Students writing in math class

I started this towards the end of the year, and it's something I'll definitely continue next year.  I would create an assignment on Edmodo that asked my students to write explanations, rules, real-world examples, etc. about a particular topic we had been working on in class.  I used Edmodo because it allowed me the ability to quickly and easily provide students feedback so they could refine and improve their response.  Below are some examples of the following assignment: Write an explanation of how to solve systems of equations. How many ways do you know? Explain how to find the solution to both equations? How do you know your solution is correct? Consider these questions when typing your response. This assignment is not due until next Friday, May 31. Click TURN IN to enter your response. Do NOT submit the assignment as a comment under this post.

1. Graphing 
Solve both equations for y to change them to y=mx+b form. Then graph both lines and the solution is the point where both lines meet. 
2. Elimination 
If needed multiply one or both of the equations by a certain number until you can eliminate or cancel out one of the variables by adding the equations. Then solve for the remaining variable. When you have solved for one variable plug it into one of the original equations and solve for the other variable. 
3. Substitution 
In one of the equations solve for either variable. Then plug that solution into the other in the place of the variable you solved for. Then using the new equation solve for the variable that is left. Once you solve for that variable plug the number into the original equation and solve for the remaining variable. 

On all three methods you can plug in your answers and if they make both equations true, you have the right answer.

Here are the three ways I know how to solve systems of equation: 
1.Graphing 
First, you make sure that the equations are in y=mx+b form. If they are not, you have to rearrange the equations so they are. After that, you use the y-intercept and plot the first point on a graph. Then, you use the slope to plot the next point. Once you have done that, you do the same thing for the second equation. Finally, you find the x and y coordinates of the point where the lines cross through each other. That is your answer. 

2. Elimination 
First, you combine the two equations. You add/subtract the x's and the y's and the numbers. If you have one variable and one number then you plug that variable into one of the equations and solve for the other variable. If you have two variables when you combine the equations, then you must rearrange the equation so one of the variables is on a side by itself (y=number+x).Then, you plug that equation into one of the original equations that you combined. If you have y=number+x then wherever the "y" is in the original equation you put "number+x" in instead and solve the equation like that. Once you find out what the variable is, you plug it into the equation from when you combined and rearranged the two equations (y=number+x). You can then find the other variable. It does not matter if you rearrange the equation to find x or y. You end up with the same answer in the end. 

3.Substitution 
First, make sure that there is one variable on a side by itself in one of the equations. If not, rearrange the equation so there is. After that, you take the equation with the variable on the side by itself and plug it in to the other equation for that variable. You should end up with two of the same variables in the equation(x and x or y and y), then solve it. Once you solve it, you take the variable that you just solved for and plug it in to the second equation that you have not solved yet. Once you solve that equation, you take the x answer from one equation and the y answer from the other and that is your answer. 

You can check your answer when solving systems of equations by plugging the x and y coordinates back in to either of the equations and see if the equation is equal. You can also solve the equations using the opposite equation you used the last time. Whatever equation you started with, start with the other equation. 

Here is another example of an assignment where my students were required to write in order to demonstrate understanding. In response to this assignment, type out the rules for exponents. When can you add the exponents, subtract the exponents, multiply the exponents? Use proper grammar, capitalize, and punctuate properly please. It is part of your grade. You may submit this assignment whenever you are ready. If you don't submit the assignment today, I will assume that you are still working on EXPONENT RULES. You have until May 31 to complete the assignment.

I found that by requiring students to write out "math", which is at times a difficult skill, they developed a deeper understanding.  I began to get comments like "I'll never forget this Mr. Oldfield", which is what I had intended in the first place.