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.
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.
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:
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.