Expressions within 10. Preparing for the game - settings

The very first examples that a child gets acquainted with even before school are addition and subtraction. It is not so difficult to count the animals in the picture and, crossing out the extra ones, count the remaining ones. Or move the counting sticks and then count them. But for a child it is somewhat more difficult to operate with bare numbers. That is why practice and more practice are needed. Don’t stop working with your child in the summer, because over the summer the school curriculum simply disappears from your little head and it takes a long time to catch up with lost knowledge.

If your child is a first-grader or is just entering first grade, start by repeating the composition of the number by house. And now we can take on examples. In fact, addition and subtraction within ten is the child’s first practical use of knowledge of the composition of a number.

Click on the pictures and open the simulator at maximum magnification, then you can download the image to your computer and print it in good quality.

It is possible to cut A4 in half and get 2 sheets of tasks if you want to reduce the load on the child, or let them solve a column a day if you decide to study in the summer.

We solve the column and celebrate our successes: cloud - not solved very well, smiley - good, sunshine - great!

Addition and subtraction within 10

And now randomly!

And with passes (windows):

Examples for addition and subtraction within 20

By the time a child begins to study this topic of mathematics, he should know very well, by heart, the composition of the numbers of the first ten. If a child has not mastered the composition of numbers, he will have difficulty in further calculations. Therefore, constantly return to the topic of composition of numbers within 10 until the first grader masters it to the point of automaticity. Also, a first-grader should know what the decimal (place value) composition of numbers means. In mathematics lessons, the teacher says that 10 is, in other words, 1 ten, so the number 12 consists of 1 ten and 2 ones. In addition, units are added to ones. It is on knowledge of the decimal composition of numbers that the techniques of addition and subtraction within 20 are based. without going through ten.

Examples for printing without going through the tens mixed up:

Addition and subtraction within 20 with a transition through ten are based on techniques for adding to 10 or subtracting to 10, respectively, that is, on the topic “composition of the number 10,” so take a responsible approach to studying this topic with your child.

Examples with passing through tens (half a sheet of addition, half a subtraction, the sheet can also be printed in A4 format and cut in half into 2 tasks):

In this lesson you will remember how numbers behave on the number line. You will look at several examples of addition and subtraction within 10, and also solve a very interesting task on this topic. You will have the opportunity to make and use your own number line.

Subject:Introduction to basic concepts in mathematics

Lesson: Adding and subtracting numbers within 10

To study this topic we use the number beam. (Fig. 1)

Rice. 1

The numbers on the number line are arranged in ascending order. As you move to the right, the numbers increase, and as you move to the left, they decrease. This property will be used when solving examples.

Let's turn to the number line. Place a pencil on the number 5. (Fig. 2)

Rice. 2

The “+” sign indicates that this is an addition; you need to move to the right along the number line.

The number 3 tells you how many steps you need to take. The steps are indicated by arcs. (Fig. 3)

Rice. 3

We stopped at 8.

The first number is 9, find it on the number line, put a pencil on the number 9. (Fig. 4)

Rice. 4

The “-” sign means subtraction; you need to move four steps to the left. (Fig. 5)

Rice. 5

We stopped at 5.

Answer: 9 - 4 = 5

Solve some examples. Each answer is a letter, at the end we will read the encrypted word. (Fig. 6)

Rice. 6

We got the word WELL DONE because we completed this task. (Fig. 7)

Rice. 7

You can make your own number line and use it when counting.

During the lesson, we remembered how numbers behave on a number line, learned to add and subtract numbers within 10 using a number line, and solved interesting examples on this topic to reinforce the material, which will help in further study of mathematics.

Bibliography

Alexandrova L.A., Mordkovich A.G. Mathematics 1st grade. - M: Mnemosyne, 2012.
Bashmakov M.I., Nefedova M.G. Mathematics. 1 class. - M: Astrel, 2012.
Bedenko M.V. Mathematics. 1 class. - M7: Russian Word, 2012.

