Balance Day

I like to start out the unit on solving equations by showing this clip from a Japanese game show.

               


After we watch the clip, we discuss what the teams had to do to win the game and how this connects with math. This usually leads to a very interesting discussion and the students make the connection between balance and equations and doing the same thing on both sides of an equation to maintain balance.
Then to reinforce this critical idea, which is the foundation of solving equations in algebra, we spend a day doing Balance Activities. In the past I have created Balance Stations and the students would spend about 5 minutes at each station and record their results.

This year I decided to ask the students to create balance activities for their peers to try. The results were amazing and I think the students got more out of designing and creating their own balance activities.

Several groups created their own balance scale to use in their activity.

Favorite Video Clips for Math Class

I would like to organize and share the various video clips I have used to introduce, teach and review different concepts in my middle school math classroom.

 The Number System


Colin Dodds - Number Types (Math Song): Nice review of the different number types and their definitions which includes:  Natural Numbers, Whole Numbers, Integers, Rational Numbers.

PEMDAS: I show this video of a traffic accident where a car runs a red light. After showing the video, I ask the students to write in their math journal about the accident. What caused the accident? Could it have been prevented? How? What does this video have to do with math? Then we discuss the importance of rules that everyone agrees on and follows in driving and math.

Triple O (Order of Operations):  Teacher turns a boring lesson on order of operations where students are falling asleep into a whole class review of the rules of order of operations by using some simple props and turning on the music.

PEMDAS Style - Order of Operations Gangnam Style Parody: Student writes and performs this video for her class. Her dancing is great!

Math Rocks! Flip It! Whip It! by Devo is the perfect song for reviewing the procedure for dividing fractions.

Nature by Numbers: Beautiful video to introduce the beauty of numbers and patterns.

ViHart: Doodling in Math: Spiral, Fibonacci, and Being a Plant [1 of 3]: My favorite part of this video is when ViHart uses graph paper to draw the golden spiral using the Fibonacci Sequence. I show the whole video and go back to this part and stop and start it several times and have the students draw it themselves. Then I have the students bring in pine cones and pineapples and we identify and count the spirals with glitter glue and colored tape.

Integer Song:  Here is a rendition of the classic math song teaching the rules for adding and subtracting integers sung to the tune of Row Row Row your Boat. I tweaked the lyrics of the third line to make them more mathematically accurate.
     Same signs add and keep
     Different signs subtract
     Keep the sign of which has more
     And then you'll be exact.

Mathematical Pi (Full Song): Great for Pi Day


Expressions and Equations

I show this clip from the Japanese game show Unbeatable Banzuke: SeeSaw 60 to introduce the idea doing the same thing on both sides when solving equations.

We're Going on a Bear Hunt (in Runescape):  I show this video to introduce the idea that solving equations involves doing inverse operations in reverse order. I also wrote a song called Going on an X Hunt. I give the students simple rhythm instruments and we sing it together. Someday I will make a video of the class singing it.

I use Dan Meyer's Graphing Stories to introduce the concept of numberless graphs and graphing functions.

Solve Me Maybe (WSHS Math Song): I love the way this school has created a tradition where students and teacher work together to create math videos.

The Weird Algebras: Algebraic Style [GANGNAM STYLE PARODY]: My students made this video and performed it in class. It was amazing--I wish I had a video of it. The video and performance was the result of a group project where students were asked to write and perform a song about solving equations.



Geometry

Tik Tok Math Song : Reviews formulas  for finding the area of square, circle, rectangle, parallelogram, triangle, and trapezoid. I like the fact that the video uses b (base) and h (height) for finding the area of all the quadrilaterals.

Call Me Maybe-"Half It Baby" (Area of a Triangle): Nice review of the connection between the area of rectangles and area of triangles. This is great to show after a discovery lesson.

Area of a circle, how to get the formula: I love this video! It cuts the circle into smaller and smaller pieces to show that the area of a circle is simply base x height where base is half of the circumference (pi x r) and the height is r.

Even better than The Shapes Song! (4 Sided Shapes - Quadrilaterals): Nice review of the properties of different quadrilaterals.

