Guide · 02 of 09

Exercises

An exercise is the checkable part of a slide — the thing the learner answers. Every exercise shares four optional lines: ask "..." (the prompt), hint "..." (repeatable — a hint ladder), ! "..." (the explanation shown after checking), and skill: "..." (the skill it tests).

expect#

A correctness check for the author, not the learner. Goes inside a numeric exercise and states, as a formula, why the answer is what it is. The compiler works it out and refuses to build if it disagrees with answer:. It's double-entry bookkeeping for math: writing answer: 0.8 next to expect: 4/sqrt(4^2+9) means a slipped decimal becomes a compile error instead of a wrong answer a student has to argue with. Nothing about it reaches the browser. Only numeric takes it, since it needs one unambiguous value to compare against.

expect: <expression>

prop	type	description
expect*	expr	closed-form value the answer must match, within tolerance

Example

For

h(x) = \sqrt{x^2+9}

, find

h'(4)

quiz#

Multiple choice. Mark the correct option with * and wrong options with -. Each option may carry a { why: "..." } giving per-option feedback shown when the learner picks it.

quiz {
  ask "Question?"
  - "wrong option" { [why: "..."] }
  * "correct option"
  [hint "..."]
  [! "explanation"]
}

Example

If a < 0, the parabola...

numeric#

A free-entry numeric answer. The learner types a number and it counts as correct if it lands within tolerance of any listed answer. Answers fold from expressions, so 64/3 or sqrt(2) are fine. tolerance defaults to a tiny epsilon (so type an exact expected value, or widen it for estimates). unit is shown as a suffix in the input.

numeric {
  ask "..."
  answer: <number>
  [answer: <another accepted value>]
  [tolerance: <n>]
  [unit: "..."]
}

prop	type	description
answer	number	an accepted value (repeatable)
tolerance	number	how far off is still correct (default ~0)
unit	string	label shown next to the input

Example

n \to \infty

, the area under x² on [0,4]?

build#

Tap tokens from the bank into slots to assemble an answer. List multiple answer: lines to accept equivalent orderings (e.g. commutative forms). Add reusable when a token can be placed more than once. Bank tokens and slots render as rich text, so "$f(a)$" is a perfectly good token. Without template, the slots are a bare row and slots defaults to the length of the first answer. With template, the slots sit inline in the text you write, which turns the same exercise into an expression builder or a fill-in-the-blank sentence. Mark each blank with ___ (three or more underscores). Underscores inside a $...$ span are left alone, so $x_1$ is safe — which also means a blank cannot go inside a math group like x^{...}; make the whole group a bank token instead. When a template is present it decides the slot count, so leave slots off.

build {
  ask "..."
  bank: ["tok", "tok", ...]
  answer: ["tok", ...]
  [answer: ["...alt ordering..."]]
  [template: "text with ___ blanks"]
  [slots: <n>]
  [reusable]
}

prop	type	description
bank	string[]	the tokens the learner can place
answer	string[]	an accepted sequence (repeatable)
template	string	text the slots sit inside; each ___ outside math is a slot
slots	number	number of slots (defaults to first answer length; unused with a template)
reusable	flag	allow a token to be used more than once

Example

Complete the power rule.

\frac{d}{dx}\left[x^{3}\right] =

\cdot

hotspot#

Tap the right spot directly on the slide's scene, rather than picking from a list or typing a value. target is a rect or circle region in scene (data) coordinates — a tap inside it is correct. The tapped point is marked on the scene; miss is shown instead of the usual explanation when the tap lands outside the target.

hotspot {
  ask "..."
  target rect (x, y) { w: <n>, h: <n> }
  [target circle (x, y) { r: <n> }]
  [miss "..."]
}

prop	type	description
target*	rect \| circle	the hit region, in scene coordinates
miss	string	feedback shown when the tap misses

Example

Tap where the parabola crosses y = 4.