Preparing for the game - settings

Any parameters and settings can be changed at any time, even during the game.
Initially the game is set up like this:
- Computation type - Addition up to 10
- Prize 1- chocolate, bonus 2- cookie
- In a gaming session 10 calculations (arithmetic examples)
- Percentage of examples that must be solved correctly to receive Prize 1 - 90%
- Percentage of examples that must be solved correctly to receive Prize 2 - 70%
You can choose any other type of calculation - depending on what the child knows and what is being taught at school at the moment. Types of calculations in the game:
- Addition, subtraction, addition and subtraction (mixed):
  - To 10
  - Up to 20 (with transition through ten)
  - Up to 20 (with and without passing through ten)
  - Up to 30
  - Up to 100
- Multiplication, division or any combination - by 1, - by 2, - by 3.......etc. up to 10
- Comparison of numbers
Set how many examples there will be in a game session. It is better to start with a small number of attempts - 5 or 10, so as not to discourage the child from continuing the game. When the child increases milk yield:) improves performance, you can move on to a serious game with 100-200 examples.
Enter the percentage of correctly solved examples for which 1st and 2nd prizes are awarded. To begin with, it is better to lower the percentage. For example, choose 70 and 50 percent for 1 and 2 premiums, respectively. Later, the rates can be increased to 90 - 70. Or even to 98% - 95% for very terribly smart children :). Enter only numbers, without the % sign!
Write down the bonuses your child will receive for 1st and 2nd place.
The settings will be saved using a cookie (a small script) and restored the next time you open the game page in your browser.

Now you can start the game!

To start the game, press the START button
When an example appears on the screen, the child must enter the answer after the "=" sign.
If we play “comparisons”, we need to enter the appropriate sign: . To do this, it is most convenient to use the buttons that appear next to the NEXT button
After entering the result, you need to press the OK button (or ENTER on the keyboard) to check whether the example was solved correctly.
If the example was solved correctly, "Correct" will appear on the screen. If no, "Wrong" is the correct answer. At the same time, the game will calculate the percentage of correctly solved examples
To move on to the next example, you need to click the NEXT button
When the session ends, the prize that the child won (or “didn’t win anything”) and the percentage of correctly solved examples during the session will appear on the screen.
To start a new session, click the START OVER button.

Big hopes:)

What can you expect from this game? Great help in completing the school curriculum! As a rule, in 5-7 days, in which the child plays for 30-40 minutes, he firmly masters the next type of calculation (for example, adding to 20 and passing through ten). And he practically stops making mistakes in class.

When studying this topic, it is necessary to ensure that children master rational computational techniques of addition and subtraction within the first ten; develop strong computing skills; achieve memorization of the results of addition and subtraction, as well as the composition of numbers from terms.

In organic connection with the study of addition and subtraction, elements of algebra and geometry are included: children become familiar with mathematical expressions, equations and inequalities. Geometric figures are examined, exercises are performed on composing figures, measuring and drawing segments, and isolating figures from a given figure.

Objectives of studying the topic:

1. Explain the meaning of addition and subtraction.

2. Develop computational techniques for addition and subtraction.

3. Develop tabular addition and subtraction skills in close connection with mastering the composition of numbers within 10.

4. Familiarize yourself with the names of the components and results of addition and subtraction. Consider the sum, difference as an expression.

6. Explain the relationship between the sum and the terms.

The methodology for introducing computational techniques can be depicted in accordance with the study plan in the form of a diagram:

- 5 - 6 - 7 - 8 - 9

+ 5 + 6 + 7 + 8 + 9

+ 2 - 2 + 3 - 3 + 4 - 4

+ 1 - 1

Study plan :

1. Preparatory stage: revealing the specific meaning of the actions of addition and subtraction, writing and reading examples, cases of adding and subtracting 1, based on the formation of a sequence of natural numbers.

2. Studying the techniques of counting and counting in groups: 2, 3, 4.

3. Study of the technique of rearranging addends for cases of adding 5, 6, 7, 8, 9. Addition tables and the composition of numbers from addends.

4. Studying the technique of subtraction based on knowledge of the relationship between the sum and the terms for subtraction cases 5, 6, 7, 8, 9.