Who can resist the Nonagon Song by They Might Be Giants to introduce polygons?

I like to use these three drawing videos to introduce 3-D geometry.  I think that by drawing the figures, students can more easily visualize the figure which is necessary for understanding and calculating surface area and volume: Stacking Cylinders in 3-D, Flowers in a 3-D Box, Treasure Chest.

What is a Prism?:  I like the way that this video shows the slicing of a solid and how you get the same shape as the base no matter where you slice it.

Gangnam Style Math (Transformation Style): Nice overview of transformations.


Statistics and Probability

Mean, Median and Mode Rap by Mr. C: Nice review of these vocabulary words.


Algebra I

Emily sings the "Quadratic Formula":  Shows the power of music to help students learn and memorize.

Quadratic Formula:  Just the music--"Pop Goes the Weasel"-- and the words to the song displayed on the screen for a classroom sing along! I memorized the quadratic formula several times over the years and then immediately forgot it after a test. It wasn't until I was doing my student teaching and learned this song from my cooperating teacher that I learned it for good--never to be forgotten.

Pythagorean Theorem Water Demo: Not a proof, but a nice, concise, and easy to understand demonstration of what the Pythagorean Theorem means.


Miscellaneous

Baby Learning to Walk: I want to use this video in class to introduce the growth mindset vs. the fixed mindset described in  Mindset by Carol S. Dweck. "Everyone is born with an intense drive to learn. Infants stretch their skills daily. Not just ordinary skills, but the most difficult task of a lifetime, like learning to walk and talk. They never decide it's too hard or not worth the effort. Babies don't worry about making mistakes or humiliating themselves. They walk, they fall, they get up. They just barge forward" (Pg. 16). I want to use this video to encourage my students to work hard and never give up and not get discouraged by mistakes.

Taking Tests Song: (Tips for Test Success) by Heath  I showed this video to my students at the beginning of the week as we started to review for state testing. I encouraged the students to have a positive attitude about the tests and described it as an opportunity to prove how hard they had worked all year and how much they had learned.

Who Wants to be a Millionaire Math Question: Which of these square numbers also happens to be the sum of two smaller square numbers?


I will be adding more as I find them and use them. Please send any video clips that you have found useful in your classroom.

Math Bully

During the first week of October (Oct. 1 - 5, 2012), New Jersey held its second annual "Week of Respect" which was created as part of the state's anti-bullying law. During the week of respect, we are asked to include something in our lesson plans that reinforces the importance of treating all people with respect. I was thinking about respect and the importance of respect in the math classroom and I realized that the kind of bullying that I usually see in a math classroom is students laughing when other  people make mistakes. I think it is very important that my students feel safe in my classroom and know that if they make a mistake that they will not be ridiculed. So for my lesson on respect I decided to talk about "math bullying." I start out the lesson by asking my students what they think a "math bully" is and that usually elicits some interesting comments. My definition of a "math bully" is something who laughs or ridicules another person when they make a mistake. Then I share with them some quotes that I found on the importance of making mistakes in the learning process.

Making mistakes simply means you are learning faster.

   --West H. Agor

Constant effort and frequent mistakes are the stepping stones of genius.

  --Elbert Hubbard

Mistakes are the portals of discovery.

--James Joyce

The many who achieves makes many mistakes, but he never makes the biggest mistake of all - doing nothing.

--Benjamin Franklin

Never say, "Oops." Always say "Ah, interesting."

--Author Unknown

It's okay to make mistakes. Mistakes are our teacher - they help us to learn.

--John Bradshaw

I have not failed. I've just found ten thousand ways that won't work.

--Thomas Edison

After we read the quotes together I shared this Respect Pledge:

And then I invited all the students to cut out a geometric shape and write their name on the shape and add it to the Respect Pledge classroom mural at the back of the room. I like the fact that this activity gives us a chance to do a quick review of some geometry vocabulary while at the same time it illustrates that we are all different and unique and we come in all shapes, sizes and colors.

