From be5b3dba7586c11c35aab1361b1bfaebfd835f57 Mon Sep 17 00:00:00 2001 From: Hananoshika Yomaru Date: Tue, 19 May 2026 16:08:20 -0700 Subject: [PATCH] Refactor question bank feature in spec, update math curriculum status to live, enhance math rendering in frontend, and add new styles for question presentation in SASS. Improve catalog styles for planned chapters and enhance visual elements for better user experience. --- content/math/directed-numbers-rates/_index.md | 336 ++++++++++++++++++ .../assets/directed-numbers-history.png | Bin 0 -> 923621 bytes content/math/directed-numbers-rates/core.html | 88 +++++ .../directed-numbers-rates/supplement.html | 236 ++++++++++++ .../widgets/number-line.tsx | 182 ++++++++++ .../widgets/ratio-demo.tsx | 118 ++++++ data/math-curriculum.json | 2 +- frontend/src/lib/render-math.ts | 22 +- spec.md | 6 - themes/openfreebooks/sass/_book.scss | 77 ++++ themes/openfreebooks/sass/_catalog.scss | 47 ++- 11 files changed, 1096 insertions(+), 18 deletions(-) create mode 100644 content/math/directed-numbers-rates/_index.md create mode 100644 content/math/directed-numbers-rates/assets/directed-numbers-history.png create mode 100644 content/math/directed-numbers-rates/core.html create mode 100644 content/math/directed-numbers-rates/supplement.html create mode 100644 content/math/directed-numbers-rates/widgets/number-line.tsx create mode 100644 content/math/directed-numbers-rates/widgets/ratio-demo.tsx diff --git a/content/math/directed-numbers-rates/_index.md b/content/math/directed-numbers-rates/_index.md new file mode 100644 index 0000000..1dedce3 --- /dev/null +++ b/content/math/directed-numbers-rates/_index.md @@ -0,0 +1,336 @@ ++++ +title = "Directed numbers, rates & ratios" +description = "Operate with negative numbers and solve ratio, rate, and proportion problems in context." +template = "chapter.html" +weight = 0 +[extra] +subject = "math" +chapter_id = "directed-numbers-rates" +strand = "Number & Algebra" ++++ + +
+

+ Numbers on a line can lie to the right of zero (positive) or to the + left (negative). Temperatures below freezing, bank overdrafts, and positions + below sea level are everyday examples of directed numbers. +

+ +

The number line

+

+ On a horizontal number line, moving right means the value increases; moving left means it + decreases. The distance from zero is the absolute value + \(|a|\). For example, \(|-5| = 5\) and \(|3| = 3\). +

+ +
+

Comparing

+

+ \(a > b\) means \(a\) lies to the right of \(b\). Any negative number is less than any + positive number. +

+
+ +

Adding and subtracting

+

+ Think in terms of movement on the line: +

+ +

+ Subtracting a negative is adding a positive: \(5 - (-3) = 5 + 3 = 8\). +

+ +

Multiplying and dividing

+
+ + + + + + + + + + + + + + + + + +
SignsResult
positive × positive, negative × negativepositive
positive × negative (either order)negative
+
+ +

Ratios

+

+ A ratio compares quantities of the same kind. The ratio \(2:3\) means “2 parts + to 3 parts” — five equal parts in total. To share \(40\) in the ratio \(2:3\), one part is + \(40 \div 5 = 8\), so the shares are \(16\) and \(24\). +

+ +
+

Sharing in ratio \(m:n\)

+

+ \[ \text{one part} = \frac{\text{total}}{m+n}, \quad + \text{first share} = \frac{m}{m+n}\times\text{total}, \quad + \text{second share} = \frac{n}{m+n}\times\text{total} \] +

+
+ +

Rates

+

+ A rate compares different units. Speed is distance per time: + \[ \text{speed} = \frac{\text{distance}}{\text{time}}. \] + A unit rate tells “how much per one” — for example \(60\) km in \(1.5\) h gives + \(60 \div 1.5 = 40\) km/h. +

+ +

Try it yourself

+

+ Use the number-line explorer to pick two directed numbers and see their sum on the line. Then try + the ratio sharer in the applications section below. +

+
+ +
+ +
+

History

+

+ For much of history, mathematicians treated only positive quantities as numbers. Negative + solutions to equations were often rejected as meaningless. Practical needs — debts, losses, + and temperatures below zero — still pushed people to work with “numbers less than nothing.” +

