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We lay out letters and numbers from counting sticks. Counting sticks for preschoolers are both learning and play
MBOU "Gymnasium"
Suvorov, Tula region.
We construct from sticks
(a collection of problems and games with counting sticks)
Developed by: Primary school teacher
Matyukova Tatyana Borisovna
Guidelines
The widely known counting sticks turn out to be not only a counting material. With their help, it is possible to introduce the child to the principles of geometry and the concept of “symmetry” in a form understandable to the child; develop spatial imagination. Puzzles with counting sticks develop interest in mathematics, the desire to exercise mental stress, and also develop the logic of thoughts, reasoning and actions.
The collection of tasks and games with counting sticks introduces game and logical tasks related to the rearrangement of different numbers of elements. Tasks develop observation and unconventional thinking, increase interest not only in the final result, but also in the process of cognition itself.
Tasks with sticks can be included in mathematics and design lessons, and can also be used in mathematics lessons as a logical warm-up.
Tasks – puzzles with counting sticks are divided into 3 groups:
1. Drawing up a given figure from a certain number of sticks;
2. Changing a given figure by removing a certain number of sticks;
3. Transformation of a given figure by rearranging a certain number of sticks.
The process of solving problems of the second and third groups is much more complex than the first group. It is necessary to remember and comprehend the nature of the transformation and the result, and constantly, during the search for a solution, correlate the result with the proposed or already implemented changes. A visual and mental analysis of the task is required, as well as the ability to imagine possible changes in the figure. Training should be aimed at developing in children the ability to think through moves mentally, fully or partially solve a problem in their minds, and limit practical tests.
Children can work with sticks either under the guidance of a teacher or independently. Puzzles promote the development of creativity and abilities, and allow you to design thematic game pieces based on a model and according to your own design. Working with chopsticks develops fine motor skills of a child's hands.
Tasks with sticks
1. Make 2 identical squares from seven identical sticks.
2. Make 3 equal squares from 10 identical sticks.
3. Make 2 squares from 10 identical sticks: large and small.
4. Make 3 equal triangles from 7 identical sticks.
5. Make 4 equal triangles from 9 identical sticks.
6. Make a square and two equal triangles from 5 identical sticks.
7. Make a square and 4 equal triangles from 9 identical sticks.
8. Make 5 triangles from 9 identical sticks.
9. From 8 sticks, make 1 square and 2 equal triangles
10. Make 5 triangles from 9 sticks.
11. Make 5 squares from 12 sticks.
12. From 6 sticks, make a triangle with equal sides, and then put 3 more sticks so that there are 5 triangles.
13. Using 9 sticks, make a square and a rectangle.
14. Make 2 identical squares and 4 equal triangles from 9 sticks.
15. From 6 sticks, make 2 equal triangles.
16. From 16 sticks, fold 5 equal squares so that you do not get a large square. Remove 4 sticks so that 3 squares remain.
17. Using 7 sticks, make a house with a pipe.
18. Make a Christmas tree from 4 sticks.
19. Make a ladder from 7 sticks.
20. Make a boat out of 7 sticks.
21. How to build a chair from a square by moving 1 stick.
22. Lay out numbers from sticks.
23. Make a house out of 6 sticks. Arrange 2 sticks to form a flag.
24. Remove 2 sticks so that 2 squares remain.
25. Remove 2 sticks so that 3 squares remain.
26. Remove 2 sticks so that not a single square remains.
27. Remove 3 sticks so that 2 squares remain.
28. Remove 2 sticks so that 2 squares remain.
29. Remove 2 sticks so that there are no squares left.
30. How many sticks need to be removed so that there are no squares left. How many sticks must be removed to leave 1 square?
31. How many squares are shown in the picture? How many sticks do you need to take to build such a figure? How many sticks must be removed to leave one square? What is the smallest number of sticks that must be removed so that not a single square remains?
32. Lay out a shape from sticks. Take one stick and break this shape into a triangle and a rectangle.
33. Lay out the sticks into a rectangle. Divide the rectangle so that it contains 4 identical squares and one rectangle.
34. In the figure, arrange 2 sticks so that you get 3 equal triangles.
35. Make a shape out of sticks. Remove 2 sticks to make 1 square.
36. Make a shape out of sticks. Remove 1 stick so that you get 2 squares.
37. Remove one stick from the figure so that 3 identical squares remain.
38. Arrange 5 sticks to make 2 squares.
39. Rearrange 2 sticks so that 4 squares remain.
40. Remove 2 sticks so that 1 square remains
41. Remove 1 stick so that 2 squares remain. Find 3 solutions.
42. Arrange 3 sticks to make 1 square. Find several solutions.
43. Remove 3 sticks so that not a single square remains.
44. Remove 2 sticks so that not a single square remains.
45. Remove 2 sticks so that 3 squares remain.
46. Remove 1 stick so that 3 squares remain.
47. Rearrange 3 sticks so that 4 identical squares become 3 identical squares.
48. In a figure consisting of four identical squares, remove 2 sticks so that 2 different squares remain.
49. In a figure consisting of 4 identical squares and a segment connecting them, rearrange 2 sticks so that you get 5 identical squares.