ISN Organization

I tell the students from day one that I don't like to waste time. On the first day of school I show them an almost empty bottle of shampoo and a nearly empty jar of peanut butter and I ask them to guess what that means about me, especially in math class. Someone usually raises their hand and says "You don't like to waste time," but I have gotten some other interesting and creative responses! On the first day of school we practice passing out papers along the rows, a la Harry Wong. We also practice passing papers back in and moving the desks to get into their "pods" for group work. I read a post during the summer which had a photo of how desks are arranged for group work. I thought the configuration was brilliant because students only have to turn the two front desks to face each other and not the back two desks. It also creates a u-shaped group which allows all the students in the group to see the teacher and board easier when instructions are given to the whole class.

I started using math journals in my classes several years ago and with all the great ideas I have gotten from math teacher blogs, the journals have been morphing into interactive notebooks. I am so excited to try foldables this year and other note taking activities. This year I am encouraging my advanced students to take their journals home every day to study and review what we covered in class. In my general classes, I allow the students to leave their journals in the classroom. I laminated some 2-sided signs for math journals, calculators and responders indicating to the students, as they walk in the door, whether they should get these items before they go to their seat. For example, one side says Math Journals Today and the other side says No Math Journals Today. I just flip it over as needed for each class. 

One thing that I have liked about math journals that stay in class is that students always have something to take notes and do practice problems in no matter what their binder looks like. But keeping the journals in the classroom presents other challenges--getting them out and putting them away every day can be time consuming and chaotic. In order to make this classroom procedure efficient, I designate a place in the classroom for each class period so that the journals are easily accessible and available to every student every day. On the left is a picture of the journals for one class period before I labeled them. On the right is a photo of the journals after I labeled them. I write the class period, color-coded, on the left and then write the last name of each student in black sharpie (I covered the names of my students with a piece of paper). This helps each student find their journal quickly and easily as they come into class and it helps me find and relocate any journals that are returned to the wrong pile.

            

I Have Who Has Games for Math

Several years ago when I found these I Have Who Has Cards on Mathwire.com, I definitely wanted to try them in my classes. I have used the multiplication facts, Algebra Variable Expressions and Geometry decks. This is a photo of some cards from the multiplication facts deck from Mathwire.com.

Each student has one or more cards on their desk and the teacher keeps any card to start the game. Begin by reading the clue on the starting card "Who has 3 x 8?" The student with the answer "I have 24" reads the answer and also the new clue below it. The game is over when you have run through all the cards and on the last card a student reads the last clue "Who has 8 x 6" and the teacher, still holding the first card, reads the answer "I have 48."

The students enjoy this game and are very engaged because they really have to listen and concentrate as each card is read, especially the students who have 2 or more cards to keep track of. I like to time the class with a stopwatch to see how fast they can run through a deck of cards and I make it a competition between my classes or try to improve the class time on subsequent days.

Last year I decided to assign a creative end of the year project to the students after I read this post from I Hope This Old Train Breaks Down and several students chose to make their own I Have Who Has deck of cards for their project. I really enjoyed watching these students figure out how to make the cards so they would work out correctly and then choose the information they wanted to put on each card. Their presentation to the class was having the class play the game they made!

Here is a link to some more I Have Who Has Cards on Mathnstuff.com which include: signed numbers, geometry (area & percent), calculus and directions for making your own cards or having students make a set for the class. The book pictured below has 38 games for 5th and 6th grades including: decimals, fractions, percents, data analysis, probability, square roots, exponents, etc., which would all be great review topics for 7th and 8th grade math classes. The book also contains directions for playing the game in different ways. For example the deck Extreme Mental Math has a maze worksheet for each student to complete during the game. "As your classmates identify the answers, draw a line to each number to complete the maze."

Has anyone else used these games in middle school math classes? What decks have worked well for you and what strategies have you used to make it an effective learning activity?

I have created a template for students to use to make their own set of I Have, Who Has? cards. Students really enjoyed making their own cards and then running the game themselves.

My First Foldable!