Preparatory work learning addition and subtraction begins from the first lessons. The cases a±1, a±2 are considered. In practice, when solving problems, it is necessary to show that the operation of combining sets corresponds to the action of addition, and the operation of removing part of a set corresponds to the action of subtraction. When they add, it becomes more than it was; when subtracted, it becomes smaller.

By the end of the study of numbering, students should have a firm grasp of how to form any number in the top ten by counting and subtracting one and, using this technique (rather than counting), be able to perform fluent addition and subtraction with one. Gradually, children generalize their observations and formulate conclusions: adding 1 to a number means naming the next number; subtracting 1 from a number means naming the number preceding it. In a specially designated lesson, all the studied cases of a ± 1 are brought into the system; under the guidance of the teacher, children compile tables “add I” and “subtract I” and then memorize them.

At the second stage consider cases of addition and subtraction of the form: a ±2, a±3, a±4, the results of which are found by counting or counting.

To emphasize, on the one hand, the similarity of computational techniques, and on the other hand, the opposite nature of the operations of addition and subtraction, the cases of “add 2” and “subtract 2” are the same as later cases of “add 3” and “subtract 3”, then “add 4” and “subtract 4” are studied simultaneously in comparison with each other.

Work on computing skills is based on the following plan:

1) preparatory exercises;

2) familiarity with calculation techniques;

3) consolidation of knowledge of techniques, development of computing skills;

4) compiling and memorizing tables.

Let's consider a method for introducing the computational technique “add and subtract 2”.

At the preparatory stage (1-2 lessons before studying the topic), it is recommended to teach children to solve examples in two actions of the form: 64-1+1, 9-1-1, so that children consolidate the ability to add and subtract one and accumulate observations: if we add ( subtract) 1 and another 1, then add (subtract) 2 in total. First, the solution to such examples is illustrated by actions with objects, for example: “Put 4 blue squares, move 1 yellow square. How many squares did you get? Move in 1 more yellow square. How many squares did you get? Write down an example: 4+1+1, explain how we solve such an example (add 1 to 4, you get 5; add 1 to 5, you get 6.”

Example 7 - 1 - 1 is also considered.

In a lesson on introducing new computational techniques, first they also perform several preparatory exercises, and then explain the technique itself.

Then they begin to consider the technique of adding and subtracting the number 2.

The teacher sets a goal for the children - to learn to add and subtract the number 2. The first examples are solved based on objective action. Example 4+2 is solved. Let these bouquets on the window represent the number 4, and these 2 bouquets on the table represent the number 2. Show how to attach these 2 bouquets to those 4 bouquets (the student transfers the flowers to the window: first one bouquet, then the second). Let's write down what Vova did. How much was added to 4 first? How much did you get? How can you add 2 to 4? To add 2 to 4, you must first add 1 to 4, you get 5, and then add another 1 to 5, you get 6).

Write on the board:

Next, the students complete the task: draw, for example, 7 apples in their notebooks, then color 2 apples, write down example 7-2 and, based on their practical work (first painted 1 apple, and then 1 more apple), explain how to subtract 2 ( subtract 1 from 7, you get 6; subtract 1 from 6, you get 5).

In the same way, a couple more tasks are considered (for example, based on illustrations in the textbook), and then they move on to solving examples with explanations of calculation techniques. As a result of this work, by the end of the lesson, children will learn how to add 2 to any number and how to subtract 2 from any number.

Using similar exercises, calculation techniques are revealed for the cases a±3 and a±4. In order for children to use their skills of adding and subtracting 2 here, when solving addition and subtraction examples with the numbers 3 and 4, they should represent 3 as 2 and 1 or as 1 and 2, and the number 4 as 2 and 2. Calculation techniques are also illustrated actions with objects and at first several examples are solved with a detailed recording of the technique.

For reception a±4, the entry could be: 5+4=5+2+2, 10-4=10-2-2. Such notes prepare students to study the properties of arithmetic operations.