50. Make a figure like this. Arrange 4 sticks to form 4 equal triangles.
51. From 12 sticks, lay out 6 equal triangles.
52. Remove 2 sticks so that 4 squares remain.
53. Arrange 3 sticks to make a house.
54. Rearrange the 2 sticks so that the coin located at the handle of the scoop is inside it.
55. Arrange 4 sticks so that you get 3 identical squares.
56. Arrange 4 sticks so that you get 4 identical triangles.
57. Move 2 sticks so that the cow is facing the other direction.
58. Make an arrow like this. Arrange 4 sticks to form 4 equal triangles.
59. Make a figure like this. Arrange 4 sticks to form 4 equal triangles.
60. Lay out the house. Move 1 stick so that the house faces the other way.
61. How many squares are there in the picture? How many sticks did it take to make the figure? Remove 1 stick like this. To make 4 equal squares.
62. How many squares are shown in the picture? How many sticks did it take to make the figure? Arrange 3 sticks to make 4 equal squares.
63. How many squares are shown in the picture? How many sticks did it take to make the figure? Arrange 4 sticks so that there are 4 identical squares.
64. In a figure of 5 identical squares, remove 3 sticks so that 3 identical squares remain.
65. Arrange 2 sticks to make 6 squares.
66. In a figure consisting of 6 identical squares, remove 2 sticks so that 4 squares remain.
67. How many squares are there in total? How many identical squares?? Remove 3 sticks so that 7 identical squares remain.
68. Remove 6 sticks so that 3 squares remain.
69. How many squares does the figure consist of? How many identical squares are included in the figure? Remove 4 sticks to form 1 large and 1 small square.
70. Remove 4 sticks to make 5 equal squares.
71. Remove 5 sticks to make 6 equal squares.
72. Remove 2 sticks so that you get 7 equal squares.
73. Remove 6 sticks to make 3 squares.
74. How many squares are there in total? How many sticks did you need? Remove 1 stick so that 6 squares remain.
75. How many squares are there in total? How many sticks did you need? Remove 1 stick so that 5 squares remain. Find several solutions.
76. Remove 2 sticks so that 4 squares remain. Find several solutions.
77. Remove 2 sticks so that 6 squares remain. Find several solutions.
78. Remove 1 stick so that 7 squares remain. Find 2 solutions.
79. Remove 1 stick so that 9 squares remain. Find several solutions.
80. Remove 2 sticks so that 7 squares remain.
81. Remove 2 sticks so that 6 squares remain.
82. Remove 2 sticks so that 5 squares remain.
83. Remove 3 sticks so that 6 squares remain.
84. Remove 3 sticks so that 4 squares remain. Find multiple solutions.
85. Remove 4 sticks so that 5 squares remain.
86. Using 16 sticks, build 3 squares in different ways.
87. Using 19 sticks, build 3 squares.
88. Make 3 squares from 20 sticks.
89. In these scales, made of 9 sticks, you need to rearrange 5 sticks so that the scales come into balance.
90. Make 4 out of three sticks without breaking them.
91. Arrange 3 matches to form three equal quadrangles.
92. There are 4 sticks in front of you. Add 5 more sticks, but in such a way that you get a hundred.
93. There are 5 sticks in front of you. Add 5 more sticks to 5 so that you get three.
94. Here is a fraction (one-seventh). You need to make one third of it, without reducing the sticks, but only by rearranging several or one of them.
95. Place 11 sticks inside this square (made up of 16 sticks) so that it is divided into 4 equal parts around the perimeter, each of these parts is in contact with the other three.
96. Whatever the example, it’s a mistake! Bring order and restore equality everywhere by moving only one stick in each example.
97. Correct this example for subtraction in three ways. Find them.
98. How many sticks can be used to make such a figure? How many squares does it consist of? Remove 4 sticks so that 7 squares remain. Find 4 solutions.
99. Fold this figure. How many sticks did you need? How many squares does the figure consist of? Remove 3 sticks so that 7 squares remain. Find 4 solutions.
100. Fold this figure. How many sticks did you need? How many squares does the figure consist of? Remove 2 sticks so that 9 squares remain. Find all the solutions.
101. Fold this figure. How many sticks did you need? How many squares does the figure consist of? Remove 1 stick so that 8 squares remain. Find 4 solutions.
102. Fold this figure. How many sticks did you need? How many squares does the figure consist of? Remove 2 sticks so that 3 squares remain. Find several solutions.
103. Fold this figure. How many squares does it consist of? How many rectangles? How many sticks did it take to make the figure? Remove 1 stick so that 5 identical squares remain. Find 2 solutions.
104. Rebuild the ship into a tank by moving 6 sticks.
105. Arrange 5 sticks and make a TV.
It is believed that children do not like mathematics. At the same time, play remains the main activity of preschoolers. That is why their learning during this period is based on games. In their work, preschool teachers need teaching aids that allow them, in a fun and playful way, to convey to children a deep understanding of basic mathematical concepts, teach them to compare quantities, give children an idea of proportionality and even some arithmetic operations. One such aid is Cuisenaire sticks.
