How to play
ROBINSON GAME is an online game for learning to solve linear equations by applying algebraic algorithms. The word algebra comes from the Arabic al-jabr, meaning "repairing" or "restoring": solving an equation means bringing order back to a disordered structure.
The idea is to turn the equation into a simpler one with the same solutions, until the value of the unknown is explicit. To do this you apply algorithms, which change from one level to the next.
On the start page you choose whether to play with integers (ℤ) or rational numbers (ℚ), and then the level. So as not to tie the unknown to one symbol, it changes between x, y and z. The equations always have exactly one solution: impossible or indeterminate equations never appear.
Level 1
U
Unite. Adds two like terms on the same side: 3x + 4x becomes 7x, 3 − 7 becomes −4. The player does the sum: the game checks it but does not do it.
A
Add. Adds the same term to both sides, even a negative one: from 3x − 5 = 7, adding 5 gives 3x − 5 + 5 = 7 + 5.
Goal: reach a form like nx = m, with n and m numbers, and estimate the value of the unknown as a decimal number. The closer the estimate to the exact value, the higher the score.
Level 2
Brackets appear, and the algorithms become broader and more efficient.
U
Unite. Now several like terms can be united at once, even inside the same bracket, leaving the number that multiplies it unchanged: 3(2x + 5x − 1 − x) becomes 3(6x − 1).
PA
Pass across. Replaces A: click a term outside the brackets and it moves to the other side with the opposite sign. PA combines A and U: moving a term is the same as adding its opposite to both sides and then uniting, on one side, the two terms that cancel out.
D
Distribute. Applies the distributive property when there is a bracket: 3(6x − 1) becomes 18x − 3. Here too the player writes the result.
Goal: as at level 1, reach nx = m and estimate the value of the unknown.
Level 3
M joins the algorithms of level 2.
M
Multiply or divide. Both sides are multiplied or divided by the same non-zero number: from 3x = 7, dividing by 3 gives x = 7/3.
Goal: isolate the unknown (x = …) and find its exact value, without estimates. That is why level 3 is played only in ℚ: even if all the coefficients of the starting equation are integers, the solution can be a fraction.
More software