The students made their first foldable in class on Friday. The students started out class by writing in their notebooks about which classroom activities helped them learn the most. Then we discussed the pyramid of learning and retention. I gave them the list of activities from the pyramid in alphabetical order and asked them to guess which activity was the most effective in terms of learning and then which activity was the least effective. Then I showed them the pyramid with the percentages and we discussed how some classroom activities are more active and some are more passive and that when students are more active, they learn and remember more. Then the supply managers got out the supply bins and we folded, cut, colored and taped the first foldable of the year.

Click here for the template.

Third Time's the Charm!

They say that the third time's the charm and I really believe that if students can successfully complete problems on a new concept three different times, then they are on their way to mastery. The first time is guided practice in class, the second time is independent practice at home and the third time is reviewing the concept the next day during the Do Now or homework review.

I have read many interesting and thoughtful posts on the homework and homework policies. It seems that many math teachers believe that independent practice is important but struggle to find the best system that works well for both students and teachers. I have definitely had that struggle.  I have tried many different strategies--some have worked well and some not so well and some have worked well but have taken up too much class time or too much of my time outside of class. Once again I want to try some new things this year in order to find the best system possible.

Start:
1) Assign fewer problems. I usually assign odd problems from the textbook and remind students frequently to check their answers in the back of the book in order to see if they are on track. I am thinking about assigning fewer problems this year (10-15 instead of 15-25). In fact, I LOVE the idea of assigning just one problem that is very rich. For example, I really like this surface area problem from Accessible Mathematics by Steven Leinwand. "Doctors estimate the amount of skin each person has using the formula S = 0.6h^2 where S is the number of square inches of skin and h is the person's height in inches. Use the formula to determine a reasonable estimate for how much skin you have. Then validate your result using a a referent such as an 8 1/2 x 11 sheet of paper and using surface area formulas. Discuss the reasons for the differences among your three estimates." (pg. 51)
2) More Productive Homework Review. By assigning fewer problems, I hope to make homework review more productive by asking students to show and explain their solutions to the class. I am starting school with a unit on problem solving and after working on one strategy in class, students will be assigned a few problems for homework. Students will also be asked to pick one problem and write out a detailed solution to show and share with the class. Then when we review the problems in class I can quickly ask students to bring solutions up to the ELMO to show the whole class and explain. And then I can ask other students if they have other ways to solve the same problem.
3) "Flipped" Classroom. I would like to experiment with using some ideas from Flipped Classrooms. Of course teachers have been doing a low tech version of a flipped classroom for years by assigning some reading from the textbook before a topic is covered in class. Any student who does this kind of preparation can gain so much more from the classroom presentation/lecture/discussion on a new topic. I want to encourage students to come to class "ready" to learn something new by having some previous exposure to the topic. As part of the homework assignment I plan to give students a link to a video on the topic we will be covering the next day in class. Khan Academy is one resource that I will use for these videos.

Continue:  
1) Daily homework check. Continue to check homework very quickly at the beginning of class by walking around the room and initialing or stamping homework that has been completed. I want this process to take less than a minute or two and so I don't "grade" the assignment at all (I do that later) and just give them a stamp if they have the homework on their desk at the beginning of class.
2) Weekly homework check. Collecting all homework assignments on Friday and entering a weekly homework grade based on effort and completion of the work and following the homework guidelines. When I "grade" homework I look for a proper heading, completion of all problems assigned, effort, marking problems right or wrong, making corrections and showing work.

Stop:
1) Grading every assignment every week. Last year I though to myself, if I still collect all homework assignments, but only look carefully and assign a grade to half of them I could save myself a lot of time and students would still know that I expect homework to be completed and would still get the benefit of independent practice. And since students are fairly consistent about doing or not doing homework, a homework grade based on only half of the assigned work would be an accurate reflection of their effort and homework completion. I plan to randomly decide each week if I am going to check homework and assign a grade or simply give them a check in the gradebook for turning in the assigned work.


I love my new homework board. I got the idea from Math = Love. THANK YOU. I plan to invite students to come up with quotes and math expressions for the calendar for bonus points. I have wanted for a long time to include motivational quotes about life and math and calendar math in my classes and I think I have finally found a way to make that part of the regular classroom routine.