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Criteria for a good mathematical problem

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Criteria for a good mathematical problem

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1. Problematization

2. Causing interest

3. Investigation

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To what extent does it allow you to problematize the study of the section?

1.1. Accepting a challenge

1.2. Complexity of the problem

1.3. Request for tools

1.4. Topic and purpose

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A Thinking Approach encourages curiosity by promoting open-ended questions and creative problem-solving. This fuels a student's desire to learn and explore. Identifying the problem clearly is the most crucial step. Without knowing what you're solving, you can't find a solution. For example, if you're lost, you first need to figure out where you are.

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To what extent does it set the context for the examination when working with the section?

3.1. Context (number of lessons)

3.2. Context (number of new concepts)

3.3. Key question of the section

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To what extent does it captivate students?

2.1. Life context

2.2. Students’ questions

2.3. Decision-making

2.4. Image

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Not yet:

Students did not have a need to learn new methods

More likely no than yes:

Individual students have a need to learn new methods

More likely yes than no:

More than half of the students have a need to learn new methods

Definitely yes:

Most students have a need to learn new methods

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Not yet:

Most of the students were able to solve the problem or simply could not figure it out

More likely no than yes:

Half of the students could not solve the problem

More likely yes than no:

Most students could not solve the problem

Definitely yes:

No one could solve the problem, including the participants of Olympiads.

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Not yet:

Most did not accepted the challenge

More likely no than yes:

Less than half accepted the challenge

More likely yes than no:

More than half accepted the challenge

Definitely yes:

Most accepted the challenge

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Not yet:

The topic and purpose of the work are reported by the teacher at the beginning of the lesson before the problem appears.

More likely no than yes:

The topic and purpose of the work are reported by the teacher at the beginning of the lesson on the basis of the problem task.

More likely yes than no:

Definitely yes:

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Not yet:

Doesn't create a display style. It will be forgotten that same day.

More likely no than yes:

Creates a display style for individual students.

More likely yes than no:

More than a half of the students will remember for a long time - a good display style

Definitely yes:

Most students will remember it for a long time - a strong display style / image.

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Not yet:

No decision required. You just need to calculate

More likely no than yes:

The purpose of the calculation is specified, but no decision needs to be made.

More likely yes than no:

The problem requires a decision, but not for the student personally.

Definitely yes:

The student must make a decision. The problem is about the student.

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Not yet:

The life context is not given at all.

More likely no than yes:

A life context is given, but it is not meaningful for most students.

More likely yes than no:

Displays the key question of the section for more than half of the students

Definitely yes:

A life context is given that is part of the world of most students

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Not yet:

The students have no questions.  They solved the problem using the selection method.

More likely no than yes:

Students have no questions, or they have questions about calculations.  They solved the problem based on previous knowledge.

More likely yes than no:

Students have questions about the methods and what they are dealing with. The problem is partially solved.

Definitely yes:

Students have questions about the methods and what they are dealing with. The problem remains without a solution; they don’t know where to start.

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Not yet:

Does not show students the key question of the section

More likely no than yes:

Displays the appearance of the key question of the section only for individual students

More likely yes than no:

Displays the key question of the section for more than half of the students

Definitely yes:

Displays the key question of the section for most students

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Not yet:

Sets context for part of the lesson or does not set it at all

More likely no than yes:

Sets the context for 1-2 lessons

More likely yes than no:

Sets the context for 3-6 lessons

Definitely yes:

Sets the context for 7 lessons or more

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Not yet:

Does not set the context for working with any difficult-to-understand concept (notion)

More likely no than yes:

Sets the context for working with one complex concept, but not the most important one for this section.

More likely yes than no:

Sets the context for working with several complex concepts or one central one

Definitely yes:

Sets the context for working with all essential concepts

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Graphical method for solving quadratic inequalities. Grade 10

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When you throw a ball into a basket on a basketball court, you want to make a 3-pointer. When thrown, the ball rises to a maximum height of 3.44 m. The thrown ball hits the hoop, moving along the same trajectory.  You are blocked by a player who is 1.73 m tall. What is the minimum step back you need to take for your 3-point shot to be successful?

