- You can already add, subtract, multiply, and divide whole numbers using written
- calculation (columns, carry, and borrow). On a number line, those values lie on or to the
- right of zero.
- Numbers can also lie to the left of zero — we call them 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
-
-
-
-
-
Signs
-
Result
-
-
-
-
-
positive × positive, negative × negative
-
positive
-
-
-
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 \(24\).
-
- 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.”
-
-
-
-
-
- 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.
- You can already add, subtract, multiply, and divide whole numbers using written
- calculation (columns, carry, and borrow). On a number line, those values lie on or to the
- right of zero.
- Numbers can also lie to the left of zero — we call them 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
-
-
-
-
-
Signs
-
Result
-
-
-
-
-
positive × positive, negative × negative
-
positive
-
-
-
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 \(24\).
-
- 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.
-
- 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.”
-
-
-
-
-
- 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.
- 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/content/math/integer-arithmetic/_index.md b/content/math/integer-arithmetic/_index.md
new file mode 100644
index 0000000..0e8cd56
--- /dev/null
+++ b/content/math/integer-arithmetic/_index.md
@@ -0,0 +1,83 @@
++++
+title = "Integer arithmetic"
+description = "Multiply and divide integers from models to symbolic rules; apply order of operations with signed numbers in multi-step expressions."
+template = "chapter.html"
+weight = 9
+[extra]
+subject = "math"
+chapter_id = "integer-arithmetic"
+strand = "Number & Algebra"
++++
+
+
+
+ This chapter extends integer work to multiplication, division, and multi-step expressions.
+
+
+
Sign rules for multiplication and division
+
+
+
+
+
Operation
+
Result sign
+
+
+
+
+
same signs
+
positive
+
+
+
different signs
+
negative
+
+
+
+
+
+ Examples: \((-3)(-4)=12\), \(18\div(-3)=-6\).
+
+
+
Why negative times negative is positive
+
+ Arithmetic rules must stay consistent with distribution. This leads to
+ \((-a)(-b)=ab\).
+
+
+
Order of operations with signed numbers
+
+ Use brackets, exponents, multiplication/division, then addition/subtraction.
+
+
+ \(5-(-2)\times 3 = 5-(-6)=11\)
+
+
+
Multi-step integer expressions
+
+ Keep signs with their numbers and rewrite subtraction as adding opposites when needed.
+
+
+
+ Checkpoint: evaluate \((-6)\times 7\)
+
+
\(-42\).
+
+
+
+
+ Checkpoint: evaluate \(36\div(-9)\)
+
+
\(-4\).
+
+
+
+
+ Checkpoint: evaluate \(8-3(2-5)\)
+
+
+ \(2-5=-3\), then \(8-3(-3)=8-(-9)=17\).
+
+
+
+
diff --git a/content/math/integer-arithmetic/core.html b/content/math/integer-arithmetic/core.html
new file mode 100644
index 0000000..cc8add4
--- /dev/null
+++ b/content/math/integer-arithmetic/core.html
@@ -0,0 +1,72 @@
+
+
+ This chapter extends integer work to multiplication, division, and multi-step expressions.
+
+
+
Sign rules for multiplication and division
+
+
+
+
+
Operation
+
Result sign
+
+
+
+
+
same signs
+
positive
+
+
+
different signs
+
negative
+
+
+
+
+
+ Examples: \((-3)(-4)=12\), \(18\div(-3)=-6\).
+
+
+
Why negative times negative is positive
+
+ Arithmetic rules must stay consistent with distribution. This leads to
+ \((-a)(-b)=ab\).
+
+
+
Order of operations with signed numbers
+
+ Use brackets, exponents, multiplication/division, then addition/subtraction.
+
+
+ \(5-(-2)\times 3 = 5-(-6)=11\)
+
+
+
Multi-step integer expressions
+
+ Keep signs with their numbers and rewrite subtraction as adding opposites when needed.
+
+
+
+ Checkpoint: evaluate \((-6)\times 7\)
+
+
\(-42\).
+
+
+
+
+ Checkpoint: evaluate \(36\div(-9)\)
+
+
\(-4\).
+
+
+
+
+ Checkpoint: evaluate \(8-3(2-5)\)
+
+
+ \(2-5=-3\), then \(8-3(-3)=8-(-9)=17\).