Cuisenaire sticks: learning by playing
In our time, no one argues with the famous statement of Vasily Sukhomlinsky that a child’s mind is at his fingertips. The ability of children to include all senses in exploring the world around them was actively used in the development of innovative methods by Nikitin, Zaitsev, and Voskobovich. In this series, a worthy place is occupied by the development of George Cuisenaire, who came up with the idea of teaching children to count and establish quantitative relationships through touch and color perception.
History of invention
Since the middle of the 19th century, pedagogy began to abandon traditional methods of teaching based on drill and coercion, and began to focus on activating the child’s interest in learning. One of the means of influencing children's interest has become a variety of original ways of teaching innovative teachers, including those based on the use of original didactic materials.
In the 20th century, the number of innovative methods and accompanying items used during training grew very quickly. In mathematics, many teachers have strived to introduce children to mathematical concepts as early as possible. One of the significant directions has become the delivery of information to the child by tactile and visual means and the activation of perception, especially at an early age.
Names such as Dienesh, Cuisenaire or Voskobovich are familiar to specialists who work using visual methods. In principle, all three worked in the same direction. However, it appears that the Belgian primary school teacher George Cuisenaire (1891–1976) was the first. Back in 1952, he wrote his book “Numbers and Colors” about the essence of the methodology he developed.
Dynes's works were published somewhat later, although for sure, the doctor of mathematics and psychology Zoltan Dyenes began them much earlier and independently of Cuisenaire. As for the recipients of this technique, Cuisenaire sticks are mainly intended for classes with children aged 1 to 7 years.
The purpose of the Cuisenaire technique is to use the principle of clarity. With its help, complex abstract concepts from the field of elementary mathematics - numbers, quantitative quantities, relationships between them - are presented in a form that is as accessible as possible to children. This helps teach your child the steps necessary to reinforce simple but important math concepts.
These actions are important because they allow one to accumulate direct experience of perception, gradually carrying out a conditional transformation of personal understanding, moving in awareness of the essence of phenomena from the concrete to the abstract.
Children have a desire to master the skills of working with counting, with the number system, measurements, and learn to do what teachers call solving educational, educational, and developmental problems.
Zoltan Dienes developed a similar system with a different form of key didactic tools, although the idea is still the same - the tactile sensation of the difference in geometric bodies gives a figurative and sensory idea of the essence of the ratios of numbers. Dynesh blocks are much more diverse. Such counting elements provide the teacher with the opportunity to use different teaching methods. But still, during the initial study of mathematics by young children, Cuisenaire rods are both more visual and simpler.
Purpose of using the manual
These sticks can be mathematically taken as a conditional set, where there are images of numbers and groups. Hidden in this set are enormous opportunities for modeling various logical and mathematical layouts. The size and color of the counting object determine the parameters of the number. Using these parameters, the understanding of conventional figurative concepts is specified. Using such “colorful and voluminous” symbolic objects for counting, preschoolers can develop a clear understanding of the essence of number.
Children approach the traditional conclusion, which states that the concept of number appeared in people as a result of household calculations and household measurements, without prompting, while performing game tasks.
From the point of view of pedagogy, independently acquired knowledge, in our case about numbers and quantities, due to its clarity, will become especially significant.
- By using sticks of predetermined colors and sizes, children more easily understand the relationships “how big or small objects are,” see the similarities and differences of objects, and learn to compare and contrast. In addition, they learn:
- The existence of a set of elementary arithmetic operations, paired and inverse to each other: addition - subtraction, perhaps even multiplication - division.
- The meaning of complex comparative concepts such as “to the left or to the right”, “longer or shorter”, “between”, “each”, “any”, “objects of the same color”, “objects not blue”, “objects of equal length " and etc.
Varieties of industrial sets of Cuisenaire wands
Now different versions of Cuisenaire counting sticks are produced. These sets may differ in the number of counting elements, color, materials from which they were made (wood or plastic).
The classic set consists of 241 elements. All items in this set are made of wood. In shape, each such stick is a rectangular parallelepiped. In cross section it is a square, the cross-sectional area of which is 1 square. cm. The original set contains sticks of ten colors. The shortest stick is a cube with a side of 1 cm. The longest is 10 cm. That is, any stick, in fact, is an analogue of a number, the specifics of which are indicated by its length in centimeters and a certain color. Counting elements painted in similar colors are visually separated by children, and these objects are combined into one “family” according to the principle of multiplicity.
Cuisenaire rods are arranged in the order of the designated numbers, from 1 to 10
This classification is important. The fact is that the ratios taken into account here are size and color. A white cube from the “white family” can be placed in the length of any of the other sticks several times. The “red family” are elements whose size can accommodate the smallest stick, a multiple of two. The “green family” consists of rods whose length is a multiple of three; rods that are multiples of five are expressed by variations of yellow, and the number 7 is usually highlighted in black, as a special “family”.
There are modified versions of similar sets of sticks. They differ in the colors used. However, the manufacturer always applies some rules.
- Identical sticks are colored the same and express the same number;
- The longer the stick, the greater the value of the number it expresses.
- The colors of the sticks represent numbers from one to ten.
