What students learn
A square root is the side length of a square with a given area: a square with an area of 81 has sides of 9, so √81 = 9. Every skill in the game comes back to that picture. Before a shootout, students choose any mix of three skills:
- Squares and Square Roots: √81 = ?, 9² = ?, and the side of a square from its area (including word problems: a square garden, rug, tiled floor or photo)
- Cubes and Cube Roots: ∛64 = ?, 4³ = ?, and the edge of a cube from its volume (including word problems: a cube-shaped box, fish tank or stack of sugar cubes)
- Estimating Square and Cube Roots: √50 is between ? and ? (students find both whole numbers), or is √50 closer to 7 or 8? The power-shot challenge asks which whole number is closest, with no choices given.
How the game works
- Numbers: regular questions use 0 to 10 for square roots, squares and sides of squares, and 0 to 5 for cube roots. The optional bonus (power shot) questions are the challenge: 11 to 16, cube roots of 6 to 10, and powers of ten such as √10,000, 100² and ∛1,000,000.
- A right answer earns the kick. Students can aim anywhere in the goal right away while the referee blows the whistle, then click (or tap, or press the space bar) to start the power, and click again to shoot. The scoring chance updates live, and it is a real probability: the chance the shot is on target times the chance it beats the keeper. Corners are hardest to save; a shot straight at the keeper, or a weak, badly timed one, gets caught. The game decides every shot with that same chance.
- A bonus question after each right answer (optional) earns a power shot with a smaller aiming circle. Word problems and "is it closer to 7 or 8?" questions appear too, and when a wrong answer matches a classic mistake, the explanation names it first.
- The keeper adapts to each student, without telling them: he starts easy, gets sharper after each goal and easier after each miss, and the power circle speeds up for strong shooters. The chance on screen always reflects it.
- A wrong answer shows why before the kick goes wild. Square roots and squares are drawn as a square of unit squares; cube roots as a 3D cube built from little cubes (4 × 4 × 4 = 64); estimates on a number line between the two perfect squares or cubes.
- The final whistle shows goals, questions right, the student's best shootout, and every missed question beside its correct answer.
Worked examples
Square root: What is √144?
12 × 12 = 144, so √144 = 12
Side of a square: A square has an area of 49 square units. How long is each side?
side × side = 49 7 × 7 = 49, so each side is 7
Estimating: √50 is between which two whole numbers?
7² = 49 and 8² = 64 49 < 50 < 64, so 7 < √50 < 8
Estimating a cube root: ∛50 is between which two whole numbers?
3³ = 27 and 4³ = 64 27 < 50 < 64, so 3 < ∛50 < 4
Cube root: What is ∛125?
5 × 5 × 5 = 125, so ∛125 = 5
Common mistakes
- Dividing by 2. Students say √64 = 32 or 8² = 16. The grid after a wrong answer shows that 8² is 8 rows of 8, not 8 + 8.
- Dividing by 3 for cube roots. ∛27 is 3, not 9.
- Estimating with the wrong neighbors. For √50, students sometimes pick 5 and 10 (half and double). Listing the perfect squares 1, 4, 9, 16, 25, 36, 49, 64… fixes it.
Key vocabulary
Words and phrases to use when you talk through the game with students. Each one appears in the game, its questions or its feedback.
- perfect square: a whole number squared, like 49, 64 or 81
- square root (√): the number that, times itself, gives the original number: √81 = 9
- perfect cube: a whole number cubed, like 8, 27 or 64
- cube root (∛): the number that, used three times as a factor, gives the original number: ∛64 = 4
Ways to use it in class
- Printables. A free worksheet with an answer key and a two-to-a-page exit ticket match this game, ready to print or save as a PDF.
- Warm-up. One shootout takes about three minutes.
- Build up the skills. Start with Squares and Square Roots, then Cubes and Cube Roots, then Estimating Square and Cube Roots.
- Class tournament. Students record goals and questions right; a missed question costs a kick, so accuracy wins.
Discussion questions
- Why is the square root of a number the side length of a square?
- √50 is between 7 and 8. Is it closer to 7 or to 8? How do you know?
- Why does 2³ = 8 mean that ∛8 = 2?
- The game says "on target 80% × beats the keeper 50% = 40%." Why do you multiply the two chances? (A 7th grade compound probability connection.)
Standards
CCSS.MATH.CONTENT.8.EE.A.2Use square root and cube root symbols to represent solutions to x² = p and x³ = p. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Squares and Square Roots (including the side of a square) and Cubes and Cube Roots (including the edge of a cube).
CCSS.MATH.CONTENT.8.NS.A.2Use rational approximations of irrational numbers to compare their size and locate them on a number line. Estimating Square and Cube Roots.
CCSS.MATH.CONTENT.6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents. Squaring Numbers.
Access and privacy
En español: the 🌐 Español button in the game's top bar switches everything students see into Spanish. No accounts, no student data: records are saved only in the device's browser. Plays with the keyboard alone (arrow keys to aim; space bar once to start the power and again to shoot (clicks and taps work the same way; Esc or the Menu button pauses, restarts, or changes skills)), with a mouse, or with touch (an on-screen number pad appears on tablets and phones). The 3D stadium needs a device that can show 3D graphics; nearly all current laptops, tablets and phones can.