Formula explorer with live sliders
Pick a real formula, drag a slider for each variable, and watch the answer update instantly. Three of them draw a shape that grows and re-shapes as you drag, so you can see what the numbers mean. Every result is computed in code, so it is never wrong. Free, no sign-up. Great for building the intuition behind ACARA AC9M7A06 (describe what happens as the values change).
Area of a circle
A = πr²The space inside a circle grows with the square of the radius, so doubling the radius makes the area four times as big. Drag the radius and watch the circle and the area change together.
Reinforces: Circles: circumference & area worksheets
Circumference of a circle
C = 2πrThe distance around a circle is directly proportional to the radius, so it grows in a straight line as the radius increases (unlike the area). Compare how the two respond to the same slider.
Reinforces: Circles: circumference & area worksheets
Pythagoras' theorem
c = √(a² + b²)The longest side of a right-angled triangle (the hypotenuse) depends on both shorter sides. Change either leg and see the triangle re-shape and the hypotenuse update.
Reinforces: Pythagoras worksheets
Compound interest
A = P(1 + r/100)ⁿMoney left to earn compound interest grows faster and faster, because each year's interest also earns interest. Nudge the rate or the number of years and watch the total climb.
Reinforces: Compound interest worksheets
Speed, distance and time
speed = distance ÷ timeSpeed tells you how far you travel each hour. For a fixed distance, taking more time means a lower speed; covering more ground in the same time means a higher speed.
Reinforces: Compound units (speed) worksheets
Things to try
- On area of a circle, double the radius (say 5 to 10) and watch the area jump by four times, not twice. That is the effect of the squared term.
- Compare area and circumference as you move the same radius: circumference grows in a straight line, area curves upward.
- On Pythagoras, keep one leg fixed and grow the other; the triangle stretches and the hypotenuse always comes out longer than either leg.
- On compound interest, nudge the rate from 5% to 10% and see how much more the total climbs over the same number of years.
Where these formulas are taught
Each explorer above links to the matching worksheet set. You can also jump straight to them:
- A = πr² — Area of a circle: Circles: circumference & area worksheets
- C = 2πr — Circumference of a circle: Circles: circumference & area worksheets
- c = √(a² + b²) — Pythagoras' theorem: Pythagoras worksheets
- A = P(1 + r/100)ⁿ — Compound interest: Compound interest worksheets
- speed = distance ÷ time — Speed, distance and time: Compound units (speed) worksheets
Common questions
- Which formulas can I explore?
- Five formulas already taught in ChalkBee's worksheets: area of a circle (A = πr²), circumference (C = 2πr), Pythagoras' theorem (c = √(a² + b²)), compound interest (A = P(1 + r/100)ⁿ) and speed (speed = distance ÷ time). Each uses the same notation as the worksheets, so the tool reinforces what is taught.
- How does it help students learn?
- By dragging one variable at a time you can see exactly what happens to the answer, which is the heart of the Australian Curriculum standard AC9M7A06: 'use formulas with several variables using digital tools, and describe what happens as the values change'. For example, doubling a circle's radius makes the circumference twice as big but the area four times as big.
- Are the results accurate?
- Yes. Every result is computed in code from the exact formula, never guessed or generated, matching ChalkBee's 'answers are never wrong' approach. The evaluation functions are covered by unit tests with hand-checked values.
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