With kids it is better to use another, simplified version of Cuisinaire sticks. It is made of plastic and contains 119 sticks in 12 colors. All sticks also have the same base - a square measuring 1 square. cm.
There is also a flat version of the sticks; it consists of strips 2 cm wide. The shortest strip is a square 2x2 cm. The length of all other strips increases by 2 in each group of colors. These strips are made of plastic or thick colored cardboard. Their color scheme is the same as that of the sticks.
This version of counting elements is very convenient to use. Unlike traditional three-dimensional objects, they are larger and at the same time more compact, their production does not require significant costs at all, and their efficiency, in terms of learning opportunities, is quite high. They are easy to make even at home.
What can you do with chopsticks:
- First of all, they are suitable for ordinary gaming manipulations. Children sort them out, arrange them in different ways and simply play with them like ordinary cubes.
- Further, they can be used to compare them as analogues of numbers, indicating the difference between them. The child clearly senses the difference between the concepts of more and less.
- Then it is possible to operate with sticks, indicating the operations of addition and subtraction. Here, sticks are used as a visual aid to teach concepts from an elementary math course.
- Preschoolers who play with sticks and arrange them into jigsaw puzzles learn their numerical values and how they can be compared as analogues of numbers.
- As a result, children are brought to the idea of arithmetic operations, which, with the visual help of tactile and visually familiar objects, become much more accessible to their understanding.
When acquaintance with Cuisenaire sticks is just beginning, children play with them as if with simple cubes, sticks, construction sets, learning, during games and activities, color, size and shape.
During this period, the initial stage of memorizing tactile and visual sensations takes place. While playing, children evaluate three-dimensional images that are substitutes for numbers by touch, in combination with colors. Getting used to them as game objects will definitely play a role when the time comes for much more serious work.
in the first stages of acquaintance, children play with sticks as building material
With further work, the sticks become a tool for teaching growing mathematicians. With their help, kids learn the elementary laws and rules of the world of numbers and some significant mathematical concepts.
As for the use of this didactic material for classes, a great variety of specific applications have been developed during the implementation of the Cuisenaire technique. Practitioners and specialists in the propaedeutics of mathematical knowledge, working with preschool children, offer, for example, the following options for activities that can be carried out with children aged two to four years:
- Let's get acquainted with chopsticks. Together with your child, look at, sort through, touch all the sticks, tell them what color and length they are.
- Take as many sticks as possible in your right hand, and now in your left.
- You can lay out paths, fences, trains, squares, rectangles, pieces of furniture, various houses, garages from sticks on a plane.
- We lay out a ladder of 10 Cuisenaire sticks from the smallest (white) to the largest (orange) and vice versa. Walk your fingers along the steps of the ladder, you can count out loud from 1 to 10 and back.
- We lay out the ladder, passing 1 stick at a time. The child needs to find a place for the missing sticks.
- You can build three-dimensional buildings from sticks, like from a construction set: wells, turrets, huts, etc.
- We arrange the sticks by color and length.
- “Find a stick the same color as mine. What color are they?"
- “Put down the same number of sticks as I have.” “Lay out the sticks, alternating them by color: red, yellow, red, yellow” (later the algorithm becomes more complicated).
- Lay out several Cuisenaire counting sticks, invite the child to memorize them, and then, while the baby is not looking, hide one of the sticks. The child needs to guess which stick has disappeared.
- Lay out several sticks, invite the child to remember their relative positions and swap them. The baby needs to return everything to its place.
- Place two sticks in front of the child: “Which stick is longer? Which one is shorter? Place these sticks on top of each other, aligning the ends, and check.
- Place several Cuisenaire sticks in front of the child and ask: “Which is the longest? Which is the shortest?
- The task is to find any stick that is shorter than the blue one and longer than the red one.
- Place the sticks into 2 piles: one has 10 pieces, and the other has 2. Ask where there are more sticks.
- Ask to show you a red stick, a blue one, a yellow one.
- Show me the stick so it's not yellow.
- Ask to find 2 absolutely identical Cuisenaire rods. Ask: “How long are they? What color are they?"
- Build a train from cars of different lengths, from the shortest to the longest. Ask what color the carriage is fifth or eighth. Which carriage is to the right of the blue one, to the left of the yellow one. Which carriage is the shortest, the longest? Which carriages are longer than the yellow one, shorter than the blue one.
- Lay out several pairs of identical sticks and ask the child to “put the sticks in pairs.”
- Name the number, and the child will need to find the corresponding Cuisenaire stick (1 - white, 2 - pink, etc.). And vice versa, you show the stick, and the child names the required number. Here you can lay out cards with dots or numbers depicted on them.
- From several sticks you need to make one the same length as burgundy and orange.
- From several identical sticks you need to make one the same length as the orange one.
- How many white sticks can fit in a blue stick?
- Using an orange stick, you need to measure the length of a book, pencil, etc.
- “List all the colors of the sticks lying on the table.”
- “Find the longest and shortest stick in the set. Place them on top of each other; and now next to each other.”
- “Choose 2 sticks of the same color. What length are they? Now find 2 sticks of the same length. What color are they?"