+
+
+
+
diff --git a/content/math/integer-foundations/_index.md b/content/math/integer-foundations/_index.md
new file mode 100644
index 0000000..89e615e
--- /dev/null
+++ b/content/math/integer-foundations/_index.md
@@ -0,0 +1,74 @@
++++
+title = "Integer foundations"
+description = "Model directed magnitude on number lines; use the zero principle and tiles to add and subtract integers, and see subtraction as adding an opposite."
+template = "chapter.html"
+weight = 8
+[extra]
+subject = "math"
+chapter_id = "integer-foundations"
+strand = "Number & Algebra"
++++
+
+
+
+ Integers extend whole numbers to include values below zero. They are useful for temperature,
+ elevation, and money balances.
+
+
+
Directed numbers on a number line
+
+ Positive numbers are to the right of zero, negative numbers are to the left. Moving right
+ increases value; moving left decreases value.
+
+
+
Compare quickly
+
\(a > b\) means \(a\) is to the right of \(b\) on the number line.
+
+
+
Absolute value and opposites
+
+ Absolute value is distance from zero: \(|-7|=7\). Opposites have equal distance from zero and
+ opposite signs, such as \(+5\) and \(-5\).
+
+
+
Adding and subtracting integers
+
+ You can think of addition and subtraction as movement on the number line.
+
+
+
\(a+b\): start at \(a\), move by \(b\).
+
\(a-b = a+(-b)\): subtracting is adding the opposite.
+
+
+ Example: \(6-(-4)=6+4=10\).
+
+
+
Zero principle with tiles
+
+ A positive tile and a negative tile form a zero pair. Add or remove zero pairs to simplify
+ without changing value.
+
+
+
+ Checkpoint: evaluate \(-3 + 8\)
+
+
\(-3 + 8 = 5\). Start at \(-3\), move 8 units right.
+
+
+
+
+ Checkpoint: evaluate \(4 - 9\)
+
+
\(4 - 9 = -5\). Equivalent to \(4 + (-9)\).
+
+
+
+
+ Checkpoint: explain why \(2-(-2)=4\)
+
+
+ Subtracting \(-2\) means adding its opposite \(+2\), so \(2-(-2)=2+2=4\).
+
+
+
+
diff --git a/content/math/integer-foundations/core.html b/content/math/integer-foundations/core.html
new file mode 100644
index 0000000..e27d007
--- /dev/null
+++ b/content/math/integer-foundations/core.html
@@ -0,0 +1,63 @@
+
+
+ Integers extend whole numbers to include values below zero. They are useful for temperature,
+ elevation, and money balances.
+
+
+
Directed numbers on a number line
+
+ Positive numbers are to the right of zero, negative numbers are to the left. Moving right
+ increases value; moving left decreases value.
+
+
+
Compare quickly
+
\(a > b\) means \(a\) is to the right of \(b\) on the number line.
+
+
+
Absolute value and opposites
+
+ Absolute value is distance from zero: \(|-7|=7\). Opposites have equal distance from zero and
+ opposite signs, such as \(+5\) and \(-5\).
+
+
+
Adding and subtracting integers
+
+ You can think of addition and subtraction as movement on the number line.
+
+
+
\(a+b\): start at \(a\), move by \(b\).
+
\(a-b = a+(-b)\): subtracting is adding the opposite.
+
+
+ Example: \(6-(-4)=6+4=10\).
+
+
+
Zero principle with tiles
+
+ A positive tile and a negative tile form a zero pair. Add or remove zero pairs to simplify
+ without changing value.
+
+
+
+ Checkpoint: evaluate \(-3 + 8\)
+
+
\(-3 + 8 = 5\). Start at \(-3\), move 8 units right.
+
+
+
+
+ Checkpoint: evaluate \(4 - 9\)
+
+
\(4 - 9 = -5\). Equivalent to \(4 + (-9)\).
+
+
+
+
+ Checkpoint: explain why \(2-(-2)=4\)
+
+
+ Subtracting \(-2\) means adding its opposite \(+2\), so \(2-(-2)=2+2=4\).
