23
Word problems
Textbook: Part 1, lesson 23, pp. 92–95
GoalKnow the stages of solving a word problem (read, plan, solve, check) and solve problems with diagrams.
New words
word problem · matnli masalaknown and unknown · ma’lum va noma’lumdiagram · sxemachecking · tekshirish
Explanation
A word problem is a written description of a real situation; we move from it to a mathematical problem. Solving has four stages. Read: read carefully, find what is known and unknown and how they are connected, and draw a diagram. Plan: decide which operations to do in which order to find the unknown. Solve: calculate following the plan, finding intermediate and final values. Check: put the answer back into the conditions. A problem can be solved by the equalizing method or by an equation.
Worked examples
Two baskets hold 52 apricots, the second has 8 fewer. Adding 8 to the second makes them equal: 52 + 8 = 60, 60 : 2 = 30 in the first; 30 − 8 = 22 in the second. Check: 30 + 22 = 52.
A gardener picked 24 kg of apples on the first day and 9 kg less on the second. Second day: 24 − 9 = 15 kg; in two days 24 + 15 = 39 kg.
Class activity
“Problem laboratory”: groups write a problem on a four-stage sheet (Read, Plan, Solve, Check) and pass it to another group to check.
Practice
1
A gardener picked 24 kg of apples on the first day and 9 kg less on the second. How many kg in two days?
39
2
Two containers hold 60 l of water, the first has 14 l more. How many litres are in the first?
37
3
Three shelves hold 100 books. The second has 6 fewer than the first and the third has 4 more than the second. How many on the first shelf?
36
4
Why do we check the answer against the conditions of the problem?
There may be a calculation error; if the answer fits the conditions it is correct.