Placeholder equations and inverse operations
Write a story as an equation with a placeholder, find the number with the inverse operation, solve riddles backwards and check by substitution.
- Germany: grade 4
Guide
An equation with a placeholder □ asks for the missing number: □ − 18 = 35. To find it you use the inverse operation (Umkehraufgabe): what is taken away is added back, 35 + 18 = 53. For a product you divide: □ · 6 = 42 gives 42 : 6 = 7.
A number riddle ("I think of a number, times 3, minus 4, the result is 17") is solved backwards: undo the last step first. 17 + 4 = 21, then 21 : 3 = 7.
Always check by substitution (Probe): put your number back into the equation. If both sides are equal, the solution is right. The solution is written as a set, for example L = {7}. In this studio the sentence is written with the box □ and the answer is typed.