Friday Fun: Exponents in the Real World

Hi guys!

I'm super excited to share this week's activity with you all. I try to come up with activities for the students to do on Fridays that are different from our day to day routine. I know the last thing I want to do on Friday is to listen to myself talk, and I'm sure the students don't want to sit and take notes every day of the week. I've thought about creating a series of some of the activities I do with my kiddos on Fridays, and decided to jump right in this week!

For the first week of school, I'm going to be going over evaluating expressions with my Algebra 1 students, including exponents. I discovered the website http://robertkaplinsky.com/ and found a great activity there on how to create strong passwords that used exponents in the real world! I decided to adapt the lesson plan I found there, and created my own worksheet to accompany the activity.

Ladies and Gentlemen, may I introduce you to Ms. B's Math Minions!

The latest and greatest social network for Math with Ms. B!

In this activity, the students create their own login information for my fictional math social network (which should definitely become a real thing). They then give guesses for how long they believe it would take a computer to crack their passwords. After the students make their guesses, I show them this video. 

The video shows that a computer can crack a simple password in seconds!

After scaring the students that all of their social media accounts will be hacked, we will go over the math that works behind password requirements. The students will discuss how different characters (uppercase letters, lowercase letters, numbers, and symbols) affect how many potential passwords a computer would have to guess before choosing the correct one. They will also discuss how different lengths affect the total amount of potential passwords, and come up with a generalized formula for amount of possible passwords for different requirements. (Amount of potential characters ^ number of characters used). 

To really bring students up to speed with password technology,  I show them this article which states that a supercomputer can cycle through 350 billion passwords per second! Second!! 

So now that they are really scared about what they decide to upload to the internet, (as they should be) I split the students up into groups of 3-4. Together they will come up with a set of password requirements that they feel will make their passwords secure. They will also use their new real world knowledge of exponents to calculate how long it would take a computer to hack a password with their group's requirements. Finally, they will decide what they believe is the single most important requirement for a strong password!

To end the lesson I will explain to them that most websites have security measures in place to prevent computers from hacking passwords using this method. If there are 218 trillion possible passwords, the probability of a computer guessing correctly withing the 5-6 tries before the website locks the account are nearly impossible. =)

And that's it! This may be a two day lesson plan depending on the amount of time you have. I intend on completing the lesson in 40 minutes, but we all know how that goes.

If you are interested in seeing the original activity, it is available for free at  http://robertkaplinsky.com/work/how-can-we-make-stronger-passwords/

If you would like to download a copy of my adaptation and accompanying worksheet, you may do so here!

Thanks for reading.

Ms. B.

Guided Practice Stations

Hello all!

Stations are probably one of my favorite activities to do with middle school kiddos. They get them up and moving out of their seats, and they are easy to create! For this weeks lesson, I created a set of math stations that cover properties of real numbers.

To make these stations I just copied problems out of our textbook and added some extra questions to each problem. I also created some easy to read data tables and added some pictures to keep things interesting. =) If you work with a science or reading teacher in the building, this can also be a great way to teach across the curriculum.

Stations are great because they help awaken the competitive nature in students. Everyone wants to finish first. I keep an answer key at my desk so when a student finishes all of the questions in his/her station, I can check over the answers. Once I approve the answers, the student can move on to the next station. This is also a great way to differentiate for different ability levels in students. Everyone begins at station 1, and as students finish each problem the class spreads out. This gives me an easy visual of who is on track and who may still need some extra help. It also provides opportunity for me to work one on one with struggling students without causing embarrassment in front of the entire class because everyone has to check answers with me before moving on.

If you would like to use these math stations in your own classroom, I have it available on my TpT store for free! You can download it here.

Do you use stations in your classroom? What are your experiences?

Thanks for reading.

Ms. B

Ordering Real Numbers Activity (Pictures coming soon!)

Hi all!

I just finished up my first activity for the school year! Yay! I'm pretty excited to try this out with my kiddos, and of course I will post an update once we complete the activity. So let's get to it!

My advanced 8th graders are starting the year off by reviewing Number Systems, specifically rational and irrational or "real" numbers. I wanted to do an activity that would get them out of their seats and review ALL of the numbers: positive, negative, rational, irrational, you name it! What better way to do this than to turn them into a giant number line!

Materials you will need:

• Plain duct tape (Colored tape works fine for this activity, as long as there isn't a pattern).
• Ruler
• Sharpie or other permanent marker
• Real Numbers Task Cards

Before class starts you will want to clear out a space to put your number line. The kiddos are going to be standing on it, so there needs to be lots of space. Create the number line by placing the duct tape on the floor in a straight line. You want the line to be as big as possible so the students aren't squished together. Using a ruler and Sharpie, label the number line in increments of two. (The increments can be different depending on class size/ability level. I have a small advanced group, so I chose two). If you are blessed with a classroom using those convenient 1 foot floor tiles you may not need a ruler. My classroom has carpet, so I need one to make my spaces even. Make sure that zero is in the center of the number line, and the line goes to positive and negative 10.  You may want to cut out the task cards prior to the activity as well. I plan on laminating mine so they last awhile, but the students can always cut them out at the beginning of the class period. 

The Activity

Pass out the task cards to each student. I'm incredibly lucky and only have 5 students in my advanced group this year, so my students will have multiples. I made my task cards two sided, so each student will be able to go at least twice.

Task Cards! Cut them out, fold them up, and you are good to go!

One by one, have each student walk to his/her place on the number line that matches the number on the task card. You can call students one by one, or I created a "Teacher Cheat Sheet" with all of the numbers I used on the task cards. Calling them up by their task card numbers gives time for students with difficult fractions or square roots to convert their number to a decimal and figure out their place on the line. While students are waiting their turn, they will plot each number on a number line worksheet. You can easily create one of these yourself at TheMathWorksheet.com. My number line on the floor is in increments of two, so I reflected that on my number line worksheet. The worksheet provides an easy way to assess students at the end of the class period, and helps to keep students engaged while they are still at their seats. 

And that's it! Continue plotting numbers on the line until the task cards run out or time runs out! I ended the lesson by reviewing which side of the number line is positive and negative, as well as what makes a rational and irrational number. 

I have this lesson uploaded on my TpT store here. The download includes a full lesson plan, 28 pre-made 2 sided task cards, Teacher Cheat Sheet, and number line worksheet! I spend a lot of time creating materials for my store, and would love it if you guys checked out some of my resources. You can also easily make your own task cards using index cards if you like. 

Sorry I'm low on pictures for this lesson at the moment, but more will be uploaded when we do the activity!

Thanks for reading.

Ms. B