Frog Flippin' (Measures of Central Tendency)

Aren't they cute?!  I found these the other day at my local dollar store.  I plan to put them to good use this year when we come to the topic of measures of central tendency.

Last year, I did an activity I called "Frog Flippin'".  I have about 10 of the medium size version of these frogs.  I asked the students to flip and measure the frog 10 times, record the data, calculate the mean, median, and mode of their frogs distances.  I then asked them to add 30 cm to their longest jump to create an outlier.  I found, at least in my experiments, the frogs were pretty consistent jumpers and didn't naturally create an outlier, so I made one exist. The students then examined what happened to the data with the outlier in it and we discussed what happened when it was taken out.

Next year, I want to add more data for analysis, even if it will take some more time.  I am still giving  this expansion some thought and tweaking but it is pretty well organized.  To expand the project, I am going to add in additional sizes to the activity.  By posing the question: "Which size frog goes the farthest?", I am hoping to intrigue the students enough that they want to know the answer themselves.

The main idea is that students will collect data for 10 flips for each frog in small groups picked by me.  Students will then need to calculate the mean, median, and mode of the data.  I want to open a discussion about how to pick the best measure of central tendency so that each size frog is represented most positively.  Which measure of central tendency should be used?  Will their chose vary by the size of the frog?

After this, I will ask if anyone is wondering anything about their data or the measures of central tendency.  I am hoping someone will wonder if more data would change the results.  I am also hoping that if there is an outlier, someone will question that as well.  Students will then gather data from their peers and recalculate the measures of central tendency.  Students are asked to make observations about what they are noticing.  Then, we'll examine outliers and the role they play in skewing data.

The original activity and the activity that I have been developing are attached if you are interested!


Original Activity:


3 Sizes Activity:

123 Switch! (Game to Practice Adding/Subtraction Integers)

 I found another great game to practice adding and subtracting integers.  The game really forces students to be flexible in how they think of number combinations.  I know that is an area that my kiddos struggle at times and they need to be much more flexible than they are.  So, when I found 123 Switch! on Tom DeRosa's blog, I Want to Teach Forever, I was thrilled!

Tom has a hand made template that students drew in their notebooks.  I see the value in that and would prefer that, but I know my kiddos and they need a game board.  So I made a template for addition and subtraction.  I am going to print them out on some fun colored paper and then glue them back to back.  With some quick lamination, they should be ready for the next school year! 

The first thing you do is pass out 7 cards to each player.  The black cards are positive and the red are negative.  The first player puts down a true equation based on the cards in their hand.  If they can't, they need to select cards from the draw pile until they can.

The next player can change 1, 2 or 3 cards by placing a card on top of one already on the board with one from their hand.  In the picture below, I could replace the 6 of diamonds with the six of hearts.  I could replace the 9 of spades with a 7 of clubs.  Then replace the 6 of diamonds with a 4 of diamonds and still have a true statement without changing the 3.  I could also just replace all three cards.  The goal is to be the first person to get rid of all of his/her cards.

The game becomes more challenging when you have to make subtraction equations.  I like that the game is challenging and competitive enough to keep the students interest.  Not to mention, it's  a great way to practice!

Here are my templates for the game boards.  I also made a direction sheet for the students.

Product Race! (Product Rule of Expoents Game)

I wanted to practice the Product Rule of Exponents Property.  My algebra kiddos worked on this last year in pre-algebra, but I am pretty sure that they will be a bit rusty.  The game that I developed is super simple, but it reviews the property.

The game board is a basic square design and the first person to return to the start square is the winner.  The students roll a die and move the number of spaces indicated on the die.  Then, they pick a card and using the expression on the game board, multiply the two expressions together.  If the student is correct and his/her peers agree, then the student may take one extra turn.  If incorrect, another student takes their turn.