+ +
+ Illustrated timeline: ancient rejection of negative roots, Indian and Chinese rules for signed quantities, European skepticism, and the development of ratios from barter to modern rates +
+ A sketch of how directed numbers and ratios were understood — from Greek reluctance to use + negative roots, through Indian and Chinese models of fortune and debt, to modern rates such + as speed and exchange. +
+
+ +

+ In India around the 7th century, Brahmagupta gave rules for operating with + positive and negative quantities (fortunes and debts). Chinese scholars used counting rods with + two colours to represent opposite signs. European acceptance grew slowly; even in the 18th century + some writers called negative roots “false.” +

+

+ Ratios and proportions appear in Babylonian and Egyptian problems (sharing grain, scaling + recipes). The modern notation \(a:b\) and systematic treatment of unit rates + became standard as commerce and science needed comparable measures — speed, price per item, and + exchange rates between currencies. +

+ +

Derivation

+ +

Why \((-)\times(-) = (+)\)?

+

+ One useful pattern: multiplication should keep the rules of arithmetic consistent. For any + real \(a\), you want \(a \times 0 = 0\). Then + \[ a \times 0 = a \times (1 + (-1)) = a\cdot 1 + a\cdot(-1) = a + a\cdot(-1). \] + So \(a\cdot(-1) = -a\). Now apply that twice: + \[ (-a)\cdot(-1) = -((-a)) = a, \] + which shows that multiplying two negatives gives a positive. +

+ +

Sharing in the ratio \(m:n\)

+

+ Suppose a total \(T\) is split into two parts in the ratio \(m:n\). Think of \(m+n\) equal + parts. Each part has size + \[ \frac{T}{m+n}. \] + The first quantity gets \(m\) of those parts: + \[ \frac{m}{m+n}\,T, \] + and the second gets \(\frac{n}{m+n}\,T\). The parts add to \(T\), as required. +

+ +

Unit rate

+

+ If \(d\) units of quantity are produced in \(t\) units of time, the average rate is + \(d/t\). “Per one hour” means divide by \(t\) when \(t \neq 0\): + \[ \text{rate per unit time} = \frac{d}{t}. \] + Re-arranging gives \(d = \text{rate} \times t\), the formula used for uniform motion. +

+ +

Checkpoints

+

+ Pause and reason before continuing. Discuss with a partner or write your work in a notebook. +

+ +
+

Checkpoint

+

+ Without a calculator: is \((-4) + (-7)\) positive or negative? Where do you land if you start + at \(-4\) and move 7 units left? +

+
+ +
+

Checkpoint

+

+ Simplify \(6 - (-2)\). Explain using “subtracting a negative is adding a positive.” +

+
+ +
+

Checkpoint

+

+ Share \(72\) in the ratio \(5:4\). How many “parts” are there in total? +

+
+ +
+

Checkpoint

+

+ A car travels \(150\) km in \(2.5\) hours. What is the average speed? Which formula did you use? +

+
+ +
+

Checkpoint

+

+ Currency A costs \(1.2\) units of Currency B per unit of A. You exchange \(50\) units of A. + How many units of B do you receive? +

+
+ +

Applications

+ +

Temperature and altitude

+

+ A weather station records \(3\,^{\circ}\mathrm{C}\) at noon and the temperature drops + \(8\,^{\circ}\mathrm{C}\) by midnight. The change is \(-8\), so the midnight temperature is + \[ 3 + (-8) = -5\,^{\circ}\mathrm{C}. \] + Altitude above sea level is positive; below sea level (e.g. Dead Sea shore) is negative + elevation relative to sea level. +

+ +

Sharing and mixtures

+

+ Paint is mixed in the ratio blue : white \(= 2:5\). For \(21\) litres total, there are + \(7\) equal parts, each \(3\) litres, giving \(6\) L blue and \(15\) L white. +

+ +
+ +

Speed and exchange rates

+

+ Walking \(6\) km in \(1.5\) h gives speed \(\frac{6}{1.5} = 4\) km/h. An exchange rate of + \(1\) USD \(=\) \(7.8\) HKD means \(100\) USD converts to \(780\) HKD by multiplying by the + unit rate. +

+ +

Question bank

+

+ Work each question, then open the solution to check your reasoning. Difficulty increases + through the sets. +

+ +

Easy

+ +
+ Which is larger, \(-3\) or \(-7\)? +
+

Answer: \(-3\) is larger (lies to the right on the number line).

