Category Archives: Freebie

Divisibility Rules

I often run into students who need to do a complex operation in algebra or even up through calculus, but they struggle because they are missing a skill from a much simpler time. One of the skills that I see students are missing is being able to quickly determine if a number is divisible by a digit between 2 and 9 in order to simplify and reduce fractions, roots, factor equations, and more. One way to fix this is through practice and learning a few tricks. Even when students are in upper level classes. It’s never too late!

To make this easier for students to learn, it helps to have a list to use, like training wheels while they work to memorize how to find possible factors. To that end, I’ve made a great printable in both color and black and white which explains each rule, then gives two examples and a counterexample so students can see at a glance how to check for divisibility. If you print it two pages per sheet, you can have all of them on one side or print them front and back so you have them just a bit bigger!

How can you use this printable to learn the rules? Well, firstly you can use the chart while doing math work. But sometimes you want a fun way to practice the skill first before you need it. To that end, try these ideas:

  • Get 3-5 (or more!) dice and roll them. Line the dice up to make a number and figure out if that number is divisible by anything between 2 and 9. For example, roll 3 dice and get a 2, a 5, and a 3. Use the number 253 (or 235 or 352 and so on) and figure out if it’s divisible using the chart. If they are successful, they get that number of points (2+5+3=8, so 8 points)
  • Using similar rules, take a deck of cards out and make numbers by picking cards at random and lining them up. This works best if you take out the aces and face cards, but leave 10. If you put 10 into a number, you can fit zeros in that you don’t normally get with dice. For example, you pick a 5, an 8, a 10, and a 3, so you have the number 58,103 to test divisibility rules on.
  • For some competition, you can have kids race against each other. If that causes too much friction, do several rounds and have the kids try to beat their own previous best scores. This can be a great 5-10 minute warm-up or break time to make the day more interesting and get the body and brain moving.
  • Math War: Each student gets half of the deck of cards. Using their own stack face-down, they flip over 3 cards to create a 3+ digit number using the rules above. In this case, assign face cards a value of 10 and aces a value of 1. Use the divisibility rules to find the largest number between 2 and 9 that is a factor of the number formed by the cards. Whoever has the largest number gets to keep all the cards and everyone lays out 3 more cards until one person has all the cards.

This skill is really useful from middle school on up. I can’t emphasize this enough. Whether students are trying to find a common denominator, write a prime factorization, or just doing mental math in general, being able to quickly determine if a large number can be broken down more easily is a huge skill for students to master. If a student is still struggling with a basic skill, learning advanced material will be that much harder.

This skill is learned in chapter 4 of my pre-algebra class, but you can get this great free resource today just for signing up for my email list below! Please share this post if you know anyone who might want the file for themselves!

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Why are labs in science important?

In the last two posts, I talked about how lab activities benefit your student, but now I’d like to switch gears a bit and discuss how you can help your student get through labs and make a success of those assignments they may be avoiding.  But first, it helps to understand some of the reasons students avoid labs.

  • They’re time consuming.
  • They require planning ahead.
  • They don’t have the materials.
  • They feel overwhelmed or confused.

For the student who does well with bookwork and can get through assignments efficiently, having to stop to complete a lab can seem frustrating or a waste of time.  Since you already know they are important, one way you can help your student is to schedule a regular lab time into your week.  If they know the time is set aside for labs, and possibly means that there won’t be bookwork for that class on that day, they will hopefully see it as less of a time drain and more of a useful tool.

Many labs that you complete will require planning ahead.  If your student doesn’t look at the lab ahead of time, they may not know that the steps will take several hours or days and won’t plan accordingly.  In addition to what they might learn in the lab, this is a great skill to learn for life.  However, bear in mind that most teens don’t have the ability to do this on their own.  The part of their brain that controls executive function, which includes planning, isn’t fully developed yet.  They may need you to model for them how to plan out the activity, and in the beginning, the planning may fall entirely to you.  If the activity will take several days, help them by getting them started each day and showing them what needs to be done.  Write out the steps and which days they need to be completed on and follow up by checking that those steps have been done so that Friday doesn’t roll in and no progress has been made.