I recycled some old file folders by putting the game board into them.  It fit really well.  I then put the directions for playing the game on the front cover and snipped the corner that had the label.  The final task will be to laminate the entire folder for durability.  I am going to keep the cards separate from the boards in their own snack sized bags.  I thought about duct taping them to the back of the folder, but I thought they would stack better without the bag of cards on the back of it.

I have kept the rules pretty basic because I find that the students have great ideas for rules of games and ways to make it harder (and easier) to win.  I also had a thought to make this a team game.  Two students will work together to multiply the expressions, write down their final answer, and show it to the other team.  The other team would also work the problem and show it to the other team.  If it matched, both teams could move an extra space.  If it wasn't a match, then the team that was correct, would get to move an extra space and the incorrect team has to move back one space.  A little more competition might be helpful to keeping interest.

The game board, directions, and cards are below if anyone would like them.  I don't like that the word formatting changed all of the letters to capitals, but until I can figure out how to fix it, it will have to do.

** Update: Much thanks to Kayla who told be how to fix the letters.  It was so simple!  I should have figured it out.  Nonetheless, I appreciate the assistance!

Zero!

As my fellow Saxon Algebra I (2009) know, Lesson 5 combines absolute value and addition of integers into one lesson.  In the past, I have taught the two ideas separate from each other and practiced the skills separately.  This year, I wanted to practice the skills together and I started hunting around the internet for a possible activity that I didn't have to create.  Well, I found it!  It is a game called ZERO! and I found it on the blog, "I Speak Math" written by Julie Reulbach.

The game is basically blackjack with the goal being to get 0, not 21.  The red cards are negative and the black cards are positive.  The student with the number closest to 0 when the cards are added is the winner of the round.  Students calculate the absolute value of each of their round totals, then at the end of the game, they add up the absolute value column.  The student with the number closest to zero, is the winner of the game.  This sounds like a blast!  I think my kiddos will love it and it reinforces addition of integers and absolute value all in one game!!

There is a link above to Julie's explanation of the game at "I Speak Math".  Her direction and score sheets are there as well.  I don't subscribe to Scribd, so I recreated the direction sheet and score sheet myself.  It is basically what Julie has, but I added learning goals, supplies, an example on the score sheet, and a reminder to turn it in for credit.  It is below if you'd like it.

A Quick Way to Make Sets of Game Cards

I got this game PEMDAS war game from Brittany at Math Made Gr8 blog. 

Whenever I make task cards for the classroom, I usually just copy them onto different colored pieces of paper or card stock, whichever is handier.  However, when I am making card games or game pieces, especially those that are done up so cute, I don't want to just copy them onto colored paper.  So, I invested in the big pack of scrapbook paper from Michael's that is 8.5 x 11" when it was on sale, of course!  Then I print out the cards/pieces.  I then just glue the two sheets together (be sure to put the glue all over the sheet) and let it dry for a bit.  Then, when I cut out the cards/pieces, all of the same set have the same back.  The final step for me is to laminate the cards/pieces.  It is very easy to sort when one piece is lost from the group.  It also looks more like playing cards when it is a card game.  I will admit, it takes a bit more work, but in the end, I think it is worth it!

Practicing Expressions and Their Vocabulary

Opps!  Should have had the "s" in coefficients in parentheses. 

The next lesson in the text is about the different parts of an expression and is very vocabulary heavy.  My challenge has been how to practice the vocabulary and do something more than just memorize the definitions. 

With some thought, I came up with two different ideas.  One of them is in the picture at the left.  I had these numbers left over from when I was "The Mathematical Wonder" superhero for the day last school year.  They got me thinking that I could have the kids make expressions and define the different parts of the expression to a partner.  It wasn't a bad idea, but I didn't feel like I was stretching them.  Then, brilliance struck and I thought, "what if their expression had to meet specific criteria?".  That would challenge them to create an expression and understand the vocabulary words! 

I created some simple task cards which you can download below.  If the dollar store is out of the numbers, I am going to use the plastic bottle tops that I've collected and my trusty sharpie to make my own set of numbers. 