+

Explanation: For negative numbers, the one closer to zero is greater.

+
+
+ +
+ Evaluate \((-2) + 9\). +
+

Answer: \(7\).

+

Steps: Start at \(-2\), move 9 units right.

+
+
+ +
+ \((-4) \times 6 = \) ______ +
+

Answer: \(-24\).

+

Explanation: Different signs → negative product.

+
+
+ +

Intermediate

+ +
+ Evaluate \(5 - (-3) \times 2\). +
+

Answer: \(11\).

+

Steps: \((-3)\times 2 = -6\); then \(5 - (-6) = 5 + 6 = 11\).

+
+
+ +
+ Divide \(84\) in the ratio \(2:5\). +
+

Answer: \(24\) and \(60\).

+

Steps: \(7\) parts; each part \(84 \div 7 = 12\); shares \(24\) and \(60\).

+
+
+ +
+ A cyclist goes \(45\) km in \(3\) h. What is the average speed? +
+

Answer: \(15\) km/h.

+

Calculation: \(45 \div 3 = 15\).

+
+
+ +

Difficult

+ +
+ The temperature was \(-2\,^{\circ}\mathrm{C}\) and fell by \(9\,^{\circ}\mathrm{C}\). Find the new temperature. +
+

Answer: \(-11\,^{\circ}\mathrm{C}\).

+

Steps: \(-2 + (-9) = -11\).

+
+
+ +
+ Put in order from smallest to largest: \(-1\), \(0\), \(-\frac{1}{2}\), \(-2\). +
+

Answer: \(-2 < -1 < -\frac{1}{2} < 0\).

+

Explanation: On the number line, further left means smaller.

+
+
+ +

Hardcore

+ +
+ \(A:B = 3:4\) and \(B:C = 2:5\). Find \(A:B:C\) in simplest form. +
+

Answer: \(A:B:C = 3:4:10\) after matching \(B\) (multiply first ratio by 2: \(6:8\), second by 4: \(8:20\) → \(6:8:20 = 3:4:10\)).

+

Steps: Align \(B\) to LCM 8: \(A:B = 6:8\), \(B:C = 8:20\), so \(A:B:C = 6:8:20 = 3:4:10\).

+
+
+ +
+ Which situation matches a negative directed number? +
+

Answer: A bank balance of \(500\) in debt (owe \(500\)) — often modelled as \(-500\).

+

Explanation: Debt below zero balance is a standard directed-number model.

+
+
+ +

References

+ +
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z_nU;wiuc=DTIrM=a_UP>2{-p}bt9>&tDL^(Xo>WuFdIjvk)^Cf+*S*Q zJYttFzfW%Z4 zP3(s8R@(N*SXl-IcC*q@a48EuKjV$EP^ss?b!=8-*N$WeR z&gCD~E*w)aM_V6cL`|c94XHn{v-S<)(YX}%0Oe{a&k4+7-iRaf(FnZhpul=&)SRoaTA;cT zXgjV3ogU4QCs3*7ux{P$3fbmYQ=VyR%$dSsW8AzL2zJ!kCZB{GYReV_fh-h+^C)}u zFuKlD?r}O@z-*^rKG2192sb9MKeD;fxR5^H{1KU4D^a$A+CfyCxTe48k_L$Xk^dK- WfN=UJ{jEFz0000 +

+ Numbers on a line can lie to the right of zero (positive) or to the + left (negative). Temperatures below freezing, bank overdrafts, and positions + below sea level are everyday examples of directed numbers. +

+ +

The number line

+

+ On a horizontal number line, moving right means the value increases; moving left means it + decreases. The distance from zero is the absolute value + \(|a|\). For example, \(|-5| = 5\) and \(|3| = 3\). +

+ +
+

Comparing

+

+ \(a > b\) means \(a\) lies to the right of \(b\). Any negative number is less than any + positive number. +

+
+ +

Adding and subtracting

+

+ Think in terms of movement on the line: +

+
    +
  • \(a + b\) — start at \(a\), move \(b\) units (right if \(b > 0\), left if \(b < 0\)).
  • +
  • \(a - b\) — start at \(a\), move \(-b\) units (equivalently, add the opposite of \(b\)).
  • +
+

