Singapore Math: Drawing Models

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This technique is one of the most powerful techniques in helping your student or child understand complex Math word problems.

It is a visual way of helping you understand the question. The concept is easy to undestand but there are some rules to follow to get the most out of this method.

Basically, 'drawing models' require you to draw boxes or rectangles to represent numbers. It enables us to compare numbers, fractions, ratios and percentages easily.

Let's look at a few simple questions so you can get a better idea about how it all works. It is very important to go through all the simple questions until you have a good understanding of how to draw models.

Make sure you try it out yourself!


Charlie and James are picking up pebbles.  Charlie picked up two-thirds as many pebbles as James.  After James threw away 16 pebbles, he has 3 fewer pebbles than Charlie.  How many pebbles did Charlie pick up?


Learn to apply this method.

Question 1

This question uses the concept of 'more than'.

The information given in this question is very straight-forward and easy to understand.  This type of question is a good starting point in learning how to draw models.

In this question, 2 quantities are given and you need to compare them to find the difference.

The first thing we have to decide is "Who has the bigger number?" Then we draw the models according these rules.

Rules to remember:

  • The size of the rectangle or box should correspond to the number; a bigger number should have a bigger box.
  • The boxes should be aligned to the left to make it easy to compare their size.
  • Add color to make the 'extra' or 'excess' portion stand out.
  • Use braces or brackets to write the number / words outside of the box. 

By looking at the models, we can tell straightaway that we need to use subtraction to find the answer, the 'more than' portion.

30 - 24 = 6

Question 2

Here is another question that uses the concept of 'more than'. Although the question is phrased differently from question 1, we draw very similar models.

In this question, 1 quantity is given and you have to find the second quantity. The difference is given to allow you to be able to compare them.

Again we have to first decide who has the bigger number and draw the 2 boxes accordingly. I like to draw the bigger box above the smaller box but you can also draw them the reverse way.

Rule to remember:

  • Learn to infer 'hidden' information.

Although the question only gives us the number of Mary's apples, we can infer that the portion of Andy's box that is the same size as Mary's box must be the same number so we write it in.

This model is slightly different from that of question 1 in that we write some numbers inside the box. We can also add a question mark to help us understand which part we need to find out.

Study both questions again to understand when to write numbers inside the box and when to write them outside the box.

Can you see that in this question we need to use addition to find the answer?

24 + 10 = 34

Question 3

This question uses the concept of 'less than'.

By drawing models, it becomes clear than 'less than' and 'more than' are closely related concepts.

In this question, 1 quantity is given and you must find the second. The difference is given so you can compare them.

Think about:

  1. Who has the bigger number?
  2. Should you write the number inside or outside the box?
  3. Where should you place the question mark?

Which operation do we need to use to find the answer?

Yes, it's subtraction.

30 - 6 = 24

Question 4

This question is similar to question 2 and uses the concept of 'more than'.

In question 2, the smaller number is given but in this question, the bigger number is given.

Can you see that although the concept is 'more than' which most students take to mean addition, this question actually requires you to use subtraction to find the answer.

30 - 10 = 20

More Questions

Eric is doing his Math homework.  He added two four-digit numbers and got the answer 7467.  He then subtracted the smaller number from the larger and got the answer 1351.  What are the 2 numbers?


Marty loves reading. He goes to the library every week. He borrowed 25 more books in June than in May. In July he borrowed half as many books as he did in May. How many books did he borrow in May if he had borrowed a total of 120 books for May, June and July?


I bought 6 pens and some books. Each pen costs $3 and each book costs $7. How many books did I buy if I paid $74 in all?


Marla finished reading her book in 3 days.  On the first day, she read 40% of the total number of pages.  The ratio of the number of pages read on the 2nd day to the 3rd day is 3:5.

If she read 18 more pages on the 3rd day than on the 2nd, how many pages does the book have altogether?


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