We have all heard “show your work” from a teacher or two. We have all groaned as we erase and rewrite the math problem, wondering why it’s necessary – why should students show their work when they already got the right answer? I’m here to explain to you that your math teacher did, in fact, have a good reason for this request. Showing your work is an important part of the math process.
What Does Show Your Work Mean?
Before we can even discuss the importance of showing your work, we have to know what it means—what it really means to show your work in math. Too often I see students write down one step (of 3 or 4 steps) of a problem and say they showed their work. This isn’t showing work in math. If you show your work properly, your math teacher should know how you reached your answer by just looking at your work. If you skip a step, your teacher won’t know where certain numbers came from (and we all know they didn’t come from thin air).
Showing Work in Math Problems: Why It’s Important
Now, to answer the age-old question: “Why do we have to show our work?” I touched on the first reason a little bit—your teacher or math tutor needs to know how you got to your answer. If you got the wrong answer, she needs to know where you made a mistake. Often, it’s a simple calculation error that made you get the wrong answer, and if the work is graded, your teacher can still give you some points for the correct logic. Your teacher can also explain the correct steps better if she knows where you went wrong in the process.
Even if your teacher isn’t grading your work, it’s still important to show your work. If you finish a problem and get the incorrect answer, you can go through your work step-by-step to see where you went wrong. This is a much easier process than completely redoing the entire problem to figure out what you did wrong.
In my opinion, this last reason for showing your work is the most important: you should show your work to organize your thoughts when solving the math problem. Math is a step-by-step process and writing down all of your steps helps you understand where to go next. If you try to do your work in your head, you may skip some steps because you have trouble visualizing the problem. Writing it all down helps you to visualize what comes next. This, in turn, will eliminate errors and having to redo math problems later.
I promise you this—the more work you do now, the less you will have to do later. The more effort you put into showing your work, the more you will retain and the less likely you will be to make mistakes.
Tips for Showing Work in Math
Showing your work will look different depending on the type of problem; however, your work should have a few basic qualities. In order to properly show your work:
- your work must be neat. If you or teacher can’t read it, it’s no use to you.
- your work should not skip any steps, no matter how minor they are.
- the steps should be in an order that makes sense—follow a flow on the paper that would make sense to you and your teacher. Do not write your work randomly or sporadically on the paper.
- your final answer should be circled. This makes for easy grading and checking later.
Of course, every teacher has different requirements for showing your work, but these are general tips to help you get started. Different math courses will require different types of work. For example, in Geometry, you will most likely have to label or draw shapes to show your work, and in a subject like Algebra, your work will be more linear on your paper.
So, next time your math teacher asks you to show your work, don’t groan—she is only trying to help you. Showing your work in math will save you time and effort in the long run. Show your work now, and save some trouble later.
Do you have any tips for showing your work in a math problem? Let us know in the comments!
Becky Adams, Curriculum Manager at A Grade Ahead
I homeschool my son and am constantly BEGGING him to show his work. He is quite bright and often shocks me by how much he is able to calculate in his head, but as we explore more difficult concepts (and longer problems with more steps) the writing of work is becoming a problem – causing consistently incorrect answers and lots of frustration. I am printing this article as one of his assignments to read – hoping a fellow teacher (vs. his mom!) will be able to get through. Thank you for the very well-written blog with rational and straightforward reasoning for showing one’s work!
The 7 standards for mathematical practice support showing your work and showing your evidence supports them in return. Writing helps the brain learn anything faster, retain it and be able to retrieve it when needed. Sometimes a child is good at a process but can’t explain why (concept) or interpret the parts of their work or what their answer means. I have started using error analysis problems where they have to explain the error rather than just solve a problem because it requires higher level thinking. I also write “show how to solve” and if they don’t show me, they aren’t even completing the task because I didn’t say give me the answer or solve, I said show or explain. If they can’t explain to you or someone else what to do, they don’t understand it at the deepest level because it requires you to think flexibly about a problem in order to explain how to do it and why it works. It requires a more in depth, wholistic understanding to add the language component to it.
Our greatest scientists, engineers etc had to explain and show people their thinking and there were 100s of incorrect answers and it took analysis of the work by multiple people to find the errors in thinking that led to our greatest discoveries. The application in the real world often involves a lot of showing and explaining in emails and documents before the math and science and money are applied to say, build a bridge so it won’t collapse and kill people…