+ Subtracting a negative is adding a positive: \(5 - (-3) = 5 + 3 = 8\). +

+ +

Multiplying and dividing

+
+ + + + + + + + + + + + + + + + + +
SignsResult
positive × positive, negative × negativepositive
positive × negative (either order)negative
+
+ +

Ratios

+

+ A ratio compares quantities of the same kind. The ratio \(2:3\) means “2 parts + to 3 parts” — five equal parts in total. To share \(40\) in the ratio \(2:3\), one part is + \(40 \div 5 = 8\), so the shares are \(16\) and \(24\). +

+ +
+

Sharing in ratio \(m:n\)

+

+ \[ \text{one part} = \frac{\text{total}}{m+n}, \quad + \text{first share} = \frac{m}{m+n}\times\text{total}, \quad + \text{second share} = \frac{n}{m+n}\times\text{total} \] +

+
+ +

Rates

+

+ A rate compares different units. Speed is distance per time: + \[ \text{speed} = \frac{\text{distance}}{\text{time}}. \] + A unit rate tells “how much per one” — for example \(60\) km in \(1.5\) h gives + \(60 \div 1.5 = 40\) km/h. +

+ +

Try it yourself

+

+ Use the number-line explorer to pick two directed numbers and see their sum on the line. Then try + the ratio sharer in the applications section below. +

+ + +
diff --git a/content/math/directed-numbers-rates/supplement.html b/content/math/directed-numbers-rates/supplement.html new file mode 100644 index 0000000..63d9a5d --- /dev/null +++ b/content/math/directed-numbers-rates/supplement.html @@ -0,0 +1,236 @@ +
+

History

+

+ For much of history, mathematicians treated only positive quantities as numbers. Negative + solutions to equations were often rejected as meaningless. Practical needs — debts, losses, + and temperatures below zero — still pushed people to work with “numbers less than nothing.” +

+ +
+ Illustrated timeline: ancient rejection of negative roots, Indian and Chinese rules for signed quantities, European skepticism, and the development of ratios from barter to modern rates +
+ A sketch of how directed numbers and ratios were understood — from Greek reluctance to use + negative roots, through Indian and Chinese models of fortune and debt, to modern rates such + as speed and exchange. +
+
+ +

+ In India around the 7th century, Brahmagupta gave rules for operating with + positive and negative quantities (fortunes and debts). Chinese scholars used counting rods with + two colours to represent opposite signs. European acceptance grew slowly; even in the 18th century + some writers called negative roots “false.” +

+

+ Ratios and proportions appear in Babylonian and Egyptian problems (sharing grain, scaling + recipes). The modern notation \(a:b\) and systematic treatment of unit rates + became standard as commerce and science needed comparable measures — speed, price per item, and + exchange rates between currencies. +

+ +

Derivation

+ +

Why \((-)\times(-) = (+)\)?

+

+ One useful pattern: multiplication should keep the rules of arithmetic consistent. For any + real \(a\), you want \(a \times 0 = 0\). Then + \[ a \times 0 = a \times (1 + (-1)) = a\cdot 1 + a\cdot(-1) = a + a\cdot(-1). \] + So \(a\cdot(-1) = -a\). Now apply that twice: + \[ (-a)\cdot(-1) = -((-a)) = a, \] + which shows that multiplying two negatives gives a positive. +

+ +

Sharing in the ratio \(m:n\)

+

+ Suppose a total \(T\) is split into two parts in the ratio \(m:n\). Think of \(m+n\) equal + parts. Each part has size + \[ \frac{T}{m+n}. \] + The first quantity gets \(m\) of those parts: + \[ \frac{m}{m+n}\,T, \] + and the second gets \(\frac{n}{m+n}\,T\). The parts add to \(T\), as required. +

+ +

Unit rate

+

+ If \(d\) units of quantity are produced in \(t\) units of time, the average rate is + \(d/t\). “Per one hour” means divide by \(t\) when \(t \neq 0\): + \[ \text{rate per unit time} = \frac{d}{t}. \] + Re-arranging gives \(d = \text{rate} \times t\), the formula used for uniform motion. +

+ +

Checkpoints

+

+ Pause and reason before continuing. Discuss with a partner or write your work in a notebook. +

+ +
+

Checkpoint

+

+ Without a calculator: is \((-4) + (-7)\) positive or negative? Where do you land if you start + at \(-4\) and move 7 units left? +

+
+ +
+

Checkpoint

+

+ Simplify \(6 - (-2)\). Explain using “subtracting a negative is adding a positive.” +