- “Take any 2 sticks and place them so that the long one is at the bottom.”
- Place three burgundy Cuisenaire counting sticks parallel to each other, and four of the same color on the right. Ask which figure is wider than the others and which is the narrowest.
- “Place the sticks from the lowest to the largest (parallel to each other). Attach the same row to these sticks on top, only in reverse order.” (You will get a square).
- “Place the blue stick between the red and yellow, the orange to the left of the red, the pink to the left of the red.”
- “With your eyes closed, take any stick from the box, look at it and name what color it is” (later you can determine the color of the sticks even with your eyes closed).
- With your eyes closed, find 2 sticks of the same length in the set. One of the sticks in your hands is blue, and what color is the other?”
- “With your eyes closed, find 2 sticks of different lengths. If one of the sticks is yellow, can you determine the color of the other stick?”
- “I have a stick in my hands that’s a little longer than blue, guess its color.”
- “Name all the sticks that are longer than the red one, shorter than the blue one,” etc.
- “Find any two sticks that are not equal to this stick.”
- We build a pyramid from Cuisenaire sticks and determine which stick is at the very bottom, which is at the very top, which is between blue and yellow, under blue, above pink, which stick is lower: burgundy or blue.
- “Put out one of two white sticks, and next to it put a stick (pink) corresponding to their length. Now we put three white sticks - the blue one corresponds to them,” etc.
- “Take the chopsticks in your hand. Count how many sticks you have in your hand.”
- Which two sticks can be used to make a red one? (number composition)
- We have Cuisenaire's white counting stick. What stick should be added to make it the same length as red.
- What sticks can you use to make the number 5? (different ways)
- How much longer is the blue stick than the pink one?
- “Make two trains. The first is pink and purple, and the second is blue and red.”
- “One train consists of a blue and a red stick. Using white sticks, make a train that is 1 carriage longer than the existing one.”
- “Make a train from two yellow sticks. Build a train of the same length using white sticks.”
- How many pink sticks can fit in an orange one?
More complex games are aimed at developing mathematical concepts, instilling counting skills and reinforcing ideas about logic. This work is carried out with children aged four years and older. However, sometimes in such work it makes sense to return to purely playful practices, reminding children that this is a conditionally playful, and not purely educational space. Experts, in this regard, recommend the following exercises:
- Lay out four white Cuisenaire counting sticks to form a square. Based on this square, you can introduce your child to fractions and fractions. Show one part out of four, two parts out of four. What is greater - 1/4 or 2/4?
- Image “Make each of the numbers from 11 to 20 using sticks.”
- Lay out a figure from Cuisenaire sticks, and ask the child to make the same one (in the future, you can cover your figure from the child with a sheet of paper).
- The child lays out the sticks, following your instructions: “Put the red stick on the table, put the blue one on the right, yellow on the bottom,” etc.
- Draw different geometric shapes or letters on a piece of paper and ask your child to place a red stick next to the letter “a” or in a square.
- You can use sticks to build labyrinths, some intricate patterns, rugs, and figures.
Belgian primary school teacher George Cuisenaire (1891-1976) developed universal didactic material for developing children's mathematical abilities. In 1952, he published the book "Numbers and Colors", dedicated to his teaching aid.
Cuisenaire sticks are a set of counting sticks, which are also called “numbers in color”, “colored sticks”, “colored numbers”, “colored rulers”. The set contains tetrahedral sticks of 10 different colors and lengths from 1 to 10 cm. Cuisenaire developed the sticks so that sticks of the same length are made in the same color and indicate a certain number. The longer the stick, the greater the numerical value it expresses.
Cuisenaire counting sticks produced by manufacturers differ in quantity, color and material (wood or plastic). To start, you can use a simplified set of 116 sticks. It contains 25 white sticks, 20 pink, 16 blue, 12 red, 10 yellow, 9 purple, 8 black, 7 burgundy, 5 blue and 4 orange. Cuisenaire sticks are mainly intended for activities with children from 1 to 7 years old.
Game tasks of colored sticks
Cuisenaire's counting sticks are a multifunctional mathematical tool that allows “through the hands” of a child to form the concept of a numerical sequence, the composition of a number, the relationships “more - less”, “right - left”, “between”, “longer”, “higher” and much more. . The set promotes the development of children's creativity, the development of fantasy and imagination, cognitive activity, fine motor skills, visual and effective thinking, attention, spatial orientation, perception, combinatorial and design abilities.
At the initial stage of classes, Cuisenaire sticks are used as playing material. Children play with them as with ordinary cubes, sticks, construction sets, as they play and practice, becoming familiar with colors, sizes and shapes.
At the second stage, the sticks already act as a tool for little mathematicians. And here children learn to comprehend the laws of the mysterious world of numbers and other mathematical concepts.
Games and activities with Cuisenaire sticks
1. Let's get acquainted with chopsticks. Together with your child, look at, sort through, touch all the sticks, tell them what color and length they are.
2. Take as many sticks as possible in your right hand, and now in your left.
3. You can lay out paths, fences, trains, squares, rectangles, pieces of furniture, various houses, garages from sticks on a plane.
