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Quick Guide to Singapore Math Modeling

Linda Allen


Quick Guide to Singapore Math ModelingHow often do your students ask to do the word problems in the math assignment first?

How often do your students volunteer to explain what their thinking is during problem solving?

And how often do your students feel successful and confident with problem solving and computation?

If your answers are rarely or never, you’re not alone. Math is one of the most challenging subjects to inspire confidence and enthusiasm in your students. But it doesn’t have to be this way.

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 In classroom’s using the Singapore Math© method of model drawing and number sense, students develop a confidence and self assurance with problem solving and the computation that is part of that problem solving.

How is Singapore Math Different?

Math is more concrete before it changes into the pictorial, and then the abstract. Model drawing IS the pictorial. Students follow a protocol that provides them with step-by-step directions that help them break apart and understand every type of problem--addition, subtraction, multiplication, division, mixed operations, fractions, decimals, percentages, ratios, and rate. Students will develop a true bridge to algebra as they generate problem solving techniques for all types of problems.

We need to keep in mind that Singapore Math© has many components, but the two most widely taught in the United States are model drawing and number sense. Model drawing is one additional problem solving strategy. It isn’t the only way. You will still teach Guess and Check, Working Backwards, Looking for Patterns, and the other commonly taught methods. Once model drawing is learned it is often the first way students choose to solve a problem.

Singapore Math© Model Drawing - Simple Word Problems

Example: There were 6 cars parked in the lot. Two of the cars drove away. How many cars were left?


There were ____ cars left.

Quick Guide to Singapore Math Modeling

6 – 2 = 4


The L in the model above stands for the cars left in the lot. The D stands for the cars that drove away. The unit bars for the cars driven away are actually slashed out to show that they are no longer with us.  The answer of 4 is then placed in the sentence written at the beginning of the problem solving, “There were 4 cars left.”

This is a pretty simple problem and you might say, “My students can work this without drawing boxes for each car.” That might be true. But this is the beginning of understanding the structure of model drawing in a simple way so that as problems become more difficult they can use the same structure to solve problems they would never have even tried before.

Students as young as second graders learn:

*how to really read the word problem in a step-by-step way,
*how to identify variables,
*how to read the problem looking for meaning,
*how to set up the problem for computation, and
*how to make sure that they are answering the question they were asked.


Singapore Math© Model Drawing - Complex Word Problems

As numbers grow larger students obviously cannot draw 50, 100 or 1000 boxes. Here is an example to show how Singapore Math works with more complex, larger number word problems.


Third grade students are tasked with dividing 72 cookies into boxes of dozens to sell at the school’s bake sale. For this problem, you will use a different model that is still very pictorial, simple, and efficient.


Example: Divide 72 donated cookies into bags of 12 to sell for $2.25. A box of 72 cookies cost the class $6.00. How much money can the class make on the 72 cookies?


The class can earn _________ on each group of 72 cookies.



In this model drawing problem, the student uses a “continuous” model for the 72 cookies and can actually divide those cookies up by repeated subtraction or by creating and using a division problem. 


After drawing the markings for the 6 dozen cookies, the student goes back to the model and labels the cost of each dozen. Then the mental math computation is shown here in a written form. It looks more complicated than the way we write it out when teaching the traditional form of multiplication, but keep in mind that students won’t continue to write this, they will do this in their heads. You’ll be so surprised to see how quickly they learn to do this!

Other Singapore Math© Instructional Strategies

There are wonderful guidelines in Singapore Math© that keep children on track and able to solve so many word problems that they never have been able to work out before. The consistency of the model drawing formula helps them feel secure in their abilities, and it stimulates their math thinking.

There are several components that we teach before the model drawing strategy. These are also fun and efficient strategies that encourage active thinking and communication of math ideas—explaining the math wisdom in stories and books and story problems, counting, rote counting, skip counting, understanding the power of ten in our number system, place value, and so many additional forms of number sense. 

Math class is no longer drudgery for students or a headache for us. Even those of us who grew up not enjoying the classic “word problems” at the end of every chunk of learning will find ourselves looking forward to the challenge! And that is an astonishing change!

Do you use Singapore Math in your classroom? Share your tips or other successful instructional strategies in the comments section!

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