+
+ +
+

Checkpoint

+

+ Share \(72\) in the ratio \(5:4\). How many “parts” are there in total? +

+
+ +
+

Checkpoint

+

+ A car travels \(150\) km in \(2.5\) hours. What is the average speed? Which formula did you use? +

+
+ +
+

Checkpoint

+

+ Currency A costs \(1.2\) units of Currency B per unit of A. You exchange \(50\) units of A. + How many units of B do you receive? +

+
+ +

Applications

+ +

Temperature and altitude

+

+ A weather station records \(3\,^{\circ}\mathrm{C}\) at noon and the temperature drops + \(8\,^{\circ}\mathrm{C}\) by midnight. The change is \(-8\), so the midnight temperature is + \[ 3 + (-8) = -5\,^{\circ}\mathrm{C}. \] + Altitude above sea level is positive; below sea level (e.g. Dead Sea shore) is negative + elevation relative to sea level. +

+ +

Sharing and mixtures

+

+ Paint is mixed in the ratio blue : white \(= 2:5\). For \(21\) litres total, there are + \(7\) equal parts, each \(3\) litres, giving \(6\) L blue and \(15\) L white. +

+ +
+ +

Speed and exchange rates

+

+ Walking \(6\) km in \(1.5\) h gives speed \(\frac{6}{1.5} = 4\) km/h. An exchange rate of + \(1\) USD \(=\) \(7.8\) HKD means \(100\) USD converts to \(780\) HKD by multiplying by the + unit rate. +

+ +

Question bank

+

+ Work each question, then open the solution to check your reasoning. Difficulty increases + through the sets. +

+ +

Easy

+ +
+ Which is larger, \(-3\) or \(-7\)? +
+

Answer: \(-3\) is larger (lies to the right on the number line).

+

Explanation: For negative numbers, the one closer to zero is greater.

+
+
+ +
+ Evaluate \((-2) + 9\). +
+

Answer: \(7\).

+

Steps: Start at \(-2\), move 9 units right.

+
+
+ +
+ \((-4) \times 6 = \) ______ +
+

Answer: \(-24\).

+

Explanation: Different signs → negative product.

+
+
+ +

Intermediate

+ +
+ Evaluate \(5 - (-3) \times 2\). +
+

Answer: \(11\).

+

Steps: \((-3)\times 2 = -6\); then \(5 - (-6) = 5 + 6 = 11\).

+
+
+ +
+ Divide \(84\) in the ratio \(2:5\). +
+

Answer: \(24\) and \(60\).

+

Steps: \(7\) parts; each part \(84 \div 7 = 12\); shares \(24\) and \(60\).

+
+
+ +
+ A cyclist goes \(45\) km in \(3\) h. What is the average speed? +
+

Answer: \(15\) km/h.

+

Calculation: \(45 \div 3 = 15\).

+
+
+ +

Difficult

+ +
+ The temperature was \(-2\,^{\circ}\mathrm{C}\) and fell by \(9\,^{\circ}\mathrm{C}\). Find the new temperature. +
+

Answer: \(-11\,^{\circ}\mathrm{C}\).

+

Steps: \(-2 + (-9) = -11\).

+
+
+ +
+ Put in order from smallest to largest: \(-1\), \(0\), \(-\frac{1}{2}\), \(-2\). +
+

Answer: \(-2 < -1 < -\frac{1}{2} < 0\).

+

Explanation: On the number line, further left means smaller.

+
+
+ +

Hardcore

+ +
+ \(A:B = 3:4\) and \(B:C = 2:5\). Find \(A:B:C\) in simplest form. +
+

Answer: \(A:B:C = 3:4:10\) after matching \(B\) (multiply first ratio by 2: \(6:8\), second by 4: \(8:20\) → \(6:8:20 = 3:4:10\)).

+

Steps: Align \(B\) to LCM 8: \(A:B = 6:8\), \(B:C = 8:20\), so \(A:B:C = 6:8:20 = 3:4:10\).

+
+
+ +
+ Which situation matches a negative directed number? +
+

Answer: A bank balance of \(500\) in debt (owe \(500\)) — often modelled as \(-500\).

+

Explanation: Debt below zero balance is a standard directed-number model.