I wanted something else to practice with that was active.  So I thought about the Kagan cooperative group technique called "Mix-'n'-Match".  I have had good success with this in the past.  If you're not familiar, students each have a card and have to go and tell someone the answer to what is on the card (or explain something to another student).  So student A explains to student B, then Student B explains to student A what was on their card.  The two students then swap cards and go talk to someone new.  This goes on for 5 minutes or so.  I like it because there is a lot of practice happening in a short time frame and it gets them up and moving.

After I made the cards, I thought that they would work well for an inside-outside circle activity.  For this activity, students make two circles with one circle inside of the other.  Students face each other so that one student on the outside circle is facing a student from the inside circle.  They talk about the cards, swap them, and then either the inside or outside circle moves while the other stands still.  There are lots of variations on this activity, so do what works for you.  Below are the cards that I made.

Stations for Real Numbers

Well, school has barely ended and I am already working on next year. There will be no rest for me this summer as I get ready to have a blended, leaning heavily towards flipped, Algebra classroom next year. Making the videos is not what I think will be the most time consuming! What is taking longer is figuring out how to use all of class time that I now have!  In some cases, it is narrowing down the activities that I have and figuring out what will be the best use of the class time.  In other cases it is finding the activity or tweaking something to better fit the topic.

The first lesson that we do in the Saxon Algebra I (2009) text is about classifying real numbers. I like the calk walk activity that I did last year, but I want to use that to review with the following week.  I want to spend the class time after the first video actually practicing classifying the numbers. For some reason, this needs more practice than I usually give it.  So I decided to set up some stations and practice and practice and practice classifying numbers in the real number system.

Here are the stations (I'm still working on the names)...

Station 1: Popsicle Stick Sort 

In this station students will be asked to sort 20 popsicle sticks with different numbers on them.  The white cups are the classifications of natural, whole, integer, rational, and irrational.  The green cups have multiple groups.  I made the categories of irrational/real, rational/real, rational/integer/real, rational/integer/whole/natural/real, and integer/whole/natural/real.  The first task at this station will be to sort the popsicle sticks into any cup that would classify the numbers.  They will then write down 3 observations about how the numbers were sorted.  The second task will be to use only the white cups and decide which is the best classification for each number on the popsicle stick.  They will then write down 3 observations about this task.

Station 2: Real Numbers Concentration

For this station, students play a traditional game of concentration (or memory), but they get a match if the two numbers flipped are from the same set of numbers and they can identify the set.  Students can't use the same set, two times in a row.  So for example, if student 1 made a match using rational numbers as the classification, then he/she couldn't make a match on their next term using rational numbers.  He/she would need to use another set.  I am also not letting them use real numbers for any of the classifications.  Also, all of the cards have a match, but depending on what set students use the last ones may be challenging to classify.

Station 3: Real Life, Real Numbers

In this station, students will be asked to sort the real life situations into the best set of real numbers.  Students will need to explain why they have picked that particular category for the situation.  The trickiest are the circular questions.  Students tend to classify those as rational when it should be irrational.  All of my examples came directly from my textbook.

Station 4: Tic-Tac-Toe: Real Number Style!

This is a basic game of tic-tac-toe with a twist: To win you need to have 3 of the same sets!  Students can pick their own numbers and classify them into any set that the number belongs.  Another student can block them by putting another number in a box and classifying it in a different set.  Some strategy will need to be used and really thinking about the sets that a number can belong.  Students may classify numbers as real in this game.  I'm going to monitor it closely and see if that is all that they are using.  I can always change the rules! :)

Station 5: Real Number Carousel

The last station that I am going to have the kiddos do is a real number carousel that is free on Teachers Pay Teachers.  I am going to have this set up for them to work on while they are waiting for a station or when they finish all of the stations.  Hopefully that will help with down time.

Sorry about the long post.  If you made it all the way to the end, then I hope that you found something useful that will make next year better!  I would love to hear how any of the activities goes for you.  I will update after I try them in the fall!