# Model Drawing for Math Problem Solving

Model Drawing is a highly effective method for solving Math questions that involve fractions and remainders. Drawing bar models allows your child to visualise the relationship between “Part” vs “Whole” clearly.

In this tutorial, we look at two questions taken from 2021 Prelim papers to help you learn how to use model drawing.

But before you read on, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

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Example 1

The first question is taken from the Tao Nan School Paper 2 and is worth 2 marks. This is a basic fraction question that can be solved using model drawing.

The key concept is that half of 3 units (3u) is \$3. Since Alan used 7 units of his allowance on food, he had 3 units left.

He spent half of the remaining 3 units, and he had \$3 left. This means the other half of the 3 units is \$3. To visualize this, a model drawing is necessary.

Step 1: Visualisation – Model the provided information

The first part of the model drawing is a long bar to represent the number of units. Alan’s allowance at first was 10 units, meaning the bar must have 10 equal parts.

Then, indicate the number of units spent on food (F). In this example, that is 7 units.

Alan spent half of his remaining allowance on stationary items. In the model drawing above, his remaining allowance is 3 units. However, 3 units cannot be split into half directly.

So, we have to split the middle unit into 2 halves to indicate that he spent half of his allowance on stationary (S). The other half would then be \$3.

Because one unit has been split into 2 halves, we have to split all the remaining units into 2 parts as well. This ensures that there are equal units throughout.

Step 2: Start solving the question

Since 3 units (3u) = \$3, then 1 unit (1u) is \$1. Because we’ve split every unit into 2 parts, Alan’s allowance will not be 10 units anymore. It will be 20 instead.

Make sure that your child or student uses the new total units when solving this type of question using model drawing.

Naturally, 20 units would be \$20, and this is the final answer to this question.

Example 2

This is a more complex question taken from the Catholic High School Paper 2, and it is worth 3 marks.

Since $\frac{3}{4}$ of the fruits were removed, $\frac{1}{4}$ of the fruits were left. That means $\frac{1}{8}$ of the apples and 30 pears = $\frac{1}{8}$ of the total number of fruits.

Step 1: Visualisation

Begin model drawing and split the bar into five equal groups.

Explanation: 5 was the original denominator, indicating the total number of fruits.

Out of 5 units, 4 were apples (A) and the rest were pears (P). Indicate that as shown in the worksheet below:

There were 4 units of apples. However, $\frac{1}{8}$ of the apples were left. In this case, we can't indicate $\frac{1}{8}$ right away. So, we have to split the 4 units into 2 groups.

To ensure that all units are the same, we also split the unit representing the pears. Now we have 10 units in total. Next, shade the unit that represents the number of apples left.

There were 30 pairs left, and we do not know how many units that represents. So, we shade a random part of the unit to indicate these remaining pears.

The two shaded portions represent $\frac{1}{4}$ of the total, and the unshaded portion would naturally be $\frac{3}{4}$ of the fruits that were removed.

Based on the shaded areas, 7 units (7u) of apples and 2 units (2u) minus 30 pears were removed.

This means that 7u and 2u - 30 is $\frac{3}{4}$ of the total number of fruits. So, the shaded 1u of apples + 30 would be $\frac{1}{4}$ of the total number of fruits. The equation forms of this information would be as follows:

To make a fair comparison during model drawing, ensure that the values on the right-hand side of both equations are the same. To convert $\frac{1}{4}$ into $\frac{3}{4}$, multiply the entire equation by 3.

The above effectively means that 9u – 30 is actually the same as 3u + 90. So, write that in another equation.

This point gets a bit tricky because your child may not yet learn to change the sign from positive to negative or vice versa when changing sides.

So, draw another smaller model representing 9u – 30. When we remove 30 from 9u, we are left with the length shown below the smaller model:

The length indicated in the second bar is also the same as 3u + 90. That means the portion between the end of 3u and the rest of the bar makes up 6 units (6u).

Therefore, 6u is 90 + 30, which would give us 120. Once this visualisation is done, you can write it in an equation form.

From here, you can determine the value of 1 unit which is 20. However, the question asked for the number of fruits that were in the box at first.

At first, we used a denominator of 5. So, our model drawing had 5 parts. However, each unit was split into 2 parts, making the new total units 10. That gives us a total of 200 fruits, and that is the final answer to this question.

I hope this tutorial was easy for you to follow, especially the second question. We used the method of elimination in simultaneous equations to solve the second question, but we did so in a way where P6 students can understand.

You might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

This will be delivered to your email inbox.

If you have any questions or suggestions, please leave them in the comments below.

You can also watch the full Model Drawing video tutorial here:

Ms Elaine Wee
Math and Science Specialist
Jimmy Maths and Grade Solution Learning Centre

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