4. Lay out a ladder of 10 Cuisenaire sticks from the smallest (white) to the largest (orange) and vice versa. Walk your fingers along the steps of the ladder, you can count out loud from 1 to 10 and back.
5. Lay out the ladder, passing 1 stick at a time. The child needs to find a place for the missing sticks.
6. You can build three-dimensional buildings from sticks, like from a construction set: wells, turrets, huts, etc.
7. Arrange the sticks by color and length.
8. "Find a stick that is the same color as mine. What color are they?"
9. “Put down the same number of sticks as I have.”
10. “Lay out the sticks, alternating them by color: red, yellow, red, yellow” (later the algorithm becomes more complicated).
11. Lay out several Cuisenaire counting sticks, invite the child to remember them, and then, while the child is not looking, hide one of the sticks. The child needs to guess which stick has disappeared.
12. Lay out several sticks, ask the child to remember their relative positions
and swap them. The baby needs to return everything to its place.
13. Place two sticks in front of the child: “Which stick is longer? Which is shorter?” Place these sticks on top of each other, aligning the ends, and check.
14. Place several Cuisenaire sticks in front of the child and ask: “Which is the longest? Which is the shortest?
15. 
“Find any stick that is shorter than the blue one and longer than the red one.”
16. Place the sticks into 2 piles: one has 10 pieces, and the other has 2. Ask where there are more sticks.
17. Ask to show you a red stick, blue, yellow.
18. “Show me the stick so it’s not yellow.”
19. Ask to find 2 absolutely identical Cuisenaire rods. Ask: "How long are they? What color are they?"
20. Build a train using cars of different lengths, starting from the shortest to the longest. Ask what color the carriage is fifth or eighth. Which carriage is to the right of the blue one, to the left of the yellow one. Which carriage is the shortest, the longest? Which carriages are longer than the yellow one, shorter than the blue one.
21. Lay out several pairs of identical sticks and ask the child to “put the sticks in pairs.”
22. Name the number, and the child will need to find the corresponding Cuisenaire stick (1 - white, 2 - pink, etc.). And vice versa, you show the stick, and the child calls the desired number. Here you can lay out cards with dots or numbers depicted on them.
23. From several sticks you need to make one the same length as burgundy and orange.
24. From several identical sticks you need to make one the same length as the orange one.
25. How many white sticks can fit in a blue stick?
26. Using an orange stick, you need to measure the length of a book, pencil, etc.
27. “List all the colors of the sticks lying on the table.”
28. “Find the longest and shortest stick in the set. Place them on top of each other; and now next to each other.”
29. “Choose 2 sticks of the same color. What length are they? Now find 2 sticks of the same length. What color are they?”
30. “Take any 2 sticks and place them so that the long one is at the bottom.”
31. Place three burgundy Cuisenaire counting sticks parallel to each other, and four of the same color on the right. Ask which figure is wider and which is narrower.
32. “Place the sticks from the lowest to the largest (parallel to each other). Attach the same row to these sticks on top, only in reverse order.” (You will get a square).
33. “Put the blue stick between the red and yellow, and the orange one to the left of the red one, and the pink one to the left of the red one.”
34. “With your eyes closed, take any stick from the box, look at it and name its color” (later you can determine the color of the sticks even with your eyes closed).
35. "With your eyes closed, find 2 sticks of the same length in the set. One of the sticks in your hands is blue, and then what color is the other?"
36. “With your eyes closed, find 2 sticks of different lengths. If one of the sticks is yellow, can you determine the color of the other stick?”
37. “I have a stick in my hands that’s a little longer than blue, guess its color.”
38. “Name all the sticks that are longer than the red one, shorter than the blue one,” etc.
39. “Find any two sticks that are not equal to this stick.”
40. We build a pyramid from Cuisenaire sticks and determine which stick is at the very bottom, which is at the top, which is between blue and yellow, under blue, above pink, which stick is lower: burgundy or blue.
41. “Lay out one of two white sticks, and next to it put a stick corresponding to their length (pink). Now we put three white sticks - the blue one corresponds to them,” etc.
42. “Take the chopsticks in your hand. Count how many sticks you have in your hand.”
43. Which two sticks can be used to make a red one? (number composition)
44. We have a white Cuisenaire counting stick. What stick should be added to make it the same length as red.
45. What sticks can be used to make the number 5? (different ways)
46. How much longer is the blue stick longer than the pink one?
47. "Make two trains. The first one is pink and purple, and the second one is blue and red."
48. “One train consists of blue and red sticks. Using white sticks, make a train longer than the existing one by 1 carriage.”
49. “Make a train from two yellow sticks. Build a train of the same length from white sticks.”
50. How many pink sticks can fit in an orange one?
51. Lay out four white Cuisenaire counting sticks to form a square. Based on this square, you can introduce your child to fractions and fractions. Show one part out of four, two parts out of four. What is greater - ¼ or 2/4?
52. 
“Make each of the numbers from 11 to 20 using sticks.”
53. Lay out a figure from Cuisenaire sticks, and ask the child to make the same one (in the future, you can cover your figure from the child with a sheet of paper).
