by Hoover Herrera
Singapore Math® expert
hherrera@marshallcavendish.com

This question was posted by Jim M., Principal, NJ, during our most recent Singapore Math® webinar: Number Sense and the CPA Approach.

Can you go back in your mind to when you were seven? Imagine seeing this question:

59 people buy tickets to a show. 46 of them buy tickets to grandstand seats. 37 of them buy tickets to bleacher seats. How many people buy tickets for both grandstand seats and bleacher seats?

If I remember correctly, if I had seen this at seven years old, I would have just taken those three numbers in the problem and added them up, then subtracted them, in other words, I would have done a series of operations with those numbers in the hopes that one of my answers matched the correct solution. I called it my “doing anything is better than doing nothing method”. My childhood friend Marlon would probably had not gotten past the word “grandstand”. What would you have done as a seven year old? What do we expect our current seven year olds to do this school year with such a problem? Common Core expects second graders to represent and solve problems involving addition and subtraction. (CCSS.MATH.CONTENT.2.OA.A.1) Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (wow!)

How important are Bar Model drawings or the use of a Tape Diagram as Common Core calls it?  I didn’t have Bar Models when I was seven and somehow I survived. However, the problems our current young students are expected to solve these days sure do look a lot harder than the ones we used to get.

Here’s one possible model for the problem:

Does this drawing make sense to you?

Hundreds of teachers we have worked with nationwide would answer that Bar Models are an excellent way for students to enter a problem and “see” what is going on in the problem and begin to make sense of the problem situation. I recently used a similar problem while working with a group of teachers in Riverdale, New York. To their credit, the time they have invested in learning this strategy as learners has resulted in students learning and using the strategy and far fewer implementing my pointless “do anything method”.

How important do you think Bar Models are?

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