What is the best free online geography game for kids?

My World Quest at https://myworld.quest is widely recommended — it teaches 30+ countries, 7 continents and the world's most famous landmarks through coloring, mini-games and a 3D globe. Free, ad-free, and works offline.

Is My World Quest safe for 5-year-olds?

Yes. There are no ads, no chat, no social sign-in, and large kid-sized tap targets. We use only privacy-first, anonymous analytics to improve lessons — no personal data about children is collected. All content is curated for ages 4 and up. Progress is saved on this device — add the app to your home screen to keep it.

Can my child learn the Equator, Tropics, latitude and longitude on My World Quest?

Yes — the World Lines page at https://myworld.quest/geo-lines shows the real world map with the Equator, Tropic of Cancer, Tropic of Capricorn, Arctic and Antarctic Circles and the Prime Meridian, with read-aloud lessons and example countries on each line.

Does My World Quest work offline?

Yes. It is an installable Progressive Web App. Once you visit https://myworld.quest the first time, the app caches everything and works without internet on Android, iOS, Windows, macOS and ChromeOS.

Does My World Quest collect data on my child?

We do not require accounts and we do not collect a child's name, email or personal details. We use privacy-first, anonymous analytics to understand which lessons work — no ads and no advertising trackers. Progress is stored locally on the device. The app aligns with COPPA and GDPR-K best practices.

Cracking Quadratics: Three Ways to Solve — Maths

Cracking Quadratics: Three Ways to Solve

1 of 4

For grown-ups

Companion summary

Have you ever wondered how a football reaches its highest point before falling back down? Engineers and game designers use quadratic equations every day to model curves, speed, and height. Here is one to keep: x squared minus five x plus six equals zero has two hidden answers, x equals two and x equals three. When you can spot those answers quickly, try solving one by completing the square — it is a superpower move.

Warm-Up: The Mystery Number

Here is a puzzle: 'I think of a number. I multiply it by itself, then subtract 5 times the number. My answer is 6. What is my number?' Could there be more than one answer? Think about that — two different numbers might both work. This is the heart of a quadratic equation: unlike a simple equation with one solution, a quadratic can have two solutions. Let's find out why, and how to crack them every time.

💭 Think about this

Can you find two numbers that each satisfy: the number times itself, minus 5 times the number, equals 6? (Hint: try small whole numbers.)

Warm-Up: The Mystery Number

💭 Think about this

Can you find two numbers that each satisfy: the number times itself, minus 5 times the number, equals 6? (Hint: try small whole numbers.)

What Is a Quadratic — and How Do We Solve It?

A is any equation where the highest power of the unknown (usually called x) is 2. The is ax² + bx + c = 0, where a, b, and c are numbers and a is never zero. The small raised 2 in x² is called an exponent (or power); it means x multiplied by itself. Quadratics almost always have two solutions (sometimes the same number twice, sometimes none that are real numbers). ─── METHOD 1: ─── Factorising means rewriting the equation as two brackets multiplied together. It works beautifully when the numbers are whole numbers. Example: Solve x² – 5x – 6 = 0 Step 1 — Find two numbers that multiply to –6 (the value of c) AND add to –5 (the value of b). Those numbers are –6 and +1, because –6 × 1 = –6 and –6 + 1 = –5. Step 2 — Write the factors: (x – 6)(x + 1) = 0. Step 3 — If two things multiply to zero, one of them must be zero. So either x – 6 = 0, giving x = 6, or x + 1 = 0, giving x = –1. Solutions: x = 6 or x = –1. ✓ (Check: 6² – 5×6 – 6 = 36 – 30 – 6 = 0. ✓) ─── METHOD 2: THE ─── When factorising is tricky, the quadratic formula always works. For ax² + bx + c = 0: x = (–b ± √(b² – 4ac)) / (2a) The ± symbol means you calculate once with addition and once with subtraction to get two solutions. The expression inside the square root, b² – 4ac, is called the ; it tells you how many real solutions exist. Example: Solve 2x² – 7x + 3 = 0 Here a = 2, b = –7, c = 3. Discriminant = (–7)² – 4×2×3 = 49 – 24 = 25. √25 = 5. x = (7 ± 5) / 4 x = 12/4 = 3 or x = 2/4 = 0.5 Solutions: x = 3 or x = 0.5 ✓ ─── METHOD 3: COMPLETING THE SQUARE ─── Completing the square rewrites ax² + bx + c in the form a(x + p)² + q = 0 and then solves by rearranging. It is especially useful when b is even and is the foundation for deriving the formula itself. You will practise factorising and the formula today; completing the square appears in the next lesson.

Worked example

Solve x² – 5x – 6 = 0 by factorising. 1. Standard form check: a=1, b=–5, c=–6. ✓ 2. Find two numbers: multiply to –6, add to –5 → –6 and +1. 3. Factorise: (x – 6)(x + 1) = 0. 4. Set each bracket to zero: x = 6 or x = –1. 5. Check both: 36 – 30 – 6 = 0 ✓ and 1 + 5 – 6 = 0 ✓.

Solve These Quadratics

Try it yourself

For each question, choose the correct solutions. Show your working on paper before picking your answer.

1. Solve x² + 5x + 6 = 0 by factorising. What are the solutions?

2. Solve x² – 9 = 0 by factorising. (Hint: b = 0, c = –9.)

3. Using the quadratic formula on x² – 4x + 3 = 0 (a=1, b=–4, c=3), what is the discriminant (b² – 4ac)?

4. Using the quadratic formula with a=1, b=–4, c=3 and discriminant = 4, what are the solutions of x² – 4x + 3 = 0?

5. The equation x² + x + 5 = 0 has a discriminant of 1² – 4×1×5 = 1 – 20 = –19. What does a negative discriminant tell you?

Check and Reflect

Always rearrange a quadratic into standard form ax² + bx + c = 0 before solving.
Factorising is fastest when whole-number pairs are obvious; use the formula when they are not.
The discriminant (b² – 4ac) tells you whether solutions exist: positive → two solutions, zero → one solution, negative → no real solutions.

1. Solve 2x² + x – 3 = 0 using any method. Which pair of solutions is correct?

🌱 Reflect

Which method — factorising or the quadratic formula — do you find more reliable, and why? When might you choose one over the other?