54. The child lays out the sticks, following your instructions: “Put the red stick on the table, put the blue one on the right, yellow on the bottom,” etc.
55. Draw different geometric shapes or letters on a piece of paper and ask your child to place a red stick next to the letter “a” or in a square.
56. You can use sticks to build labyrinths, some intricate patterns, rugs, and figurines.
If the proposed games-tasks are few, you can lay out different figures according to the pictures-schemes. Ready-made diagrams can be found in the book by V. Novikova and L. Tikhonova “Educational games and activities with Cuisenaire sticks. Handout." Using this manual, you can make a flat version of cardboard sticks (cut them out of a colored insert). If such cardboard strips are glued onto strips of a magnet, then you can play with them by attaching them to a refrigerator or magnetic board.
Subject: Problem solving. Working with counting sticks.
Target: Introduce simple arithmetic problems using counting sticks.
Tasks:
- Continue to learn how to compose and solve simple arithmetic problems involving addition and subtraction of numbers within 10.
- Introduce children to the structure of the task.
- Learn to carefully write down the solution to a problem in a notebook.
- Continue teaching children to answer questions.
- Develop attention, memory and thinking.
- Foster independence, perseverance and accuracy in work.
Material: counting sticks (for each child 20 counting sticks of different colors - 10 green, 5 pink and 5 orange); a simple pencil, a notebook with a large square - for children; for the teacher: a set of numbers from 1 to 10 and a ball for the game.
Methods and techniques: explanation, clarification, demonstration, questions for children, help, evaluation, praise.
Progress of the lesson.
Organizing time
Educator:
Good morning!
Sit down correctly, guys.
Listen carefully!
Are you all ready for class?
Children: Yes!
Educator: Hello, mathematics!
Progress of the lesson:
Educator:
“Guys, today our guests are primary school teachers...”
Today in our lesson they will see that you are cheerful, smart and brave guys, you know how to count, compare and solve problems well. If you are not afraid of difficulties, then let's begin! .
Children line up in a column and take turns answering the teacher’s questions:
1. What day of the week is it today? Yesterday? Tomorrow? 2. How many days are there in a week? (7) Name them 3. How many days off are there in a week? (2)
4. How many fingers are there on one hand? (5)
5. How many suns are there in the sky? (1)
6. How many paws do two dogs have? (8)
7. How many fingers are there on two hands? (10)
8. How many suns are there in the sky at night? (0)
9. How many ears do two cats have? (4)
10. How many eyes does a traffic light have? (3)
Guys, today we will learn how to compose and solve problems. Take green counting sticks and place 6 counting sticks in front of you. Count how many sticks you got?
- That's right, 6 green counting sticks.
- Now take one orange or pink stick and place it next to the green ones.
- How many counting sticks are there in front of you?
- Correctly 7 counting sticks.
- Let’s come up with a problem about what we just did.
- There were 6 sticks in front of you. You put down 1 more stick. How many counting sticks are there now? This is the task you and I have.
- Guys, a task always has a condition and a question.
- The condition of our task is this: we had 6 counting sticks. We added 1 more stick.
- Which of you can repeat the conditions of the problem?
- Well done, guys did it.
- The condition is a short story. The condition always contains numbers. What are the numbers in this problem?
- The correct numbers are 6 and 1.
- There is also a question in the problem. What is the question in this problem?
- How many counting sticks are there?
- Guys, does everyone understand what the condition and question in the problem are?
- Let's repeat the condition and question of our task once again.
- Problem condition: there were 6 sticks, 1 more stick was added.
- Problem question: How many sticks are there?
- Let's write down our task in a notebook.
(the teacher lays out or writes numbers on the board).
6 + 1 =
- There is also an answer in the problem.
- What is the answer to this problem?
- Correct, 7. Write down the solution to the problem. 6 + 1 = 7
- Place 9 counting sticks in front of you.
- Now remove the 4 sticks.
- How many counting sticks do you have left?
- Let us repeat the conditions of the problem.
- Problem condition: We laid out 9 counting sticks. Then we removed 4 sticks.
- What is the question of the problem?
- Question: How many counting sticks are left?
- Guys, let’s write down the problem in your notebook.
9 – 4 =
- What is the answer to this problem?- Correct, 5. Write down the solution to the problem.
9 – 4 = 5
- We will solve one more problem with you.
- Place 7 green counting sticks in front of you.
- Add 3 more sticks of a different color.
- Guys, this is the condition of the task.
- Which of you can tell the question of this task?
- Question: How many counting sticks did you get?
- Write down the task in your notebook.
7 + 3 =
- What is the answer to the problem?
- That's right, 10. Write it down.
7 + 3 = 10
- Let's solve the last problem for today.
- Place 8 counting sticks in front of you.
- Now remove 5 sticks.
- This is the condition of our task.
- What is the question of this task?
- Question: How many counting sticks are left?
- Write down the task in your notebook.
8 – 5 =
- What is the answer to this problem?
- Correct, 3. Write down the solution to the problem.
8 – 5 = 3
- How did you solve this problem?
- That's right, you took away 5 sticks from 8.
