Monday, March 26, 2018

Math in Focus: Bar Models with Manipulatives


At my school we use Math in Focus (Singapore Math) program, and with state testing coming up my fourth graders need a lot of review using bar models for problem solving.  This is by far the most challenging chapter (is it just us?).  For those of you who aren't familiar with MIF, one of the earlier fourth grade math word problems might be:

My sister had $8,359, and I had 3,596 less than her.  How much did we have altogether?

Well, my first year I think I was even more scared than they were (at first, since they didn't know better).  Even many adults, at first glance, estimate the answer to nearly $12,000 instead of the actual answer of over $13,000.  Although I'm more familiar with the content now, it's still a struggle for a lot of my students to master the sample problems as they become more complex than this one, and to complete them independently.  Like most programs, Singapore talks about a gradual release of responsibility.  And like most programs, we start with manipulatives before requiring abstract thinking.  Yet there were no manipulatives for bar models; just visuals.  Until now.


All I did was cut strips of paper cut into 2 different sizes.  The yellow paper is a Post It note with the sticky side holding the strips in place.  For my students, "Noun 1" and "Noun 2" were replaced with "Me" and "My sister."  

I told my class to remember these things as we progressed through the chapter:
1.  Bar models are just a tool to make solving math word problems easier; they are not there to make us crazy.  
2.  Bar models are at their most useful in fourth grade problems for helping us keep track of who has the bigger amount, who has the smaller amount, the difference, and the combined total.  


In the above problem, I told my students, "I have some money.  My sister has some more.  Decide where to put the little bar, and where to put the big bar."  Everyone was able to do that, so I told them that in this case, they'd know when it came time to draw the bars and put the bigger number with the right person, they could do it.

Below, I asked them to show me how much we had altogether.  Easy.  Indicate both.  That funny bracket in the book could be indicated with just their fingers.  Again, it totally took away the pressure of "I can't draw that weird mustache thing," (although they love when I draw it because hey, mustaches are cool, haha).


Below, I asked them to cover up all the extra money my sister had so that it looked like we had the same amount.  That covering up was "taking away" the extra. I told them that what I was doing for this sort of question was to subtract.


In the problem below, I told them, "I have some money.  My sister has some more.  Show me how much more."  Those funny brackets they show in the book were indicated with their fingers.  I told them if they were looking for the difference between the two bars, it's a smaller amount than the bigger bar, so they'd know they'd subtract.


The activity was a huge hit.  Notice that no numbers were mentioned today!  It was all about conceptualizing the process using manipulatives.  Kids whose computation is shaky could follow along at the same level as everyone else.  Even those kids who don't like to write were successful.  And an unexpected side effect to using these bars was that when it was time to start drawing them, all but two students had them lined up correctly on the left!  I wanted to go back to do this lesson all over again with my former students from last year who kept drawing the bars right after the words instead of lining them up correctly.

The next logical step for this lesson is, of course, to use numbers to introduce computation.  I start small (small numbers) and differentiate the numbers used for my class.  There's still minimal writing, and students move the bars around, but this time they also move around the numbers.  We followed up with a fun, free website I describe in this post.  I have this engaging bar model activity available for you too!

Readers, are any of you using Math in Focus/Singapore Math?  Do you have any tips you can share on how to survive chapter 3 with bar models?





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