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Practical (subject) method.
Students can solve this problem, relying only on their life experience and owning an account from 1 to 10.
Denote each fish by a circle. Let's draw 10 circles and designate the caught fish: l - bream, o - perch. Integral Calculator https://www.stepcalculator.com/integral-calculator.html
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To answer the question of the problem, you can not perform arithmetic, since the number of pikes caught corresponds to those circles that are not marked (there are three of them). Words to Pages Converter https://www.stepcalculator.com/wordstopages.html
GPA Calculator https://www.stepcalculator.com/gpa-calculator.html Arithmetic method.
This method is based on arithmetic operations.
3 4 = 7 (p.) - caught fish;
10–7 = 3 (p.) - pike.
To answer the question, the tasks performed 2 actions.
Algebraic way.
This method is based on the introduction of an unknown variable and on finding it.
Let x be the caught pike. Then the number of all fish can be written by the expression: 3 4 x - all fish.
By the condition of the problem, it is known that the fisherman caught only 10 fish. So: 3 4 x = 10. Solving this equation, we answer the question of the problem: x = 3.
Graphic way.
This method of solution is close to practical, but is more abstract in nature and requires special explanation. Each task object is indicated by a segment.
Picture
This method, as well as practical, allows you to answer the question of the problem without performing arithmetic operations.
The combined method.
It can be used simultaneously graphic and arithmetic methods.
1) 3 4 = 7 (p.) - caught fish;
2) 10–7 = 3 (p.) - pike.
Methods for solving tasks on the example of a specific task
Task. The boy had 90 books. 28 he put on the first shelf, 12 on the second, the rest on the third. How many books are on the third shelf.
Various forms of recording the solution to a problem:
a) Decision on actions:
1) 28 12 = 40 (q.)
2) 90–40 = 50 (c.)
Answer: 50 books on the third shelf.
b) For actions with an explanation:
1) 28 12 = 40 (K.) - on 1 and 2 shelves together,
2) 90–40 = 50 (K.) - on the 3rd shelf.
Answer: 50 books.
c) With questions:
1) How many books are on the 1st and 2nd shelves?
28 12 = 40 (q.)
2) How many books are on the 3rd shelf?
90–40 = 50 (c.)
Answer: 50 books on the third shelf.
d) Expression:
90 - (28 12)
When writing a solution to a problem by an expression, you can calculate its value. Then the record of the solution to the problem will look like this:
90 - (28 12) = 50 (q.)
Ways to design a short record on the example of a specific task
Task. One cutter had 15 m of fabric, the other 12 m. Of the whole fabric, they tailored the dresses, spending 3 m each. How many dresses did they tailor?
1st method: 1) 15 12 = 27 (m),
2) 27: 3 = 9 (p.).
Answer: 9 dresses tailored.
2nd method: 15: 3 12: 3 = 9 (p.)
Answer: 9 dresses tailored.
3rd method: 1) 15: 3 = 5 (p.),
2) 12: 3 = 4 (p.).
3) 5 4 = 9 (p.).
Answer: 9 dresses tailored.