+
+
+
+
diff --git a/content/math/percentage-applications/_index.md b/content/math/percentage-applications/_index.md
new file mode 100644
index 0000000..713ceba
--- /dev/null
+++ b/content/math/percentage-applications/_index.md
@@ -0,0 +1,69 @@
++++
+title = "Percentage applications"
+description = "Relate fractions and decimals to base-100 ratios; calculate percent increase and decrease in financial and real-world contexts."
+template = "chapter.html"
+weight = 11
+[extra]
+subject = "math"
+chapter_id = "percentage-applications"
+strand = "Number & Algebra"
++++
+
+
+
+ Percent means “per hundred.” This chapter connects percent, fraction, and decimal forms and
+ applies them in everyday contexts.
+
+
+
Percent, fraction, decimal
+
+ \(35\% = \frac{35}{100}=0.35\)
+
+
+ Convert by multiplying or dividing by 100 as needed.
+
+
+
Finding part and whole
+
+ To find \(p\%\) of a quantity \(Q\), use \(\frac{p}{100}\times Q\).
+
+
+ \(18\%\text{ of }250 = 0.18\times250 = 45\)
+
+
+
Percent increase and decrease
+
+ Percent change compares new and original values.
+
+ Ratios compare quantities. Rates compare quantities with different units. Both are essential
+ for scale, speed, and pricing.
+
+
+
Part-to-part and part-to-whole ratios
+
+ A ratio \(2:3\) means two equal parts compared with three equal parts. Total parts are \(2+3=5\).
+
+
+ If a class has 12 boys and 18 girls, boys:girls is \(12:18=2:3\), and boys:total is \(12:30=2:5\).
+
+
+
Equivalent ratios
+
+ Multiply or divide both parts by the same nonzero number.
+
+
+ \(3:5 = 6:10 = 12:20\)
+
+
+
Unit rates
+
+ A unit rate is “per one.” If 180 km takes 3 hours, speed is \(180\div3=60\) km/h.
+
+
+
Proportional relationships
+
+ For proportional relationships, \(y=kx\). Graphs are straight lines through the origin where
+ slope is the constant of proportionality \(k\).
+
+
+
+ Checkpoint: share 56 in ratio \(3:4\)
+
+
Total parts \(=7\), one part \(=8\), shares are 24 and 32.
+
+
+
+
+ Checkpoint: 45 dollars for 6 kg, find unit price
+
+
\(45\div6=7.5\). Unit price is 7.5 dollars per kg.
+
+
+
diff --git a/content/math/ratios-and-rates-foundation/core.html b/content/math/ratios-and-rates-foundation/core.html
new file mode 100644
index 0000000..5116b9d
--- /dev/null
+++ b/content/math/ratios-and-rates-foundation/core.html
@@ -0,0 +1,47 @@
+
+
+ Ratios compare quantities. Rates compare quantities with different units. Both are essential
+ for scale, speed, and pricing.
+
+
+
Part-to-part and part-to-whole ratios
+
+ A ratio \(2:3\) means two equal parts compared with three equal parts. Total parts are \(2+3=5\).
+
+
+ If a class has 12 boys and 18 girls, boys:girls is \(12:18=2:3\), and boys:total is \(12:30=2:5\).
+
+
+
Equivalent ratios
+
+ Multiply or divide both parts by the same nonzero number.
+
+
+ \(3:5 = 6:10 = 12:20\)
+
+
+
Unit rates
+
+ A unit rate is “per one.” If 180 km takes 3 hours, speed is \(180\div3=60\) km/h.
+
+
+
Proportional relationships
+
+ For proportional relationships, \(y=kx\). Graphs are straight lines through the origin where
+ slope is the constant of proportionality \(k\).
+
+
+
+ Checkpoint: share 56 in ratio \(3:4\)
+
+
Total parts \(=7\), one part \(=8\), shares are 24 and 32.
+
+
+
+
+ Checkpoint: 45 dollars for 6 kg, find unit price
+
+
\(45\div6=7.5\). Unit price is 7.5 dollars per kg.