+
+
+ +

References

+
    +
  • Brahmagupta, Brāhmasphuṭasiddhānta (628 CE) — early rules for signed quantities.
  • +
  • HKDSE Compulsory Part curriculum — Number and Algebra strand (directed numbers, ratios, rates).
  • +
+
diff --git a/content/math/directed-numbers-rates/widgets/number-line.tsx b/content/math/directed-numbers-rates/widgets/number-line.tsx new file mode 100644 index 0000000..4b55540 --- /dev/null +++ b/content/math/directed-numbers-rates/widgets/number-line.tsx @@ -0,0 +1,182 @@ +import katex from "katex"; +import { createEffect, createMemo, createSignal } from "solid-js"; +import { renderMathInContainer } from "../../../../frontend/src/lib/render-math"; + +const MIN = -10; +const MAX = 10; +const WIDTH = 400; +const PAD = 28; +const PLOT = WIDTH - 2 * PAD; + +function formatNum(n: number) { + if (Number.isInteger(n)) return String(n); + return (Math.round(n * 100) / 100).toString(); +} + +function renderLatex(latex: string) { + return katex.renderToString(latex, { throwOnError: false, strict: "ignore" }); +} + +function toX(value: number) { + const t = (value - MIN) / (MAX - MIN); + return PAD + t * PLOT; +} + +function NumberLine() { + const [a, setA] = createSignal(3); + const [b, setB] = createSignal(-2); + let canvasRef: HTMLCanvasElement | undefined; + const sum = createMemo(() => a() + b()); + + const equationHtml = createMemo(() => + renderLatex(`${formatNum(a())} + (${formatNum(b())}) = ${formatNum(sum())}`) + ); + + const redraw = () => { + const canvas = canvasRef; + if (!canvas) return; + const ctx = canvas.getContext("2d"); + if (!ctx) return; + + const h = 120; + const dpr = window.devicePixelRatio || 1; + canvas.width = WIDTH * dpr; + canvas.height = h * dpr; + ctx.setTransform(dpr, 0, 0, dpr, 0, 0); + + const style = getComputedStyle(canvas); + const grid = style.getPropertyValue("--math-grid").trim() || "#e5e5e5"; + const axis = style.getPropertyValue("--math-axis").trim() || "#a8a29e"; + const curve = style.getPropertyValue("--math-curve").trim() || "#9a6b2e"; + const root = style.getPropertyValue("--math-root").trim() || "#2563eb"; + const vertex = style.getPropertyValue("--math-vertex").trim() || "#4a6b4a"; + const bg = style.getPropertyValue("--math-canvas-bg").trim() || "#ffffff"; + + ctx.fillStyle = bg; + ctx.fillRect(0, 0, WIDTH, h); + + const y = h / 2; + ctx.strokeStyle = grid; + ctx.lineWidth = 1; + for (let v = MIN; v <= MAX; v++) { + const x = toX(v); + ctx.beginPath(); + ctx.moveTo(x, y - 4); + ctx.lineTo(x, y + 4); + ctx.stroke(); + } + + ctx.strokeStyle = axis; + ctx.lineWidth = 2; + ctx.beginPath(); + ctx.moveTo(PAD, y); + ctx.lineTo(WIDTH - PAD, y); + ctx.stroke(); + + ctx.fillStyle = axis; + ctx.font = "10px IBM Plex Mono, monospace"; + ctx.textAlign = "center"; + for (let v = MIN; v <= MAX; v += 2) { + ctx.fillText(String(v), toX(v), y + 18); + } + + const drawTick = (value: number, color: string, radius: number) => { + const x = toX(value); + ctx.fillStyle = color; + ctx.beginPath(); + ctx.arc(x, y, radius, 0, Math.PI * 2); + ctx.fill(); + }; + + const av = a(); + const bv = b(); + const sv = sum(); + + drawTick(av, root, 6); + drawTick(bv, vertex, 6); + drawTick(sv, curve, 7); + + ctx.strokeStyle = curve; + ctx.lineWidth = 2; + ctx.setLineDash([6, 4]); + ctx.beginPath(); + ctx.moveTo(toX(av), y); + ctx.lineTo(toX(sv), y); + ctx.stroke(); + ctx.setLineDash([]); + }; + + createEffect(() => { + a(); + b(); + sum(); + redraw(); + }); + + return ( +
+