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Quadratic equations. Grade 9.

For St. Valentine's Day, the boys of the class decided to make a surprise for the girls and placed a comic measuring 12 cm x 18 cm on a sheet of paper with an area of ​​280 cm². At what equal distance from the edges of the sheet it is necessary to pull the comic back, so that it is in the middle? Does a problem always have a solution?

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Numerical inequalities. Grade 8.

1.     On the first day of September, my brother calculated that he had saved 300 euros during the summer.  “I have twice as much,” his sister boasted. The brother promised himself that he would save 15% of the initial amount of money every month. Without knowing her brother’s promise, the sister continued to save 5% of her initial amount of money every month.

2.     What is the fewest number of months when the brother's savings will be bigger than the sister's?

3.     Can it happen that the brother's savings will be 1.5 times bigger than the sister's? Justify your answer.

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Linear equations. Grade 7.

At the end of the school year, 7th- grade students took part in the competition Adventure Time. In the final, team members had to throw balls into a basket. In total, the team members made 1225 throws. For each hit, the team was awarded 4 points; if the ball did not hit the basket, then 2 points were deducted from the team. How many times did the guys hit the basket if the team scored 2226 points in total during this competition?

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Operations with ordinary fractions. Grade 6.

Alisa Selezneva, fleeing from space pirates, rushes across Planet X on an all-terrain vehicle towards the “time machine” at a speed of 4815 km/min, whereas the pirates are chasing her at a speed of 445 km/min. Will the pirates be able to catch up with Alice?

• If they will, how long will it take the pirates to catch up with her? The current distance between them is 12 km.

• Will Alice have time to escape from the pirates if she needs to cover another 192 km get to the “time machine”, and if it takes her 2 extra minutes to start the car engine?

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Parallelogram and its properties. The area of ​​a parallelogram. Grade 7.

The parking area, excluding entrance, equals 0.15 hectares. How many parking spaces can be placed in a 2-row parking lot using the pattern shown in the picture? Write a plan to solve the problem.

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Direct proportionality. Grade 6.

Jonas family lives in Kaunas and plans to go to Riga, the capital of Latvia, for the weekend. Jonas suggested to his parents that he will calculate the budget for the trip. He found out that the distance from Kaunas to Riga is 256 km, and that the least amount of fuel is consumed if you go all the way at a constant speed of 90 km/h. Besides, Jonas learnt that their car consumes 8 litres of fuel per 100 km.

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Surface area and volume of a prism. Grade 7.

A sheet of origami paper has the shape of a square, the side length of which is 210 mm. From a sheet of origami paper, you need to make a box without a lid. To do this, you need to cut equal squares from the corners of the sheet and then bend the attained involute. At what length of the sides of the cut-out squares will the box have the greatest volume? What is the outer surface area of ​​the box without the lid in this case?

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Pythagorean Theorem. Grade 8.

There were 20 minutes left before sunset. Will Martinas have time to take a selfie at sunset if the height of the mountain is 318 m and the average speed of ascent is 10 km/h?

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Trapezoid. Grade 8.

In the small town of N, there is an old hangar that has not been used for a long time. One day, the children became interested in it. When they tried to climb onto the roof, they found that it was tilted and supported by four pillars. During their little adventure, they also noticed that one of the pillars stood exactly halfway between the large and the small ones, and the other pillar stood halfway between the small and the medium ones. These two pillars suffered the most over time and required a replacement. To make new support poles, the guys needed to find out the height of these destroyed middle pillars, provided that the height of the large pillar was 2.85 m, and the height of the small one was 2.25 m.

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Trapezoid. Grade 8.

A construction company orders 25 windows from a metal structures plant, a sample of which you are given in the photo. You can see the dimensions of the glass (in cm) in the picture. The cost of 1m² of glass is 165 euros. Calculate the cost of the glass required to make these windows.