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Why is the Singapore model drawing an effective tool to teach younger students algebra? Can tutors use this method in maths tuition? What are the available free tools that teaches young students how to use this method? Learn all this and more in this article.

Solve maths word problems using model drawing.

Why use model drawing

Model drawing is effective because of the systematic and consistent way it is taught. Each level addresses distinct operations and number relationships—addition and subtraction in first level, multiplication and division in second level, fractions and ratios in third and fourth levels—so students can visualize and solve increasingly complex problems. 

In Singapore, students learn to represent these objects with rectangles that enable them to see the number relationships, instead of focusing on the objects of the problems. Rectangles are used because they are easy to draw, divide, represent larger numbers, and display proportional relationships. Model drawing is a useful tool for students to learn about algebra.

Bar Modelling examples

Students are first introduced to model drawing to represent part/part whole situations that can be solved with addition or subtraction. 

Addition:

The first problem might be as simple as: 

Henry has 17 breadsticks. His friend has 14. How may do they have altogether? 

maths addition
maths tuition tools addition

Students would draw one bar, divided into two parts, one slightly longer than the other. In this problem the two parts are “known,” and the student must add to find the whole or the “unknown.” 

Subtraction:

There are 28 cookies in a bowl. 17 are from students. The rest are from the school. How many are from the school? 

maths tuition subtraction
maths tuition tools subtraction

In this problem, the student knows the whole and one part, and can solve for the missing part either by adding up or subtracting, so students understand the relationship between addition and subtraction. 

Students solve for an unknown variable at a pictorial stage, which aids the transition into the abstract. 

Multiplication/Division:

The sum of two numbers is 40. The larger number is three times the smaller number. Find the two numbers. Imagine drawing the smaller number as a rectangle. Then the larger number would be three of them and the sum of the two is 40. The student quickly visualizes that the sum of the four bars is 40, and that 40 ÷ 4 = 10 for the smaller number and 30 for the larger one.

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maths tuition tools multiplication

Fractions/Ratios:

At higher level, bar modelling can be used for solving more complex problems involving fractions and ratios.

Keita spent 4/7 of his money on a pair of shoes. The shoes cost $48. How much money did he have at first? 

maths tuition fractions
maths tuition tools fractions

The comparison problem might read: There are 3/5 as many girls as boys. If there are 85 boys, how many girls are there?

maths tuition ratios
maths tuition tools ratios

Useful tools 

Parents and tutors can consider using online website mathplayground as an introduction to the modelling. There are videos, and default templates for the students.

Process:

Step 1: Watch part-whole videos

These videos provides step by step explanation how students can transition the word problem into bar modelling. For more complex problems, there are videos explaining multi steps bar modelling.

Step 2: Watch comparison videos

These videos provides step by step explanation how students can transition the comparison word problem into bar modelling.

Step 3: Hands-on practice 

After the concept videos, students should get some practice. Select thinking blocks addition.

Step 4: Create own word problems

Finally, students can reinforce their learning by creating word problems of their own. It is a good practice for them to identify the known variables, and deciding which variable should be the unknown. Make it more fun for them by encouraging them to use their friend’s names, and actual items that they come across in daily life. Need more practice? Use past year exam papers from top schools.

Interested in this maths method? Learn more from one of our maths tutors.

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