Number-line addition

+
+
+
+ + setA(Number(e.currentTarget.value))} + /> +
+
+ + setB(Number(e.currentTarget.value))} + /> +
+
+
+
+ { + canvasRef = el; + redraw(); + }} + class="math-widget__canvas" + width={WIDTH} + height={120} + role="img" + aria-label={`Number line showing ${formatNum(a())} plus ${formatNum(b())} equals ${formatNum(sum())}`} + /> +
{ + if (el) renderMathInContainer(el); + }} + > + Blue: \(a\). Green: \(b\). Gold: sum \(a+b\). Dashed segment shows the move from \(a\) to + \(a+b\). +
+
+
+
+ ); +} + +export default NumberLine; diff --git a/content/math/directed-numbers-rates/widgets/ratio-demo.tsx b/content/math/directed-numbers-rates/widgets/ratio-demo.tsx new file mode 100644 index 0000000..ecd26f8 --- /dev/null +++ b/content/math/directed-numbers-rates/widgets/ratio-demo.tsx @@ -0,0 +1,118 @@ +import katex from "katex"; +import { createMemo, createSignal } from "solid-js"; + +function formatNum(n: number) { + if (Number.isInteger(n)) return String(n); + return (Math.round(n * 100) / 100).toString(); +} + +function renderLatex(latex: string) { + return katex.renderToString(latex, { throwOnError: false, strict: "ignore" }); +} + +function RatioDemo() { + const [partA, setPartA] = createSignal(2); + const [partB, setPartB] = createSignal(5); + const [total, setTotal] = createSignal(28); + + const sumParts = createMemo(() => partA() + partB()); + const shareA = createMemo(() => (partA() / sumParts()) * total()); + const shareB = createMemo(() => (partB() / sumParts()) * total()); + + const formulaHtml = createMemo(() => + renderLatex( + `${partA()}:${partB()} \\Rightarrow ${formatNum(shareA())} : ${formatNum(shareB())} \\text{ from total } ${formatNum(total())}` + ) + ); + + return ( +
+
+

+ Split {formatNum(total())} in the ratio{" "} + + {partA()}:{partB()} + + . Each of the {sumParts()} equal parts has size{" "} + {formatNum(total() / sumParts())}. +