+
+
+
diff --git a/data/faq.json b/data/faq.json
index 9528b7a..eb3c7b6 100644
--- a/data/faq.json
+++ b/data/faq.json
@@ -14,26 +14,32 @@
{
"id": "how-different",
"type": "comparison",
- "question": "How is Open Free Books different from GeoGebra, Math is Fun, and Wikipedia?",
- "intro": "We respect these projects — they solve different problems. Open Free Books is a free, open-source textbook library on the web.",
+ "question": "How is Open Free Books different from LibreTexts, Open Textbook Library, Project Gutenberg, and OpenStax?",
+ "intro": "We respect these projects — they solve different problems. On many platforms, you find lots of different books for a single subject. With Open Free Books, there's just one textbook per subject—designed to be comprehensive so people everywhere can use it for any curriculum. That way, you don't need to pick between competing choices—you can just focus on learning. Oh, so this platform usually only provides static HTML without any interaction or just a PDF, but in OpenFreeBooks we have interactive demos An alleged map that are tailor made to visualize complex idea in simple ways.",
"peers": [
{
- "name": "GeoGebra",
- "url": "https://www.geogebra.org/",
- "role": "Interactive geometry and algebra tools, activities, and classroom apps.",
- "contrast": "Open Free Books publishes structured textbook chapters and learning paths, not a general-purpose construction sandbox."
+ "name": "LibreTexts",
+ "url": "https://libretexts.org/",
+ "role": "Open educational resource platform with broad textbook collections and institutional adoption.",
+ "contrast": "Open Free Books is a focused open textbook library with curriculum-shaped pathways, lightweight static delivery, and contributor-driven book structure."
},
{
- "name": "Math is Fun",
- "url": "https://www.mathsisfun.com/",
- "role": "Friendly reference pages, games, and explanations across many topics.",
- "contrast": "Open Free Books is curriculum-shaped: ordered chapters, prerequisites in the catalog map, and authored books — not a grab-bag of articles."
+ "name": "Open Textbook Library",
+ "url": "https://open.umn.edu/opentextbooks",
+ "role": "A catalog and discovery hub for openly licensed textbooks with reviews and adoption support.",
+ "contrast": "Open Free Books publishes and maintains textbooks directly in the open repository, including chapter sequencing and prerequisite maps."
},
{
- "name": "Wikipedia",
- "url": "https://www.wikipedia.org/",
- "role": "Encyclopedic, community-edited reference on almost everything.",
- "contrast": "Not a wiki-style fact pile. We publish opinionated paths from prerequisite to mastery — structure on purpose, not everything about X."
+ "name": "Project Gutenberg: Free eBooks",
+ "url": "https://www.gutenberg.org/",
+ "role": "A public library of free eBooks, especially classic works and historical texts.",
+ "contrast": "Open Free Books is built for active learning: modern textbook chapters, guided progression, and curriculum alignment rather than archival eBook distribution."
+ },
+ {
+ "name": "OpenStax",
+ "url": "https://openstax.org/",
+ "role": "Peer-reviewed open textbooks for major school and college subjects.",
+ "contrast": "Open Free Books emphasizes community-authored web textbooks with transparent GitHub workflows and adaptable chapter-level contribution."
}
],
"ofb": "Free forever, no ads, no commercial upsell, and open on GitHub for anyone to fix or extend."
@@ -102,6 +108,16 @@
"The open web is more durable: HTML and JavaScript are stable foundations likely to remain usable for decades. Building high-quality, future-proof educational materials now — with AI assistance but web-native outputs — is the practical long-term approach."
]
},
+ {
+ "id": "content-perfect",
+ "type": "standard",
+ "question": "Why isn’t the content perfect?",
+ "answer": [
+ "No textbook is perfect — whether it’s a PDF, a printed book, or an online resource. Learning evolves, and so does our understanding of what makes content useful and accurate.",
+ "Open Free Books may not be flawless, but it’s built on lasting web standards: HTML, JavaScript, and CSS. This means chapters are readable on any device, by anyone, anywhere — making them among the most accessible textbooks in the world.",
+ "We set high standards for academic quality, and the catalog is always improving. Every chapter is open for review and enhancement by contributors, so progress never stops."
