Visualizing Orders of Operations
I believe there are certain things that we as teachers should require our students to memorize. In math, students simply must know the correct order of operations or they will be frustrated and discouraged when they get the wrong answers to fundamental math problems over and over again, often not knowing why. But at the same time we need to give examples of where and why order of operations matter. This activity builds upon a well known mnemonic, PEMDAS, (“Please Excuse My Dear Aunt Sally and the elementary level version MDAS – “My Dog Always Sleeps”, my own rendition), with pictures that demonstrate examples of why these rules are needed.
This activity includes colorable worksheets, (which I call ‘PictoNotes’), that students can use to help them memorized the Order of Operations mnemonics, (PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction. The elementary version usually omits the ‘P’ and ‘E’ so, MDAS; also included.) Perhaps more importantly, this activity helps to lay the foundations of more abstract mathematical concepts like variables. (Great for a Math Center activity!)
In addition, you get ‘PictoNotes’ that visually demonstrate why order of operations is needed to get the correct answer. On the first two examples I have drawn pictures to help create a narrative for each rule; the remaining PictoNotes I have deliberately left for you and/or your students to create their own stories. (Note: you and your students do not need to be artists to do these activities. Simple stick figures can be used, (or ‘star people’), and it is more important that the student can visualize the mathematical principle rather than draw a beautiful picture).
There are many ways to do this activity. For example, you can teach the mnemonic first and then have students complete the worksheets; OR you can give the students the PictoNotes first and then see if they can discover the correct order of operations on their own. In either case, have students share stories about what they think is happening in each case. Even though the pictures are simplistic, the stories you will hear are often quite elaborate. (Creating narratives and groups discussions about math is perhaps the most important thing we can do as educators to make math more interesting and memorable.)
This packet includes:
9- Black and white printable PictoNote worksheets for traditional photocopying
9- Color digital Pictonote worksheets or presentation templates, designed for digital devices, e.g. an iPad or tablet, or for teacher use in power point, or interactive white board presentations.)
Help make math fun and meaningful.
This unit activity meets or exceeds 21st Century and STEM learning expectations, and Common Core learning outcomes. (I think STEM, which stands for science, technology, engineering and math, should be changed to STEAM, where 'A' stands for Art. What do you think?)