Logic game “Find a pattern. Logic game "Find a pattern Continue the series by drawing the following figures
Tasks aimed at finding mathematical patterns improve the ability to reason and think logically, help to learn how to compare, generalize and draw conclusions. This game activates the mental activity of the child and will have a significant impact on the formation of figurative thinking, the development of intelligence and ingenuity.
Print the cards offered on the site and give them to the child to work with.
A mathematical pattern is a rule according to which a chain (row) repeats, replaces or changes the properties of certain elements in accordance with the established rule.
Before the kid proceeds to the task, explain to him with a few examples what a pattern is, how it can be established between the various links of the series (numbers, letters, geometric shapes). When solving the first tasks, help him with hints and additional questions that will help in reasoning about which number or figure should continue the chain. Let him carefully examine the drawing and try to independently determine what the basis of its regularity is and what the next element of the series should be. At the end, let him draw his correct answer - a figure or object that continues the row.
Find a pattern and continue the series
This is an educational article in mathematics, before starting classes, we recommend that you read the introductory part
In this lesson, we will talk about tasks in which you need to find some kind of pattern, continue the sequence, or, using the found pattern, answer the question of the problem. Such tasks develop logic, attention and imagination.
The first task is to find patterns in the picture. When solving problems with pictures, it is worth looking at how the neighboring ones differ, what pictures are in each row, column, what order of the pictures.
Task 1.
Find a pattern and color the last square.
Solution.
You can see that there are only three colored squares different kind: 1) the left half is black, the right half is white; 2) the left half is white, the right half is a cross; 3) the left half is a cross, the right half is black. Moreover, in the first and second rows, all the squares are different. Therefore, in the third row, the squares should also be all different. The second and third types are there, which means that the first is missing.
In the following tasks, you need to continue the sequence. Usually, if you want to continue a numerical sequence, then you should look at the difference between neighboring numbers, at their sum, or notice some other property.
Task 2.
Continue the number line: 1, 2, 4, 7, 11, …
Solution.
Let's look at the difference between neighboring numbers. The difference between the first and second is 1. The difference between the second and third is 2. The difference between the third and fourth is 3. The fourth and fifth - 4. Probably the difference between the fifth and sixth is 5.
So the sixth number is 11 + 5 = 16.
Answer:
Task 3.
Continue the number series: 1, 2, 4, 8, ...
Solution.
You can see that 1 + 1 = 2, 2+ 2 = 4, 4 + 4 = 8. This means that each number is twice the previous one - the sum of the previous one with itself. And then next number equals 8 + 8 = 16.
Answer:
More difficult is the search for patterns in non-numeric sequences. For example, in the lesson "Through the Looking Glass" there was the following task:
Task 4.
Set a pattern and draw another figure in place of the ellipsis.
Solution.
Since this task was in the “Through the Looking Glass” topic, it is logical to assume that its solution, one way or another, is connected with the mirror. Indeed, these drawings were obtained by reflection in a mirror. The thin black lines show where the mirror was placed. It is at this point that the main figure ends and its mirror reflection begins.
So, if we erase all the mirror reflections of the shapes, we get this picture:
In it, we recognize the numbers in their record, which is used on postal envelopes. If you look at the envelope, you can see how the number 7 is written on it. And now let's draw its mirror image. We get the next figure we need. You can continue this exercise with the remaining numbers.
Answer:
The sequence is numbers written as it is customary on postal envelopes, but together with their reflections. Another figure:
So far, we've talked about finding patterns if we have one sequence. There are cases when, instead of one sequence, 2-3 examples are offered, showing how to determine the third by the first two elements. In particular, such tasks are popular when performing tests that determine the level of IQ.
Find a pattern and draw the third figure in the bottom row.
Solution.
You can see that the third figure in each line is obtained by "merging" the first two. Therefore, to obtain the desired picture, you need to combine the first two pictures of the third line.
Answer:
Another type of task for finding patterns is most often numerical examples enclosed in any geometric shapes. Let's look at an example task.
Task 6.
What number should be in the third circle instead of the question mark?
Solution.
Consider carefully how the numbers are arranged in circles. The largest numbers are at the bottom. Worth checking, maybe it's the sum of two other numbers? We check: 5 + 1 = 6 is correct, 3 + 4 = 7 is correct. Our hypothesis was confirmed. Therefore, since 2 + 2 = 4, the number 4 should be used instead of the question mark.
Answer: The number should be 4.
We wish you success!
