Why Fluency Needs Creative Application
The ultimate goal of fluency and number sense practice is not speed, it’s the ability to think flexibly about numbers and apply them in meaningful ways.
A simple multiplication fact like 5 × 8 doesn’t live in isolation. It shows up again and again across a student’s academic life: in fractions, algebra, trigonometry, calculus, physics, economics, and beyond. When students truly understand numbers, they can recognize and use those relationships wherever they appear.
One of the clearest signs of mastery is the ability to use knowledge creatively, not just recall it on demand.
What Are Number Portraits?
That’s where Number Portraits come in.
In a Number Portrait task, each student is given a number, expression, or equation and asked to create a visual, creative representation of it using Tile Farm Studio. This process reveals far more than whether a student can compute correctly. It shows how they reason, how flexibly they think, and how deeply they understand the mathematics involved.
Fluency That Encourages Thinking, Struggle, and Joy
Number Portraits naturally invite productive struggle. Students test ideas, revise their work, and refine how they represent a mathematical idea. In doing so, they demonstrate real fluency—not just correctness, but understanding.
Just as importantly, Number Portraits turn fluency and number sense into something joyful and expressive. Even students who are typically quiet or hesitant often light up when given the chance to share their thinking visually. The activity has a low floor, high ceiling, and wide walls, allowing every student to engage while leaving room for depth, creativity, and extension.
What Does This Look Like in Practice?
The best way to understand Number Portraits is to see students’ work.
Below are examples of Number Portraits spanning a wide range of mathematical ideas. Each one beautifully expresses how students use fluency as a tool for thinking and expression.
1. Representations of 10
The image above shows six diverse representations of 10 made by students in Pasadena, CA. Can you see how each Number Portrait represents the number 10?
2. Artistic Addition Fact
The image above, made by a student from Tucson, AZ shows how number portraits can connect fluency with things that are personally meaningful to students.
3. Multiple Representations of Multiplication
Number portraits are a fantastic way for students to display their understanding of multiplication facts. The example above shows nine different representations a student made of the fact 3*9=27.
4. Order of Operations
Number portraits can turn difficult to grasp concepts like order of operations into simple artistic representations that are easy to understand. This Number Portrait is an artistic visual representation of (2*6 + 1)*6 =78 78.
5. Colorful Fractions
Even just a single Number Portraits activity can do wonders for developing students’ fraction sense. The canvas above is one students’ beautiful representation of ⅔ * ¼ = ⅙ .
Want to bring more creativity to your fluency and number sense routines?
Contact us for a demo or sign up for a free trial of Tile Farm Academy today!