To make a maths explainer video for a class assignment, choose one result or one method, not a chapter, and write a script that answers why it works before it shows how to do it. Structure it as question, picture, method, one fully worked example, a check, and the most common mistake. Say every symbol in words as well as writing it, keep each equation on screen short, and put one step on each scene. At 150 spoken words a minute, a 400 to 500 word script makes a three minute video, which is the length most teachers set. Then check every number on every scene by hand, because a drawn equation with one wrong sign loses the marks the whole video was meant to earn.

What the marker is looking for

A maths video is not marked like a film. Most rubrics for this kind of assignment come down to four things, and the first two carry most of the weight.

Notice that nothing here rewards animation for its own sake. A teacher watching thirty of these is looking for the moment where you explain the step most students only memorise. That moment is the assignment.

Pick a result small enough to explain properly

The usual mistake is choosing a topic that is really a unit: "quadratics", "trigonometry", "probability". In three minutes you can explain one idea well or six ideas badly.

Good sizes for a three minute maths video:

• Why completing the square works, and how it gives the quadratic formula
• Why the angles in a triangle add up to 180 degrees
• Why 1 + 2 + 3 + ... + n equals n(n + 1)/2
• What the derivative of x² means on a graph, and why it is 2x
• Why the probability of at least one six in four rolls is 1 minus (5/6)⁴, about 0.518
• What an eigenvector is, as the arrow a matrix only stretches (there is a full version in eigenvectors and eigenvalues explained visually)

Each of these has one picture at its centre. If you cannot say what the central picture is, the topic is either too big or not yet understood, and the second one is worth finding out before you start recording.

The structure, scene by scene

Use the same six parts for almost any result.

1. The question. One sentence the viewer could not answer before watching.
2. The picture. The diagram that makes the answer feel obvious. Area for algebra, a graph for calculus, a tree or grid for probability.
3. The method. The general steps, each tied back to the picture.
4. A worked example with real numbers. Every line shown, nothing skipped.
5. The check. Substitute the answer back in, or test it a second way.
6. The common mistake. The one error the teacher sees every year, and why it is wrong.

Parts 2 and 6 are what separate a strong video from a recording of a textbook page. Most student videos skip both.

Worked example: completing the square, drawn as a square

Here is a full scene list for a three minute video solving x² + 6x = 16. About 430 words of narration.

Scene 1, the question. "Solve x squared plus six x equals sixteen. You cannot just square root both sides, because of the six x. Completing the square is a way of making that six x disappear into a perfect square." On screen: x² + 6x = 16.

Scene 2, the picture. "Read x squared as an actual square, x by x. Read six x as a rectangle, six by x." On screen: a square labelled x on each side, and a 6 by x rectangle beside it.

Scene 3, split the rectangle. "Cut the six by x rectangle in half. Two strips, each three by x. Attach one to the right of the square and one to the bottom." On screen: an L shape, the x by x square with a 3 by x strip on two sides.

Scene 4, the missing corner. "This is nearly a bigger square, x plus three on each side. Only one corner is missing, three by three, which is nine. So add nine to both sides." On screen: the corner shaded in, labelled 9, and the line x² + 6x + 9 = 16 + 9.

Scene 5, the new square. "The left side is now a complete square, x plus three, all squared. The right side is twenty five." On screen: (x + 3)² = 25.

Scene 6, solve. "So x plus three is five, or x plus three is minus five. That gives x equals two, or x equals minus eight." On screen: x + 3 = ±5, then x = 2 or x = -8.

Scene 7, the check. "Check both. Two squared is four, plus twelve is sixteen. Minus eight squared is sixty four, minus forty eight is sixteen. Both work." On screen: 4 + 12 = 16 and 64 - 48 = 16.

Scene 8, the common mistake. "The picture only shows lengths, and lengths are positive, so it finds x equals two and hides minus eight. The algebra does not care. Whenever you square root both sides, write plus or minus." On screen: ±5 circled.

Scene 9, the general rule. "Every time, halve the coefficient of x, square it, add it to both sides. Do that with a x squared plus b x plus c equals zero and you get the quadratic formula." On screen: (b/2)² added, and the formula x = (-b ± √(b² - 4ac)) / 2a.

Scene 8 is the one a teacher will remember. It shows you know where the picture stops being trustworthy, which is a better sign of understanding than any amount of neat algebra.

Saying maths out loud

Narration that reads symbols badly is hard to follow. A few rules that fix most of it:

• Say what a symbol means, not what it looks like. "x squared", not "x two". "The square root of twenty five", not "root sign twenty five".
• Name brackets by what they group. "x plus three, all squared" is clear. "Open bracket x plus three close bracket squared" is not.
• Never read a long expression at all. Put it on screen and describe what it does: "the quadratic formula, which gives both solutions at once".
• Pause after each equals sign in the worked example. One short sentence per line of working, so the line appears as the narration reaches it.

Check every number, on every scene

Drawn and generated visuals are usually right about the shape of a diagram and occasionally wrong about its contents. In maths, the contents are the mark. Before you export, pause on each scene and check:

• Every coefficient, sign and exponent matches your written working.
• Labels on diagrams match the numbers in the narration (a strip labelled 3 by x, not 6 by x).
• The order of the lines in the working is the order you solved it.
• Plus or minus signs, fractions and square roots are drawn correctly, not approximated.

Fix wrong scenes one at a time in the editor rather than regenerating the whole video. If a formula keeps coming out wrong, simplify what is written on that scene and let the narration carry the rest.

Make it

1. 1

   Choose one result and write its question

   One sentence the viewer cannot answer yet. If it needs two sentences, the topic is too big for one video.

2. 2

   Find the central picture

   Area, a graph, a number line, a tree diagram. Sketch it on paper before writing any narration.

3. 3

   Write the script in six parts

   Question, picture, method, a worked example with real numbers, a check, and the common mistake. Aim for 400 to 500 words for three minutes.

4. 4

   Paste the script into openCanviz

   Set the target length and choose Keep my wording, so the narration says exactly the maths you checked. Whiteboard style suits maths because the working appears the way it would on a board.

5. 5

   Check every number on every scene

   Signs, exponents, labels and the order of the working. Fix any wrong scene in the editor, and simplify on-screen text where a formula is crowded.

6. 6

   Watch it as the marker

   Once through without pausing. If any step is announced but not explained, add one sentence of why to that scene.

Common questions

Can I use a generated voice, or does it have to be mine? Check the brief. Many maths teachers assess the explanation, not your delivery, so a generated voice reading your script is fine. If your own voice is required, record it and replace the generated narration; the drafted scenes still give you a timed script to read from.

How much algebra should be on screen at once? One or two lines. If a step needs four lines of working, split it across two scenes. The viewer cannot read ahead and listen at the same time.

Is it fine to explain something I learned from a YouTube video? Yes, if the script and the worked example are yours and you credit the source where your school expects it. Choosing your own numbers for the example is the easiest way to make sure the explanation is really yours. How to make a video for a school project covers AI use and academic honesty in more detail.

What if my topic really needs smooth animation? Some maths, like a grid being transformed, is clearer with continuous motion. A few labelled stages, drawn one after another, still carry the idea for a class video. How to make a maths YouTube channel like 3Blue1Brown on a budget explains when coded animation is worth the hours.

Does the same approach work for physics? Mostly, with one extra step: the mechanism. See how to make a physics explainer video that actually explains.