "Spider Web Angle Measuring" worksheet. The first version and this worksheet were moved from the Halloween Geometry to the Halloween Measurement section.

2. One-, two-, three-, and four-digit addition worksheets, named, "Through the Dark Forest" and decorated with scary trees were included in the Addition and Subtraction Section.

3. An original coordinate point plotting activity called, "Cartesian Art Jack-o'-Lantern" was also created and was designed with the older student in mind, mainly because of the scope of the numbers and the number of points involved.

As usual, if you have any suggestions for new math worksheets for the Halloween page or any other page, please let us know by replying to or commenting on this post.

Canadian Thanksgiving

Since Thanksgiving in Canada is this weekend, we doubled the number of worksheets available on our Thanksgiving Math Worksheets page today! Of course, those of you in the U.S. will benefit a little later in November. Perhaps we'll get around to making even more choices by then. Please feel free to send us a suggestion if there is something you'll be working on in November.

New Thanksgiving Math Worksheets

1. We added four versions of a sorting/ordering worksheet based on the newest version on the number sense page. For this one, though, we added some turkeys and pumpkins and some units of measure. So, instead of just sorting random numbers, students now sort the masses of turkeys or pumpkins in lbs or kgs (your choice).

2. There are five new picture patterning worksheets. The most basic one is for sorting shapes. We chose four shapes that we thought would represent Thanksgiving and put them all on the same page. There are also picture patterns with two attributes in various combinations: shape/size, shape/rotation, and size/rotation. For an extra challenge, try the three attribute version with shape/size/rotation all mixed together. Note that it is possible that there is more than one answer to each pattern, so a suggested answer is given on the answer keys.

3. The third and final type of worksheet we added is a ratio worksheet in two versions. The first is comparing only part to part ratios which is suitable for younger children. The second type also includes part to whole ratios for more advanced children.

The images on these worksheets are all from http://openclipart.org/ which is a great place to get quality images for own projects.

For all those in Canada who are celebrating Thanksgiving this weekend, enjoy your day off, family, friends, and good times and thanks for visiting Math-Drills.com for all your math worksheet needs.