+ ]
+ },
{
"id": "subjects",
"type": "standard",
diff --git a/data/math-curriculum.json b/data/math-curriculum.json
index fa9cedf..e1caebb 100644
--- a/data/math-curriculum.json
+++ b/data/math-curriculum.json
@@ -45,14 +45,6 @@
},
{
"from": "integer-arithmetic",
- "to": "directed-numbers-rates"
- },
- {
- "from": "ratios-and-rates-foundation",
- "to": "directed-numbers-rates"
- },
- {
- "from": "directed-numbers-rates",
"to": "polynomials-expansion-factorisation"
},
{
@@ -172,7 +164,7 @@
"to": "loci"
},
{
- "from": "directed-numbers-rates",
+ "from": "ratios-and-rates-foundation",
"to": "statistical-charts-averages"
},
{
@@ -304,7 +296,7 @@
"slug": "integer-foundations",
"title": "Integer foundations",
"description": "Model directed magnitude on number lines; use the zero principle and tiles to add and subtract integers, and see subtraction as adding an opposite.",
- "status": "planned",
+ "status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
@@ -322,7 +314,7 @@
"slug": "integer-arithmetic",
"title": "Integer arithmetic",
"description": "Multiply and divide integers from models to symbolic rules; apply order of operations with signed numbers in multi-step expressions.",
- "status": "planned",
+ "status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
@@ -340,7 +332,7 @@
"slug": "rational-number-operations",
"title": "Fractions and decimals",
"description": "Convert between fractions, terminating decimals, and repeating decimals; add, subtract, multiply, and divide rational numbers and mixed numbers.",
- "status": "planned",
+ "status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
@@ -358,7 +350,7 @@
"slug": "percentage-applications",
"title": "Percentage applications",
"description": "Relate fractions and decimals to base-100 ratios; calculate percent increase and decrease in financial and real-world contexts.",
- "status": "planned",
+ "status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
@@ -376,7 +368,7 @@
"slug": "ratios-and-rates-foundation",
"title": "Ratios & rates foundations",
"description": "Formulate part-to-part and part-to-whole ratios, find equivalent ratios, compute unit rates, and graph proportional relationships.",
- "status": "planned",
+ "status": "live",
"curriculumCoverage": {
"Foundation": "core",
"IGCSE": "core",
@@ -390,24 +382,6 @@
"Gaokao": "related"
}
},
- {
- "slug": "directed-numbers-rates",
- "title": "Directed numbers, rates & ratios",
- "description": "Operate with negative numbers and solve ratio, rate, and proportion problems in context.",
- "status": "live",
- "curriculumCoverage": {
- "DSE": "core",
- "IGCSE": "core",
- "Common Core": "core",
- "Singapore": "core",
- "UK GCSE": "core",
- "Foundation": "related",
- "IB": "related",
- "A-Level": "related",
- "AP": "related",
- "Gaokao": "related"
- }
- },
{
"slug": "polynomials-expansion-factorisation",
"title": "Polynomials: expansion & factorisation",
diff --git a/package.json b/package.json
index 3f19335..255fb71 100644
--- a/package.json
+++ b/package.json
@@ -7,7 +7,8 @@
"sync:chapters": "bun scripts/sync-chapters.ts",
"generate:site-metadata": "bun scripts/generate-site-metadata.ts",
"build:js": "bun run sync:chapters && vite build",
- "build": "bun run check:static-html && bun run validate:curriculum && rm -f themes/openfreebooks/static/main.css public/main.css && bun run build:js && bun run generate:site-metadata && zola build && bun run index:search",
+ "build:site": "bun run generate:site-metadata && zola build && bun run index:search",
+ "build": "bun run check:static-html && bun run validate:curriculum && rm -f themes/openfreebooks/static/main.css public/main.css && bun run build:js && bun run build:site",
"index:search": "pagefind --site public --glob \"**/index.html\" && rm -rf static/pagefind && cp -R public/pagefind static/pagefind",
"dev:js": "bun run sync:chapters && vite build --watch",
"dev": "bash scripts/dev.sh",
diff --git a/static/feed.xml b/static/feed.xml
index b8650ae..a3bc0f9 100644
--- a/static/feed.xml
+++ b/static/feed.xml
@@ -4,7 +4,42 @@
Open Free Books
https://openfreebooks.org/
Recent updates to Open Free Books pages and live chapters.
- Thu, 21 May 2026 16:54:30 GMT
+ Thu, 21 May 2026 17:43:39 GMT
+
+ Integer foundations
+ https://openfreebooks.org/math/integer-foundations/
+ https://openfreebooks.org/math/integer-foundations/
+ Thu, 21 May 2026 17:43:39 GMT
+ Model directed magnitude on number lines; use the zero principle and tiles to add and subtract integers, and see subtraction as adding an opposite.
