9
Mathematical problems and equations
Textbook: Part 1, lesson 9, pp. 34–39
GoalBuild the mathematical model (an equation) of a problem; find an unknown addend, minuend or subtrahend; make inverse problems.
New words
equation · tenglamaroot of an equation · tenglamaning ildiziunknown · noma’luminverse problem · teskari masala
Explanation
In a problem some quantities are known and some are unknown. If the problem is written with mathematical symbols, we get its mathematical model. An equality containing an unknown is called an equation; the number that turns it into a true equality is the root (solution) of the equation. Unknown addend: if x + a = b then x = b − a. Unknown minuend: if y − a = b then y = b + a. Unknown subtrahend: if a − z = b then z = a − b. We check a root by substituting it into the equation. Swapping what is known and what is unknown gives an inverse problem.
Worked examples
x + 36 = 91 → x = 91 − 36 = 55. Check: 55 + 36 = 91, correct. y − 17 = 40 → y = 40 + 17 = 57.
Direct problem: a container had 120 l of water, 45 l was used, so 120 − 45 = 75 l is left. Inverse problem: after using 45 l, 75 l is left, so there were 75 + 45 = 120 l at first.
Class activity
“Inverse problem workshop”: a group solves “A basket had 64 apples, 19 were given away”, then swaps the unknown to make and solve two inverse problems.
Practice
1
Solve the equation x + 58 = 134.
76
2
Solve the equation y − 125 = 380.
505
3
Solve the equation 200 − z = 74.
126
4
Why do we subtract the difference from the minuend to find an unknown subtrahend?
Because minuend = subtrahend + difference, so subtrahend = minuend − difference.