Patterns, Expressions, Equations... Oh My!

I have always been pretty confident in my vocabulary and my ability to understand words and place them in the proper context; maybe it’s the English major in me.  However, this math course is entirely popping my word-ego! Twice now I have been completely dumbfounded by the true definition of words I always thought to be synonymous with other math terms.

Number 1: Sum and Product

For my entire math career I have assumed these two words could be interchanged. Maybe this was because of a miscommunication somewhere in my education and maybe its because I just was not paying attention but I always thought they were one and the same. It was not until this year that I learned the word sum was in reference to addition and product to multiplication. Further more, I had absolutely no idea that subtraction and division also had their own ‘total’ words in difference and quotient (and embarrassingly enough it’s taken me about three weeks to remember this one!)

Number 2: Equation and Expression

Again, for some reason I always felt as though these two words were interchangeable. I actually had mostly forgotten about math ‘expressions’ entirely until reading the chapter on ‘patterning and algebra’ in the ‘Making Math Meaningful’ textbook. To be fair, these two are very similar and I can see how students would confuse them. Pertaining to algebraic equations I have now mastered that equations are an expression equal to something else. Therefore equations will have an equal sign, where expressions will not!

©Careccia’s Class Blog

This week one of our instructors told the class that if there is one thing we should take away from our lessons in teachers college it is differentiated instruction, that is, planning lessons and assessments to suit the individual needs of all students. One of the important aspects of differentiated instruction is providing students with choice.

            This week in class we were discussing Patterning and Algebra. The first activity we did had us working with our table groups to sort 16 cards into the 4 patterns they were demonstrating. The patterns were represented through graphs, tables, expressions and models. It was our job to sort the 16 cards into the four matching groups. We also had the opportunity to use 'snap blocks' to give us a concrete example and help visually demonstrate the patterns in a larger form than the model allowed. I really liked this activity because to me, it was an example of differentiated instruction that wasn’t structured towards any particular individual but catered to the possibility of different learning styles. And even though all students would be expected to sort through all four representations, it ensured that there should be a type that would be initially understandable to all learning styles and therefore at least allow everyone to START solving the problem.  For example, I was partial to the Tables or T-charts and used them as my starting point before trying to match them with the other representations.

          I really enjoyed watching the video about three-part lessons. The Brock lesson plan we have been provided is extremely detailed and a little bit daunting. Watching the video about the implementation of lesson plans and seeing the three stages really clarified the information for me. Seeing and hearing the teachers thoughts while going through the process made it much easier to grasp and also demonstrated the positive effects of co-teaching (it's always good to have more than one perspective!)

I did my learning activity presentation this week and have discovered the thing that will be my biggest stepping-stone for teaching – the actual teaching part. Yes, I am aware that standing in front of a group of people is a part of teaching but I never realized how nervous it would make me (mind you, there’s something significantly scarier when its your peers rather than a group of children!). Luckily, Pat showed us a quote beforehand that saved me from letting my feelings about my presentation defeat me...

'Don't cary mistakes with you, place them under your feet and use them as stepping stones' 

I think this may be my new mantra as I work my way through teachers college (and especially my experiences in math!)… after all, this presentation won’t be the first time I feel I could have done better and it definitely won’t be the last! 

Always remember to keep moving forward! :)