Test your knowledge!
For the smartest and most talented students, we hold a remote Internet Olympiad on the site. Immediately after passing the Olympiad, the results and a complete analysis of tasks for working on bugs are shown. Depending on the success of the Olympiad, electronic diplomas and commendations.
Each participant receives an email certificate participant.
1. Attention game "Count - don't make a mistake" (3 min)
Rules of the game: students take turns calling numbers in a chain in order: 1, 2, 3, 4, etc. If a number is divisible by 3 or contains the number 3, it is not pronounced, and the student says "Bom".
The game is played for elimination: the student who made a mistake sits down, and the next student starts counting from the very beginning.
2. Checking homework (5 min)
The teacher reads out the variants of the algorithms, and the children try to fulfill them as a whole class (inaccuracies in the compilation of the algorithm are noted along the way).
3. Exercise to search for patterns in the number series (6–7 min)
Number series with regularities are series in which numbers are related to each other according to a certain rule.
4-5 number rows are pre-written on the board. The teacher invites the children to find the pattern of their construction and continue the number series: name the next two numbers.
In the course of completing the task, the teacher writes down the correct answers on the blackboard and indicates in brackets what actions the series was formed by (several explanations are possible).
Examples of number series:
After the end of the work - a discussion: into which groups according to the method of solution can these numerical series be divided?
For example:
- each subsequent number is obtained by performing one constant arithmetic operation. For example: +8.2, etc.;
- each subsequent number is obtained by performing several constant arithmetic operations. For example: +4–3;:52 etc.;
- each subsequent number is obtained by performing operations with numbers that are in a certain sequence. For example: +1,+2,+3; - 7, - 5, - 3, etc.
Then it is proposed to draw up an algorithm on how to solve numerical series. For example (if the action is permanent):
Step 1: fix the difference between two adjacent numbers.
Step 2: define the series construction rule.
Step 3: Test this rule on another pair of numbers.
Step 4: Using this rule, determine the next number in the series.
4. Exercise "Test yourself" (5 min)
There are drawings with numbers on the board, you need to put the right number instead of a question. Drawing examples:
1. "Locomotive":
2. "House":
3. "Steps":
After finishing work - analysis of the correctness of the task (in the "house" the sum of the numbers in the windows is equal to the sum of the numbers in the roof and in the door; in the "steam locomotive" the product of the numbers in the wheels is equal to the number in the pipe; in the "steps" the upper cube is three times the sum of the lower ones) and drawing up a short algorithm for solving such tasks.
5. Work in groups "Continue the row" (6–7 min)
Each group receives 3-4 drawings to find patterns in rows with figures. It is necessary to continue the pattern. It is possible that all groups can have the same drawings. Drawing examples:
To check, the teacher opens the answers to all tasks on the board.
6. Exercise to find patterns in a series of shapes (10 min)
A series of drawings on the board. It is necessary to choose the missing figure from the four numbered ones and explain your choice.
At the end of the work - analysis: how it was necessary to complete the task.
For example:
Step 1. Determine what parts the drawing consists of: head, ears, mustache, torso, tail.
Step 2 Determine for each line which parts change and which do not: the ears of all cats are the same, all other parts change.
Step 3. Set for each line, what options each of the changing parts is expressed in: torso: circle, square, triangle; head: circle, square, triangle; tail: right, left, straight; mustaches: one pair, two pairs, three pairs.
Step 4. Determine what options are missing in the 3rd line: a round head, a pair of mustaches, a square body, a tail to the right side.
Step 5. Choose a picture that matches this description: number 3.
7. Homework (3–4 min)
Draw similar drawings in which you need to insert the missing figure.
It is advisable to discuss the topics of the drawings: little men, geometric figures, animals, houses, cars, etc. - that is, any objects that are a collection of separate parts; what options each part can be represented: the size, shape, color, number of parts, direction of lines, etc. can change.
Checking the completion of this homework is carried out in a mathematics lesson.
8. Task for ingenuity (3-4 minutes)
One egg is boiled for 5 minutes. How long do 3 eggs boil? (5 minutes)
A rooster weighs 4 kg on one leg. How much does a rooster weigh on two legs? (4 kg)
A carriage drawn by six horses traveled 3 km. How many miles did each horse run? (3 km)
The boy walks to school 10 minutes. How much time will he spend if he goes along with his sister? (Unknown: the time may remain the same, may decrease (if the sister hurries the boy) or increase (if they talk enthusiastically along the way).)