+
+
+ Integer arithmetic
+ https://openfreebooks.org/math/integer-arithmetic/
+ https://openfreebooks.org/math/integer-arithmetic/
+ Thu, 21 May 2026 17:43:39 GMT
+ Multiply and divide integers from models to symbolic rules; apply order of operations with signed numbers in multi-step expressions.
+
+
+ Percentage applications
+ https://openfreebooks.org/math/percentage-applications/
+ https://openfreebooks.org/math/percentage-applications/
+ Thu, 21 May 2026 17:43:39 GMT
+ Relate fractions and decimals to base-100 ratios; calculate percent increase and decrease in financial and real-world contexts.
+
+
+ Fractions and decimals
+ https://openfreebooks.org/math/rational-number-operations/
+ https://openfreebooks.org/math/rational-number-operations/
+ Thu, 21 May 2026 17:43:39 GMT
+ Convert between fractions, terminating decimals, and repeating decimals; add, subtract, multiply, and divide rational numbers and mixed numbers.
+
+
+ Ratios & rates foundations
+ https://openfreebooks.org/math/ratios-and-rates-foundation/
+ https://openfreebooks.org/math/ratios-and-rates-foundation/
+ Thu, 21 May 2026 17:43:39 GMT
+ Formulate part-to-part and part-to-whole ratios, find equivalent ratios, compute unit rates, and graph proportional relationships.
+ Advanced trigonometry
https://openfreebooks.org/math/advanced-trigonometry/
@@ -243,13 +278,6 @@
Wed, 20 May 2026 20:17:25 GMTSimplify and combine algebraic fractions; rearrange formulas in science contexts.
-
- Directed numbers, rates & ratios
- https://openfreebooks.org/math/directed-numbers-rates/
- https://openfreebooks.org/math/directed-numbers-rates/
- Wed, 20 May 2026 20:17:25 GMT
- Operate with negative numbers and solve ratio, rate, and proportion problems in context.
- Polynomials: expansion & factorisation
https://openfreebooks.org/math/polynomials-expansion-factorisation/
diff --git a/static/og.jpg b/static/og.jpg
index 5503cd0..1925004 100644
Binary files a/static/og.jpg and b/static/og.jpg differ
diff --git a/static/sitemap.xml b/static/sitemap.xml
index da32a9b..af68b9b 100644
--- a/static/sitemap.xml
+++ b/static/sitemap.xml
@@ -72,10 +72,6 @@
https://openfreebooks.org/math/deductive-geometry/2026-05-21T16:54:30.000Z
-
- https://openfreebooks.org/math/directed-numbers-rates/
- 2026-05-20T20:17:25.000Z
- https://openfreebooks.org/math/exponential-logarithmic/2026-05-21T07:33:01.000Z
@@ -88,6 +84,14 @@
https://openfreebooks.org/math/functions-graphs/2026-05-21T07:33:01.000Z
+
+ https://openfreebooks.org/math/integer-arithmetic/
+ 2026-05-21T17:43:39.596Z
+
+
+ https://openfreebooks.org/math/integer-foundations/
+ 2026-05-21T17:43:39.989Z
+ https://openfreebooks.org/math/introduction-trigonometry/2026-05-21T16:54:30.000Z
@@ -124,6 +128,10 @@
https://openfreebooks.org/math/normal-distribution-z-scores/2026-05-21T16:54:30.000Z
+
+ https://openfreebooks.org/math/percentage-applications/
+ 2026-05-21T17:43:39.595Z
+ https://openfreebooks.org/math/permutations-combinations-probability/2026-05-21T16:54:30.000Z
@@ -144,6 +152,14 @@
https://openfreebooks.org/math/quadratic-equations/2026-05-20T20:17:25.000Z
+
+ https://openfreebooks.org/math/rational-number-operations/
+ 2026-05-21T17:43:39.472Z
+
+
+ https://openfreebooks.org/math/ratios-and-rates-foundation/
+ 2026-05-21T17:43:39.210Z
+ https://openfreebooks.org/math/sequences-series/2026-05-21T07:33:01.000Z
-