Concrete, Representational and Abstract

A few weeks ago I came across the blog Math Coach's Corner which really prompted me to consider how I can use the concrete and representational stages more in maths. It's because of this blog that I decided to have the kids use counters then draw pictures when working on their Maths Daily Puzzlers. Because of these stages, they are now writing number sentences which really correspond with the word problem. This skill can actually be very difficult at times and I think it will give them great preparation for when they start algebra.


Last week we had a math's test on graphing and interpreting data tables. One question asked, how much longer is Africa's Nile River than Australia's Murray River? I sat with two students today and they reattempted the question with my support and using our problem solving techniques.



We circled the pertinent data in the table (6700 km for Nile River, 2500 km for Murray River). They laid out counters, using 6 to show the Nile River and 2 to show the Murrary River. I used my pen to demonstrate that "how much longer" is the missing part (or the question mark part).





The girls then drew the problem using lines and labelling the length.

I suggested to the girls that they refer back to the counters and write a simple number sentence as a model. Once they did this, they had no problems looking at their drawing then writing the corresponding equation.

They were also able to apply their knowledge of inverse operations in order to solve it. Excellent job girls! Next stop - using counting on and other methods to solve such subtraction problems mentally!

I am more convinced than ever regarding the importance of using the concrete and representational stages when students are tackling challenging problems.