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Unit Bars

My kids don’t solve word problems.

They just don’t. I’ll ask them to read a problem, and they’ll sound out the words. Then i’ll ask them what the question was about, and I’ll only get blank stares. Further probing only results in “I don’t know”. These are kids that will happily follow through anything else i give them, but when they hit word problems, they go to pieces.

When they run across a word problem on tests, their usual strategy is to just add up all the numbers they see. even then, they’ll skip numbers that are written out as words rather than digits.

At the CMC South conference a couple of months ago, I attended a seminar on SIngapore Math, in particular the use of unit bars in solving word problems. It was a short seminar, with only a couple of examples.

Example of unit bars in action

I’m sure it was intended to promote sales of the Singapore Math textbooks, but that wasn’t part of my budget, and I wanted to be able to incorporate this into my other lessons, rather than having to buy into one single system (no matter how good it may be).

Fortunately, or unfortunately, this coincided with my acquisition of a school sponsored ibook and a copy of Keynote. I made up a set of slides and worksheets and tried them out on my kids.

(edit – the development of unit bars in this is questionable – it reflects my early attempts at understanding the concepts. There isn’t necessarily one right way to do this, but the bits and pieces serve a purpose. in this case, i was projecting the “3” onto equal sized rectangles, and breaking things down in units of 3. that’s not necessary, but it is reasonable to draw lines where the different pieces match up, since that’s a technique that will be used quite a bit later.)

This slide isn’t quite representative of how the lesson moved dynamically. The problem builds, with the red text as a prompt at each step. I put a couple of problems into the slideshow, the first one as an example to allow the students to copy, the second one used as verification after the students had finished the prompted part of the problem. Even though it was rather text heavy, it provided the new information bitwise, and in context, so that most of my students managed to follow along pretty well.

Changed i intend to make for the next time around include:

  • More pictures. put up a picture first, then fade in the question, and then fade out the picture to make room for solving the problem. My kids don’t do well with words, and a picture will help draw them in.
  • Fading the question out after the unit bars have been drawn and asking the students to recreate the question.
  • Providing just unit bar drawings, and asking students to create word problems from them.
  • Providing intermediate lessons before #4 where they have opportunities to solve the same types of problems, but this time without the contextual clues of having them all be the same type.

Things i learned in the process:

  • How to build slides, and how to use the slide as the building block for jumping through the steps, and builds within the slide to work through each step. This allowed me to backtrack quickly, and then proceed forward at the slower pace.
  • Create the final slide for a problem first, and then duplicate it and delete bits to make the earlier slides. This is the easiest way to keep everything lined up. I also used the textbox for the final answer as the location for the prompts to provide some consistency.

Overall, this lesson went well, though my pacing could have used some improvement (there were several points where the kids were complaining that they “got it already”). My administrator came in, and was suitably impressed, though that may speak more to the environment I’m teaching in than anything else.

{ 5 } Comments

  1. Ben Chun | December 18, 2007 at 1:59 am | Permalink

    Welcome to the block!

    My question on the slide you’re showing… why units of 3 and then a little unit of 1?

    In the Singapore example, they’re using the bars to represent unknowns. This is helpful because it gives some kind of concrete visual representation to the abstract variables. It lets students start drawing a picture that parallels the word problem, before they fully understand what it’s asking.

    So in the problem you’re showing, why can’t the students just draw dots or hash marks to represent magazine subscriptions?

  2. Stephen Pierce | December 18, 2007 at 9:42 am | Permalink


    We offer a book delaing with the above approach. It is called 8 Step Model Drawing. It might be of interest to you. Please feel free to visit our website.

  3. Mr K. | December 18, 2007 at 10:18 am | Permalink

    > why units of 3 and then a little unit of 1?

    because i was still getting familiar with the concepts. the way i’d teach it now is to draw one block of 3, and one bigger one of four. it’s not necessary for this problem, but it does lay the groundwork for looking for equivalent amounts.

    stephen – thank you – i will check it out.

  4. T. Henderson | January 11, 2010 at 10:27 am | Permalink

    Thanks for this site. I too attended a Singapore Modeling workshop and walked away with the same thoughts. Your site makes it easier. I do have questions about Algebra. How can the unit bars be easily understood with Algebra?

  5. Burt | January 13, 2010 at 12:55 am | Permalink

    Mr. K, you might be interested in the Singapore Maths Teacher website. It was created by a former Singapore Math teacher, and it shows how they solve problems in Singapore Math, including but not limited to the block models. The site is well done and gave me a good sense of their approach to problem solving.