- What answer did you receive?
- 3 sticks left.
- Now let's play with you a little.
The game “Which number is missing” is played.
The teacher lays out a number line from 1 to 10 on the board. Children close their eyes. The teacher removes some number. Children raise their hands and name which number is missing. You can complicate the game and remove 2 numbers.
Physical exercise. "Who is the most attentive"
Target: strengthen children’s ability to perceive a task by ear (number of claps), compare actions with words; develop attention and reaction speed.
Progress: The teacher explains to the children the rules of the game, with one clap the children walk around the room, with two claps they get into the stork pose, with three claps they get into the frog pose. The winner is the one who has never made a mistake, i.e. the most attentive.
Educator : Guys, we solved problems with the help of counting sticks, and now let’s play a game“Lay out a geometric figure.”
These can be geometric shapes, houses, or just snowflakes.
At the end of the game, I praise all the children and note the most beautiful, neatly laid out figures.
Then a didactic game is held
“Name the geometric shapes and put them together into shapes.
Game "Butterfly on a Flower"
Game "What, where?"
Target: strengthen children’s ability to navigate in space, distinguish between right and left sides, use words and prepositions (right, left, in front, behind; above, below, between); develop dexterity and speed of reaction.
Material: ball.
Progress: The game takes place in a circle with a ball. The teacher takes the ball, throws it to one of the children and asks: “What’s to your right?” The child catches the ball, answers the question and becomes the leader.
Questions for children: “What is over your head? Who's ahead of you? What's behind you? Who's on your left? Who's on your right?" Etc. The game is played at a fast pace.
(on the board there is a large illustration for the fairy tale "Turnip")
The turnip sat firmly in the ground,
One can't do it alone.
And after the old grandfather
The tail is long and stretches.
Everyone came to one.
How many were there in total? (6)
Educator: What fairy tale are these characters from?
Children: From the Russian folk tale "Turnip"
How much is grandma worth? (second)
What about grandfather? (first)
Who is third? (granddaughter)
Who stands between the granddaughter and the cat? (Bug)
Who's standing last? (mouse)
Educator: Guys, what does this fairy tale teach?
Children: Friendship, the need to help each other, etc. ( children's answers)
Educator: “Well done guys, you are all very attentive! You did an excellent job with all the tasks.
Guys, what did we do in class today?
- That's right, they solved problems, laid out counting sticks, played games, found the missing number and named the neighbors of the number.
- Did you enjoy solving problems?
- Every task necessarily has a condition and a question.
- I liked how you worked today.
Games - puzzles with counting sticks.
Children of senior preschool age enjoy solving riddles, solving various puzzles, and love games of ingenuity. One of the most accessible types of ingenuity tasks are games with counting sticks. They are also called problems of ingenuity of a geometric nature, because the solution involves the creation of various shapes and the transformation of some figures into others. During such games, preschoolers willingly overcome significant difficulties and can give up momentary desires that arise in the course of performing a particular game task. In addition to the pride of knowing one’s intelligence and confidence in one’s abilities, games - puzzles with counting sticks develop such qualities as perseverance, perseverance in achieving a goal, resourcefulness, develop constructive skills, mental and creative activity.
To play, you will need a set of student counting sticks or any sticks of the same length and thickness, strips of cardboard, even matches from which the sulfur has previously been removed. If you play with children, you can give oral tasks. If a child plays alone, it is good to prepare cards on which the conditions of the game task are written (if he can read), or it is schematically indicated how many sticks should be taken, what transformation should be made and what figure should be the result.
For example: from 7 sticks you need to make 3 triangles.
It is good if children come up with problems themselves and write (model) them for solution by other people (children or adults).
Tasks - puzzles with counting sticks can vary in difficulty level:
To compose given figures from a certain number of sticks. For example, to make a rhombus from 5 sticks:
Rectangle of 8:
To transform shapes by removing a given number of sticks.
For example, remove 4 sticks to make 3 squares:
Remove 8 sticks to make a cross:
To transform figures by rearranging sticks.
For example, move 1 stick so that the house faces the other way:
Arrange 3 sticks so that the cow waves her tail and looks back:
When children have mastered all 3 difficulty levels of puzzle games, encourage their creativity in creating their own versions of logic problems. Create longer and more complex tasks. Using sequential transformations, compose stories and fairy tales.
In the meantime, you are just learning, we invite you to guess the author’s problem - a puzzle:
We'll take 6 sticks
And let's build a new house!
If 2 is rearranged,
They won’t be able to live in that house,
It is no longer a house, but a flag.
Who can do this?
I wanted to dig-
I need to put the stick away
And shift the other one.
So I'll get the spatula!
Is it ready for you?
Let's move the stick again
And let's take one below
And we'll put it in a box.
The chair is out!
Relax!
How many sticks? Count.
Did you count?
There are four of them!
Spread your legs wider
The back must be put down -
The chair will serve as a table!
If you're not tired of it,
We continue our work:
Let's make a road sign
Or a triangular flag.
2 shifted again
And we got the arrow!
Only the arrow broke -
There is only one stick left.
We'll put it on the table -
We can make a triangle!