Tap the scene above, or tab to it and aim with the arrow keys.

sketch#

Draw directly on the slide's scene — a freehand curve, a handful of tapped points, or a dragged straight line. curve and points check against near landmark points (the drawn shape must pass within tol of each); curve is checked as a connected stroke, points as independent taps. line checks the drawn segment's slope against slope (within slopeTol) and that it passes within tol of through. Pairs naturally with a reveal { ... } block for predict-then-reveal.

sketch curve {
  ask "..."
  near (x, y)
  [near (x, y) ...]
  [tol: <n>]
}
sketch points {
  ask "..."
  near (x, y)
  [near (x, y) ...]
  [tol: <n>]
}
sketch line {
  ask "..."
  through (x, y)
  slope: <n>
  [tol: <n>]
  [slopeTol: <n>]
}

prop	type	description
near	(number, number)	a landmark point (repeatable)
through	(number, number)	point the line must pass near (line mode)
slope*	number	expected slope (line mode)
tol	number	position tolerance, in scene units
slopeTol	number	slope tolerance (line mode, default 0.5)

Example

Draw

y = (x-1)^2 - 3

— vertex and both crossings roughly right.

Draw on the scene above, or tab to it and use the arrow keys.

match#

Tap-left-then-tap-right pairing. Tap a left item, then tap the right item it belongs with — at least two pair lines are required. decoy adds extra right-side entries that never pair with anything, making the match harder to guess. The right column is shuffled (seeded off the left texts, so it stays put across re-renders of the same exercise).

match {
  ask "..."
  pair "left" -> "right"
  [pair "left2" -> "right2" ...]
  [decoy "extra wrong right"]
  [hint "..."]
  [! "explanation"]
}

prop	type	description
pair	"left" -> "right"	a correct pairing (repeatable, min 2)
decoy	string	an extra unpaired right-side option (repeatable)

Example

Match each derivative rule to its result.

Tap one on the left, then its partner on the right. They turn the same color. Tap either one again to undo.

Match with

order#

Put a shuffled list of items back into the right order. The item lines are declared in their correct sequence — that's both the answer and the source of the tokens shown (shuffled) to the learner. decoy adds extra tokens that don't belong in the sequence at all. Like build, but without the operator/operand token styling and without separate bank:/answer: arrays — there is exactly one correct order.

order {
  ask "..."
  item "..."
  [item "..." ...]
  [decoy "..."]
  [hint "..."]
  [! "explanation"]
}

prop	type	description
item	string	a step in the correct sequence (repeatable, min 2)
decoy	string	an extra token that isn't part of the sequence (repeatable)

Example

Order these steps of order of operations.

sort#

Drop each item into the bin it belongs to. Declare at least two bin groups; every item listed under a bin is shown in a shuffled tray and has to be put back. Reach for this when the lesson is about telling cases apart (which rule opens a derivative, which kind of discontinuity a function has), where a multiple choice only ever probes one case at a time. An item may appear in exactly one bin, or the compiler refuses to build, since there would be no single right answer. Items render as rich text, so "$x^2\sin x$" is a fine item.

sort {
  ask "..."
  bin "Label": ["item", "item", ...]
  bin "Other label": ["item", ...]
  [hint "..."]
  [! "explanation"]
}

prop	type	description
bin	string: string[]	a labelled bin and the items belonging in it (repeatable, min 2)

Example

Which rule opens each derivative?

table#

Fill in the blanks of a function table. Each row: line lists one value per column — plain numbers are given, blank(<answer>) marks a cell the learner fills in (the argument is the expected value, and folds from an expression like any other answer). Every row needs the same number of cells; at least one cell across the whole table must be a blank(...). tolerance applies to every blank. Correctness is shown per-blank plus an overall "X / N correct" count — partial credit is surfaced but never blocks Continue, same as every other exercise.

table {
  ask "..."
  [header: ["col", "col", ...]]
  row: <value|blank(answer)>, <value|blank(answer)>, ...
  [row: ...]
  [tolerance: <n>]
}

prop	type	description
header	string[]	column headings (optional)
row*	value, value, ...	one row — mix plain numbers and blank(answer) cells (repeatable)
tolerance	number	how far off a blank can be (default ~0)

Example

Complete the table for f(x) = x² - 1.

x	f(x)
-2
-1
0
1
2

Exercises

expect#

expect: <expression>

prop	type	description
expect*	expr	closed-form value the answer must match, within tolerance

