A 2-session unit for middle school, high school, or adult learners. Students take a reference image, divide it with a numbered grid, calculate the scale factor by hand, then redraw it cell by cell at a larger size on paper or canvas — the classic technique painters call squaring up. The unit finishes by contrasting this pencil-and-ruler method with AR tracing, so learners understand the maths under both, and when each is the right tool.
Same reference, same number of cells, bigger squares. Multiply every measurement by the scale factor and the proportions ride up untouched — that is squaring up.
Level
Intermediate
Grade band
MS–HS / adult
Sessions
2 × 45 min
Total time
90 minutes
Overlay
Square grid
Learning objectives
By the end of the unit, students will:
Explain why a grid lets a reference be enlarged accurately by hand without freehand guessing
Calculate a scale factor from the ratio of a large cell to a small cell, and apply it consistently
Set up matching grids on a reference and a larger surface, keeping the same number of rows and columns
Draw an enlargement cell by cell, treating each cell as a small, self-contained drawing problem
Compare the hand grid method with AR tracing and judge when each approach suits the job
Standards alignment
VA:Cr2.1.8aDemonstrate willingness to experiment, innovate, and take risks to pursue ideas, forms, and meanings that emerge in the process of art-making or designing.
VA:Cr1.2.7aDevelop criteria to guide making a work of art or design to meet an identified goal.
VA:Re7.2.7aAnalyze multiple ways that images influence specific audiences.
Materials
A reference image per student — a printed photo or a simple line drawing at index-card or quarter-sheet scale works best
Larger drawing surface: cartridge paper, a sketchbook spread, or a small stretched canvas
Ruler, set square or T-square, sharp pencils, and a good eraser
Calculators for the scale-factor step, or let students do the arithmetic by hand
Optional: an internet-connected device to set up the square-grid overlay in the free browser tool for planning, plus a phone with the AR app for the session 2 comparison
Lesson sequence
1
Grid the reference and find the scale factor
45 minutes
Warm-up · 5 min
Show a small reference photo beside a large drawing made from it. Ask "How do you copy this up to twice the size and keep the face from looking stretched?" Collect guesses. Name the two honest answers students reach for — tracing and grids — and explain that today is the grid, the method Renaissance workshops called squaring up, which needs nothing but a ruler and careful counting. It is the same idea behind every overlay in the tool, done here entirely by hand so the maths is visible.
Main activity · 30 min
(6 min) Students rule an even grid over their reference — a 4-by-4 grid of one-inch squares suits a first attempt — then number the columns 1–4 across the top and letter the rows A–D down the side. The labels are the address system that keeps cell (C2) on the reference matched to cell (C2) on the enlargement. Students who want a clean check can set the same grid on the image in the square-grid overlay.
(8 min) Introduce the scale factor as one division. If a reference cell is 1 inch and the enlargement cell will be 3 inches, the scale factor is 3 ÷ 1 = 3. Every measurement — line lengths, gaps, the curve of a jaw — gets multiplied by 3. Students choose a target size, compute their own factor, and write it at the top of the sheet.
(10 min) Students measure two or three features inside one cell (say, "the stem meets the top edge 0.3 in from the left") and multiply by the scale factor to predict where that feature lands on the big grid ("0.9 in from the left of the large cell"). This rehearses the transfer before any large drawing begins.
(6 min) Rule the enlarged grid on the working surface: the same number of rows and columns, each square the enlarged cell size, numbered and lettered to match the reference exactly.
One cell, scaled by hand. A feature 0.3 in into the reference cell lands 0.9 in into the enlarged cell — same fraction of the cell, three times the distance.
Reflection · 10 min
What does the scale factor multiply — only line lengths, or the gaps and empty spaces too?
Why does keeping the same number of rows and columns matter more than the size of the squares?
Where do you predict your drawing will drift tomorrow, and how could the labelling catch the error early?
2
Draw the enlargement, then compare with AR
45 minutes
Warm-up · 5 min
Recap the plan: the whole reference is intimidating, but a single cell is not. Point at one square on your own enlarged grid and copy just the line inside it, out loud — "the line enters the left edge, curves up, and leaves the top." That narration is the entire method. Students will repeat it, cell after cell.
Main activity · 30 min
(20 min) The core move: students redraw the reference one cell at a time, copying only what crosses that single square. They are told not to look at the whole picture — just where each line enters the cell, where it leaves, and how it curves between. Drawing one small cell at a time is what makes a large, detailed reference manageable.
(4 min) Mid-point check: stand back. The lines should connect cell to cell into a recognisable enlargement. If a line jumps at a cell border, the count or the entry point is off — fix it now while the pencil is still light.
(6 min) Contrast with AR. Show the same reference locked over a sheet of paper in the AR app, where the phone camera holds the image in place so the artist can outline it directly without ruling any grid. Discuss the trade-off honestly: the grid method needs no device and teaches the underlying proportion maths, while AR skips the grid entirely and is faster once you have it. The free browser grid tool stays free and browser-only; the AR app is a separate paid add-on that adds the on-surface tracing a browser cannot do.
Left: the grid method — one line entering and one leaving each cell, repeated. Right: AR holds the reference on the surface with no grid at all. Same goal, different route.
Reflection · 10 min
Where did your enlargement hold proportion best, and where did it drift? Can you trace the drift to a specific cell?
Did working one cell at a time make the reference feel less intimidating? Why might that be?
After seeing AR, which method would you reach for next — and what does the grid method teach that AR can quietly skip?
Computes and applies the scale factor correctly throughout
Computes it correctly with minor application slips
Has the idea but applies it inconsistently
Cannot yet find the scale factor
Grid setup & labelling
Both grids match in count and are clearly numbered
Grids match with small labelling gaps
Grids partly match or labelling is unclear
Grids do not correspond
Proportional accuracy
Enlargement holds proportion across nearly all cells
Holds proportion in most cells
Noticeable drift in several cells
Proportions broadly lost
Method comparison
Explains clearly when to use the grid method vs AR and why
Compares the two with minor gaps
Names a difference but reasoning is thin
Cannot yet contrast the methods
Extensions
The same design at three scale factors. Proportion is locked to the grid, not the size — that is the whole trick of squaring up.
Cross-disciplinary (math): Connect the scale factor to ratio and proportion. Have students prove that doubling the scale factor quadruples the area, and discuss why paint and time budgets grow faster than the drawing does.
Reduce instead of enlarge: Flip the method with a scale factor under one to shrink a large reference to a sketchbook. The maths is identical; only the direction changes.
Differentiation: Students who need support use a 3×3 grid and a simple silhouette; advanced students use a finer grid on a detailed portrait and the square-grid overlay for tighter registration.
History & technique: Research how squaring up moved a small cartoon to a full fresco, and where modern artists now reach for AR tracing instead — and what each choice trades away.
