3 Ways Using Math Can Improve Students’ Drawings

Schools generally divide subjects into isolated bodies of knowledge which neither inform nor advance one another. Even though art educators are skilled at bringing cross-curricular connections into the classroom, they can sometimes be met with resistance. Students often say things like, “This is art class. Why are we talking about math?”

However, whether it’s mixing paint colors or drawing an image, using math in the art room is essential. Plus, the more you show students how using math can improve their work, the less they’ll complain when you make them get out the rulers.

Here are three ways math and drawing go hand-in-hand.

1. Measurement

It’s no secret students struggle using rulers. Besides being important for several forms of art, being able to use a ruler has value in numerous areas of life. The use of measurement tools is the foundation of fields like construction, carpentry, and engineering.

One way to improve students’ ruler skills is to assign a drawing that requires replicating an image to scale.

For example, let’s say you give students an image that is 5″x 8″ and give them a piece of drawing paper the same size. If the image is a monkey and the monkey’s head is 1.75″ in height and 1.5″ in length, students can measure out that same size for their drawing.

monkey with ruler

Rendering in this way uses mathematics and mirrors how computers generate imagery. This type of exercise will show students how keeping things proportional is a key of drawing realistically.

2. Ratio and Proportion

Using math to calculate scale is another opportunity to advance interdisciplinary skills. Administrators love when you can reinforce content from other areas. The beauty of working with ratio and proportion in the art room is that it has benefits for our subject as well. Most of the time, students are not trying to draw something in the exact size as their source image. However, it’s important to keep the same proportions when drawing for accuracy.

Having students create a simple formula to scale up an image is a great way to work on this concept.

Let’s use the same monkey as an example. If the monkey measures 6″ from the feet to the top of the head and the monkey’s head measures 1″,  we now know the ratio of height-of-head to total height is 1 to 6.

monkey with ruler

The student can then create an equation to ensure they will keep the correct head-to-height ratio in their drawing. Let’s say the student wants their drawn monkey to be 24″ high. Using a simple equation, the student can calculate exactly how high the head should be to ensure the correct proportions.

In the equation below, “1” represents the height of the head on the source image, “6” represents the height of the body on the source image, “24” represents the height of the drawn body, and “x” represents the height of the drawn head. Solving for “x” the student knows the drawn head must be 4 inches high. equation

The student can use this same type of equation to calculate anything about the monkey such as ratio of eye size to head size.

3. X/Y Axis

Another technique allowing artists to scale up a drawing is the well-known grid method. While this method sometimes stirs up debate, it’s a smart technique to use when transferring smaller sketches into larger final pieces. This can be especially true when working on murals, where a 10″ sketch needs to become a 50′ painting.

What students may not be aware of is this method is based on the X/Y axis.

Gridding is essentially dividing a composition into quadrants, and then creating more elaborate increments of division within that quadrant system. When doing a gridding exercise, students must be able to use this system to align objects in the right way to ensure accuracy.

The X/Y axis is also helpful when working with facial proportion. Many art educators teach students to divide the face into quadrants and line up features using the X/Y axis as a guide. Therefore, constantly reinforcing the concept of the X/Y axis and showing why it is useful beyond the walls of the math classroom can help students see how their knowledge can transfer between subjects.

We should welcome math in the art room. It provides helpful ways for students to solve creative problems. Regardless of your teaching style, it’s important to break down the walls of segregation between subjects. Students do not benefit from the belief that math, or any other subject, has no business in art class. Let’s not miss opportunities to help students see connections between subjects and how one can inform and advance another. Even if math does not play an obvious role in our own practice, we need to value math as a tool to inform the arts.

How do you use math in your own classroom or artistic practice?

What questions or concerns do you have about bringing math into the art room?

Matt Christenson

Matt is a high school visual arts and mural design teacher in San Francisco, CA who strives to cultivate maximum creative potential in all students.


  • J

    Hate to be the one to say it, but that tail does NOT look like a tail in the thumbnail on the main page

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