Example

For

h(x) = \sqrt{x^2+9}

, find

h'(4)

quiz#

Multiple choice. Mark the correct option with * and wrong options with -. Each option may carry a { why: "..." } giving per-option feedback shown when the learner picks it.

quiz {
  ask "Question?"
  - "wrong option" { [why: "..."] }
  * "correct option"
  [hint "..."]
  [! "explanation"]
}

Example

If a < 0, the parabola...

numeric#

numeric {
  ask "..."
  answer: <number>
  [answer: <another accepted value>]
  [tolerance: <n>]
  [unit: "..."]
}

prop	type	description
answer	number	an accepted value (repeatable)
tolerance	number	how far off is still correct (default ~0)
unit	string	label shown next to the input

Example

n \to \infty

, the area under x² on [0,4]?

build#

build {
  ask "..."
  bank: ["tok", "tok", ...]
  answer: ["tok", ...]
  [answer: ["...alt ordering..."]]
  [template: "text with ___ blanks"]
  [slots: <n>]
  [reusable]
}

prop	type	description
bank	string[]	the tokens the learner can place
answer	string[]	an accepted sequence (repeatable)
template	string	text the slots sit inside; each ___ outside math is a slot
slots	number	number of slots (defaults to first answer length; unused with a template)
reusable	flag	allow a token to be used more than once

Example

Complete the power rule.

\frac{d}{dx}\left[x^{3}\right] =

\cdot

hotspot#

hotspot {
  ask "..."
  target rect (x, y) { w: <n>, h: <n> }
  [target circle (x, y) { r: <n> }]
  [miss "..."]
}

prop	type	description
target*	rect \| circle	the hit region, in scene coordinates
miss	string	feedback shown when the tap misses

Example

Tap where the parabola crosses y = 4.

Tap the scene above, or tab to it and aim with the arrow keys.

sketch#

sketch curve {
  ask "..."
  near (x, y)
  [near (x, y) ...]
  [tol: <n>]
}
sketch points {
  ask "..."
  near (x, y)
  [near (x, y) ...]
  [tol: <n>]
}
sketch line {
  ask "..."
  through (x, y)
  slope: <n>
  [tol: <n>]
  [slopeTol: <n>]
}

prop	type	description
near	(number, number)	a landmark point (repeatable)
through	(number, number)	point the line must pass near (line mode)
slope*	number	expected slope (line mode)
tol	number	position tolerance, in scene units
slopeTol	number	slope tolerance (line mode, default 0.5)

Example

Draw

y = (x-1)^2 - 3

— vertex and both crossings roughly right.

Draw on the scene above, or tab to it and use the arrow keys.

match#

match {
  ask "..."
  pair "left" -> "right"
  [pair "left2" -> "right2" ...]
  [decoy "extra wrong right"]
  [hint "..."]
  [! "explanation"]
}

prop	type	description
pair	"left" -> "right"	a correct pairing (repeatable, min 2)
decoy	string	an extra unpaired right-side option (repeatable)

Example

Match each derivative rule to its result.

Tap one on the left, then its partner on the right. They turn the same color. Tap either one again to undo.

Match with

order#

order {
  ask "..."
  item "..."
  [item "..." ...]
  [decoy "..."]
  [hint "..."]
  [! "explanation"]
}

prop	type	description
item	string	a step in the correct sequence (repeatable, min 2)
decoy	string	an extra token that isn't part of the sequence (repeatable)

Example

Order these steps of order of operations.

sort#

sort {
  ask "..."
  bin "Label": ["item", "item", ...]
  bin "Other label": ["item", ...]
  [hint "..."]
  [! "explanation"]
}

prop	type	description
bin	string: string[]	a labelled bin and the items belonging in it (repeatable, min 2)

Example

Which rule opens each derivative?

table#

table {
  ask "..."
  [header: ["col", "col", ...]]
  row: <value|blank(answer)>, <value|blank(answer)>, ...
  [row: ...]
  [tolerance: <n>]
}

prop	type	description
header	string[]	column headings (optional)
row*	value, value, ...	one row — mix plain numbers and blank(answer) cells (repeatable)
tolerance	number	how far off a blank can be (default ~0)

Example

Complete the table for f(x) = x² - 1.

x	f(x)
-2
-1
0
1
2