Sometimes the planning process will include gathering materials.  Just as the planning may initially fall to you, so might the materials-gathering process.  If the book is broken into units or chapters with multiple labs, try gathering the materials to a single box or cabinet (if it is safe to store the materials together).  Demonstrate how to organize the materials by activity and soon your student will be able to follow your model and gather future materials themselves.

And the final reason many students avoid lab activities is that they feel overwhelmed.  This is often a combination of the first three obstacles and by following the steps above, your student can often avoid this issue.  If labs also overwhelm you, try starting by breaking the labs for a course into groups, then follow the steps above.  Get out a calendar and plan for when each activity must start and how long it will take, giving yourself lots of buffer room for life and mistakes.  Plan to do a little each day or set aside an entire day for labs, whichever works best for your family.  Then gather the materials for the first few labs.  Separate and label the material so you can see what you have and what still needs to be found.  If you see the lab as small steps it won’t be so overwhelming and is much more likely to be done. Think of it like cooking a meal, you My Post Copy (4)don’t do all the steps at once and it’s much less overwhelming if you have all the pieces together before you start.  Planning is your best weapon when it comes to labs. In the end, it’s ok if you don’t do every lab, but make an effort to do a good chunk of them.

And finally, my biggest piece of advice is to let students do the labs themselves and that struggling is alright, even good, for your student.  It’s the struggle during learning that makes the connections in our brains and doing the lab for your student won’t help them in the long run but working by their side and showing that you are learning right along with them will do wonders for their self-confidence and interest in the material they are studying.  Even if you are familiar with the experiment, showing your interest and enthusiasm in the subject will help ignite a fire of interest in your student, even if the topic at hand isn’t their favorite subject.  Lab activities are important, and more importantly, totally doable for both the scientist and non-scientist alike!  If one activity doesn’t work, chalk it up to experience and move on.  Use what you’ve learned to make the next activity a success!

Find a great FREE lab activity here that you can practice with!  It’s fun and it doesn’t count toward your grade, so try it out with your student and see if you both don’t have fun and learn at the same time!  Comment below with how it turned out!

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Freebie Friday – OpenStax Textbooks

by Kristen Lauria

For my first Freebie Friday post, I’d like to tell you all about an awesome group of textbooks available online (or downloadable in pdf or in iBooks) for absolutely NOTHING!  These books are written by the same people who write most textbooks, PhDs and the like, who really know what they are writing and how to explain difficult subject matter.  Plus the textbooks are peer-reviewed, which means they’ve had lots of eyes on them who have the knowledge and experience to look for errors and fix them before they get to a student.

I got started using OpenStax textbooks last year when I started teaching physics and AP physics online (see here to look at the course description and sign up!).  I wanted a textbook that was thorough and would provide rigorous questions for my students to practice with, but without the usual high price tag of a high school or college level textbook.  My answer was found with OpenStax.

OpenStax offers more than 20 textbooks, not just physics, and they are all available to thepublic at no charge.  There are often even other materials available to students that will help them use the textbooks in the best ways possible, including an answer key that has some, but not all, of the solutions including the work that went along with solving it.  If you register as a teacher (as a parent), you can access even more materials.

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Image courtesy of OpenStax.org Press Kit. Updated September 15, 2017.

If you are looking for books to use with an AP course (which you can register to teach as a homeschooling parent.  Look for a blog post on this coming soon!), there are many choices for AP courses through OpenStax that have AP style questions right inside the book in each section and in the problems at the end of each chapter.  Currently available are Physics, Economics, and Biology.

If you’re wondering about OpenStax themselves, they are a non-profit affiliated with Rice University.


Please comment below and let me know if you’ve used any of the textbooks that OpenStax offers.  Or do you know of another great textbook resource?