Model Drawing (Bar Modeling or Singapore Math)
Last year I was introduced to a strategy known as Singapore Math. I have since seen it referred to as Bar Modeling or Model Drawing. I was hesitant about any “new” strategy and very reluctant about anything that would take away from the beauty of “pure mathematics”. It only took one short training session to convince me that this is what had been missing in my classroom. I have tried many techniques such as tables, charts, and graphic organizers to help students with word problems with little success. This is one strategy that spans grade levels and abilities to help all students be successful in math. There are many great, free resources to help teachers get started.
I met with a fifth grade team today to work through a story problem that appeared very difficult at first:
Meg has 120 flowers at her flower stand. Of all the flowers, 1/4 are red,
1/8 are pink, and 1/8 are blue. Of the other half, 1/3 are yellow and
2/3 are purple. How many are there of each color?
If you are like most students, a problem with this much information and this many fractions scares you. I could see the the wheels turning in their heads as they were thinking things like: common denominator, multiplication of fractions, can we skip this one?
We first wrote the answer with a blank for our numbers. I love this technique for so many reasons!
Meg has __ red, __ pink, __ blue, __ yellow, and __ purple flowers.
We then decided what we were counting or talking about: Flowers. We drew a unit bar after the word flowers. (Hint: If the problem involves fractions, use a long unit bar. You will probably have to divide it.)
Next, we read the problem and pause to add in the information:
“Meg has 120 flowers at her flower stand.”
“Of all the flowers, 1/4 are red.” This means I need to divide my drawing into fourths.
“1/8 are pink, and 1/8 are blue.” I need to go back and divide the other pieces are divided into eighths.
“Of the other half, 1/3 are yellow.” Oh no, I should not have divided the second half of the bar into eighths. I will create another bar underneath it and divide it into thirds.
“and 2/3 are purple.” How many of each color?
Looking at the first bar, there are 8 sections, so each section contains (120 divided by 8) 15 flowers.
The second bar represents half of the 120 flowers, there are 60 flowers to share among three groups. This means there are 20 flower in each subgroup.
Now, all a student has to do is count of the number of flowers for each color group.
Meg has _30_ red, _15_ pink, _15_ blue, _20_ yellow, and _40_ purple flowers.
The great thing about the bar modeling process is it can be adapted for all levels of mathematics. I have seen fifth grade students solve a systems of equations using the bar modeling method. I know that all students do not need to use this method, but it is important that even the accelerated learners have a method or tool to use when the math becomes challenging.