My Crazy Friend

I used "My Crazy Friend" for the first time in my classroom last week. "My Crazy Friend" is a teaching technique that allows the teacher to introduce a new idea or method of solving a certain type of problem without becoming the one and only authority in the classroom. It also allows students to consider the idea from My Crazy Friend along with other ideas that are generated by students in the classroom. I asked the students how to convert 2/3 into a percent. Here is a list of ideas solutions that they came up with: 66.7%, 67%, 66.6%, 66.67% and 66.66% (repeating). No one in the class came up with 66 2/3%. So I said, I have this crazy friend who says that one way to convert fractions into decimals is to multiply the fraction by 100%. The students tried it and there were some exclamations of surprise when they realized that this gave them the percent in mixed number form. We then spent some time discussing why and how this method works and one student contributed to the discussion by explaining that since 100% = 1, multiplying by 100% does not change the value of the fraction.

Here is a graphic organizer that I use to summarize how to convert from fraction to percent and from decimals to percents using this method. It also shows the opposite--converting to fractions and decimals from percents by dividing by 100. I print this out on a half sheet of paper and the students tape it into their math journals for reference.

Favorite Holiday Gifts!

Math related gifts are the best!

Thanks to my sweet daughter and my wonderful sister!

Mathles to Mathles

I was so excited to read about a new game structure designed by Kate Nowak at f(t) that can be used to practice problems in math classes. She called it Graphles to Graphles because she designed the game to give her Algebra 2 students the opportunity to practice sketching graphs given certain constraints.

But the game seems very promising for my middle school math classes, so I have been thinking about different topics sixth grade students could practice and review using this same structure.

1) Prime Factorization

2) GCF and LCM

3) Number Lines

4) Multiplying and Dividing Fractions

5) Multiplying and Dividing Decimals

6) Graphing Inequalities

7) Solving Equations

8) Area of Polygons

9) Plotting Points and finding Area and Distance on the Coordinate Plane

10) Volume and Surface Area

It really seems that you could make "Mathle" cards for any math problem or topic and then use this game structure to provide students with a fun and engaging way to practice. One thing I really like about this game is how students take turns being the referee whose role in the game is to evaluate the work of the other students in the group and then determine the winner for each round.

I think this game would be especially good for students who are just learning how to solve equations. Students can often solve simple one-step equations in their heads and have a difficult time understanding why they need to write out the steps by showing inverse operations on both sides of the equations. I try to emphasize the importance of Balance and then insist on Algebraic Style. Mathles to Mathles: Solving Equations Edition would be a great opportunity for students to not only find the solution, but also practice and be rewarded for good equation solving skills like showing inverse operations on both sides of the equation and checking solutions.

Inverse Operations Game

This is a game I call Name that Operation. I use it to help the students build on prior knowledge of inverse operations and then use that to understand the connection between squares and square roots, cubes and cube roots and then later in the year, distributive property and factoring. Here are some slides I use in class to play the game:

Students quickly see that you must add 4 to go from 5 to 9 and then subtract 4 to go from 9 to 5 and now they understand the game.

Students see +8 and -8. Then I ask for a different operation and they see *3 and /3. 

Now they see *7 and /7 and then I ask if there is another way to write 7*7 and some students know that 7^2 means 7*7. So then I ask, what would be the inverse operation for squaring a number. Usually some students are familiar with square roots. This next slide shows where the term square root might have come from.

Then I show the next slide to make the connection to geometry: the length of the side of a square squared is the area, the square root of the area of a square gets you back to the side of a square.

And this slide is used later in the year to help students see the connection between distributive property and factoring.

Algebraic Style

One of the most challenging things about teaching one-step equations is trying to convince students that they should show their work and do inverse operations on BOTH sides of the equations. Most students can solve one-step equations using mental math and see no reason to show their work on one side of the equation, let alone both sides! After working on one-step equations for a few days, I decided to create a game where groups would solve problems collaboratively and receive points by solving one-step equations "algebraic style."

I started class by playing this song that was written by students in my Pre-Algebra class from last year: Algebraic Style.
Students work in groups of four and solve one-step equations in a relay race format--each student in the group takes a turn coming to the white board in the front or back of the classroom and does one part of the problem and then passes the dry erase marker to the next person on the group. Here are the four steps that I want to see from each group:
1) Write the problem on the board
2) Show inverse operations on both sides of the equation
3) Find the solution
4) Check the solution

When all the groups completed a problem, I walked around the room and award points based on Algebraic style (inverse operations on both sides of the equation), correct solutions, cooperative group work, following directions, etc. I also awarded points to students who could find or explain errors in the student work around the room.

And then to add a twist towards the end of class, I put up a list of songs the students could choose from that offered another style they could add to their algebraic style. I chose a student randomly to select a new style and then played the accompanying song while groups solved the next equation. Here is the list of different styles I came up with:

1) Gangnam Style

2) Disco Style:  Bee Gees Stayin Alive

3) Robot Style:  Daft Punk Robot Rock

4) Mrs. Dalton’s Favorite Song Style:  Washed Out Call it Off

5) Electronic Style:  SNAP Rhythm is a Dancer 

6) Pop Style  Dynamite Taio Cruz

7) Electric Slide Style

8) Kermit Style:  Rainbow Connection

9) Harry Potter Style

10) Batman Style:  Dark Knight  Introduce a Little Anarchy

11) Video Game Style:  Mario Theme Song
12) YMCA Style
13) 70s Style: ABBA Dancing Queen
14) Star Style:  Cold Play A Sky Full of Starts

p.s. I don't show the music videos, I just use these links to play the songs.

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.