+
+ ); +} + +export default RatioDemo; diff --git a/data/math-curriculum.json b/data/math-curriculum.json index eba6232..36c5fa9 100644 --- a/data/math-curriculum.json +++ b/data/math-curriculum.json @@ -53,7 +53,7 @@ "slug": "directed-numbers-rates", "title": "Directed numbers, rates & ratios", "description": "Operate with negative numbers and solve ratio, rate, and proportion problems in context.", - "status": "planned", + "status": "live", "curriculums": ["DSE"] }, { diff --git a/frontend/src/lib/render-math.ts b/frontend/src/lib/render-math.ts index bebe467..c12955e 100644 --- a/frontend/src/lib/render-math.ts +++ b/frontend/src/lib/render-math.ts @@ -7,12 +7,18 @@ const DELIMITERS = [ { left: "\\[", right: "\\]", display: true }, ]; -export function renderBookMath() { - document.querySelectorAll(".book-prose, .book-callout").forEach((el) => { - renderMathInElement(el, { - delimiters: DELIMITERS, - throwOnError: false, - strict: "ignore", - }); - }); +const RENDER_OPTIONS = { + delimiters: DELIMITERS, + throwOnError: false, + strict: "ignore" as const, +}; + +export function renderMathInContainer(el: HTMLElement) { + renderMathInElement(el, RENDER_OPTIONS); +} + +export function renderBookMath() { + document + .querySelectorAll(".book-prose, .book-callout, .math-widget__caption") + .forEach(renderMathInContainer); } diff --git a/spec.md b/spec.md index bb7e91d..1181341 100644 --- a/spec.md +++ b/spec.md @@ -16,12 +16,6 @@ we have a catalog of subjects. Each subject will have chapters. Each chapters ca we need to have a question bank feature. since this is purely static sites, question answer needs to be determined and able to grade in advanced. -1. multiple-choice -2. short-answer -3. fill-in-the-blank -4. choice -5. ranking - question bank not only show answer but also steps, explanation, calcultion. ## Chapters requirements diff --git a/themes/openfreebooks/sass/_book.scss b/themes/openfreebooks/sass/_book.scss index 49b59f0..e1ca3f4 100644 --- a/themes/openfreebooks/sass/_book.scss +++ b/themes/openfreebooks/sass/_book.scss @@ -375,6 +375,83 @@ a.book-chapter-link:focus-visible { max-width: 960px; } +.book-question { + margin: 1rem 0; + border: 1px solid var(--card-border); + border-radius: 12px; + background: var(--card-bg); +} + +.book-question__prompt { + position: relative; + padding: 14px 18px 14px 2.75rem; + font-weight: 500; + line-height: 1.55; + cursor: pointer; + list-style: none; +} + +.book-question__prompt::-webkit-details-marker { + display: none; +} + +.book-question__prompt::marker { + content: ""; +} + +.book-question__prompt::before { + content: ""; + position: absolute; + left: 1.125rem; + top: 1.35em; + width: 0.45em; + height: 0.45em; + border-right: 2px solid var(--accent); + border-bottom: 2px solid var(--accent); + transform: rotate(-45deg); + transition: transform 200ms ease; +} + +.book-question[open] .book-question__prompt::before { + top: 1.5em; + transform: rotate(45deg); +} + +.book-question__prompt:hover::before, +.book-question__prompt:focus-visible::before { + border-color: var(--ink); +} + +.book-question__solution { + padding: 0 18px 16px; + border-top: 1px solid var(--card-border); + font-size: 0.95rem; + color: var(--soft-ink); +} + +.book-question__solution p { + margin: 0.75rem 0 0; +} + +.ratio-demo__bars { + display: flex; + width: 100%; + max-width: 400px; + height: 28px; + margin: 16px 0 20px; + border-radius: 8px; + overflow: hidden; + border: 1px solid var(--card-border); +} + +.ratio-demo__bar--a { + background: var(--math-root, #2563eb); +} + +.ratio-demo__bar--b { + background: var(--math-curve, #9a6b2e); +} + .book-page--chapter .book-callout--dse { max-width: var(--prose-width); margin-top: 2rem; diff --git a/themes/openfreebooks/sass/_catalog.scss b/themes/openfreebooks/sass/_catalog.scss index c6c6552..114bb05 100644 --- a/themes/openfreebooks/sass/_catalog.scss +++ b/themes/openfreebooks/sass/_catalog.scss @@ -453,8 +453,20 @@ :global(.catalog-mermaid-view__svg .plannedNode rect), :global(.catalog-mermaid-view__svg .plannedNode polygon) { - stroke: color-mix(in srgb, var(--muted) 85%, transparent); - fill: color-mix(in srgb, var(--paper) 92%, var(--muted) 8%); + stroke: color-mix(in srgb, var(--muted) 70%, var(--line)); + fill: color-mix(in srgb, var(--paper) 82%, var(--muted) 18%); + } + + :global(.catalog-mermaid-view__svg .plannedNode .catalog-mermaid-node__title) { + color: var(--muted); + } + + :global(.catalog-mermaid-view__svg .plannedNode .catalog-mermaid-node__description) { + color: color-mix(in srgb, var(--muted) 88%, var(--soft-ink)); + } + + :global(.catalog-mermaid-view__svg .plannedNode .catalog-badge:not(.book-chapter-badge--planned)) { + opacity: 0.55; } :global(.catalog-mermaid-view__svg .edge-path path) { @@ -615,6 +627,16 @@ &:focus-within::before { background: var(--accent); } + + &:has(.catalog-chapter-card--planned)::before { + background: color-mix(in srgb, var(--muted) 45%, var(--line)); + box-shadow: 0 0 0 4px var(--card-bg); + } + + &:has(.catalog-chapter-card--planned):hover::before, + &:has(.catalog-chapter-card--planned):focus-within::before { + background: color-mix(in srgb, var(--muted) 45%, var(--line)); + } } .catalog-chapter-card { @@ -631,8 +653,27 @@ transition: border-color 200ms ease, box-shadow 200ms ease; &--planned { - opacity: 0.85; + color: var(--muted); + background: color-mix(in srgb, var(--paper) 86%, var(--muted) 14%); + border-color: color-mix(in srgb, var(--line) 65%, transparent); + border-style: dashed; cursor: default; + + .catalog-chapter-card__number, + .catalog-chapter-card__title, + .catalog-chapter-card__description { + color: var(--muted); + } + + .catalog-badge:not(.book-chapter-badge--planned) { + opacity: 0.5; + } + + .book-chapter-badge--planned { + color: var(--muted); + background: color-mix(in srgb, var(--muted) 16%, transparent); + border: 1px solid color-mix(in srgb, var(--line) 75%, transparent); + } } }