In word problems, it is common that students are faced with models as shown below (with the parts of the 2 bars not being equal). We have to teach them how to further “simplify” the bars so that we can find the answer we want. I guess most of us would have taught our students the technique of breaking the bars into common parts.
There will be a need to ask questions so that the students see why there is a need to find a common part. In this case, image the total is 72.
Possible questions to ask: Are the yellow and white parts equal ? Why can’t we say “2 yellow parts + 3 white parts = 5 parts”? How can I further simplify these bars (i.e leading on the need to find the common part and hence the need to find the common multiple o 2 and 3) ? Why must we choose the lowest common multiple of 2 and 3?)
Do note that in the video the parts are shaded in the same colour if they are equal.
One of the feature of the MaPS is that the same parts are shaded in the same colour. Bring the students’ attention to the fact all the common parts are shaded in the same colour (i.e. pink). Hopefully, this will let the students visualize what is going on when we break the bars into common parts.
My view is that students need to be convinced on why there is a need to find the common part. Hopefully, this reasoning will be etched on their minds and can adopt this very useful technique when there is a need.