The exercises are performed until they become solid skills. At first, the examples are solved with detailed explanations of the calculation method out loud, gradually the explanations are shortened, and then they are spoken briefly to oneself. In order to develop skills, oral exercises are included (oral counting, games “silent”, “relay race”, “ladder”, “circular examples”, etc.). Arithmetic dictations are very useful - oral calculations with answers shown in cut-out numbers or writing answers in notebooks. A variety of written exercises are also performed in solving examples and problems. Particularly valuable are exercises with elements of creativity and guesswork: create examples, problems, correct incorrectly solved examples, insert a missing number or action sign in the examples: -3=7. 8- =6, 8+0=10; 6*4=10, 6*4=2.

Exercises with equalities and inequalities are effective for developing computational skills: compare expressions and insert the signs “>”, “<» или «=»: 7+2*7, 10-З* 4; проверить, правильно ли поставлены знаки в заданных равенствах и неравенствах: 6+4<10, 6+3>10, 8+2=10; insert the appropriate number to get the correct entry: 10-4<, 5+2>, 5+3=.

Comparison of expressions is carried out on the basis of comparison of their values (5 + 2> 6, since 7 is greater than 6), so children strengthen their calculation skills with the help of such exercises.

It is important that students understand that by adding two numbers, we get a new number and that, accordingly, this number can be expressed as the sum of two numbers: if 6+2=8, then 8=6+2; if 5+3=8, then 8=5+3, etc. For this purpose, special exercises are offered, for example: “Make up examples of addition with the answer 7 and replace the number 7 with a sum similar to 0+0=7, 7= = + ".

The final point in working on each of the techniques (a±2, a±3, a±4 is the compilation and memorization of tables). Part of each table is compiled collectively under the guidance of the teacher, and part - independently. Along with the addition and subtraction tables, it is useful to create a table of the composition of numbers from terms, for example:

2+2=4 4=2+2 4-2=2

3+2=5 5=3+2 5-2=3

4+2=6 6=4+2 6-2=4

8+2=10 10=8+2 10-2=8

At this stage of learning addition and subtraction, students become familiar with the terms: addition, subtraction, addend, sum, and later with the terms minuend, subtrahend, difference.

At first, these terms are used by the teacher (for example, when dictating examples to children for oral calculation), but children must be encouraged in every possible way to use these new words, asking them to read the examples in different ways (when checking independent work), and fill out tables like:

It is useful to trace along the way how the sum (difference) changes - increases or decreases and under what conditions this happens.

At the next, third stage, they study the addition technique for the cases of “add 5, 6, 7, 8, 9.” When adding within 10 in these examples, the second term is greater than the first (1+9, 2+7, 3+5, 4+6, etc.). If we use a permutation of terms in the calculations, then all these cases will be reduced to the previously studied forms: a+1, a+2, a+3, a+4. In order for children to understand the use of the permutation technique, it is advisable to first reveal to them the essence of the commutative property of addition.

You can introduce children to the commutative property of addition like this. Students are asked, for example, to put 4 blue triangles and move 3 red triangles towards them. How many triangles are there in total? How to find out? (Write down 4+3=7.) Then the task is given to swap the blue and red triangles and move 4 blue triangles to the 3 red triangles. Write down which example has now been solved (3+4=7). Read both examples with the names of numbers when adding. They compare the examples, that is, they find how the examples differ and how they are similar (the terms are rearranged, they are swapped, but the sum is the same).

Similarly, another 2-3 such pairs of examples are considered (from illustrations on the board, from pictures in the textbook, etc.). Then, with the help of the teacher, the children formulate a conclusion: rearranging the terms does not change the sum.

Next, they reveal the method of rearranging terms, i.e., they show exactly when the commutative property is used in calculations. For this purpose, practical problems are solved. For example, you need to put together 2 bags and 7 bags of flour, standing separately. What is more convenient to do this: bring 2 bags to 7 bags or 7 bags to two bags? Children, based on life observations, give an answer to the question of the problem. Then they solve with explanation a pair of examples of the form: 1+3, 34-1, 2+4, 4+2; compare calculation methods and figure out how to add numbers faster. Based on such exercises, children come to the conclusion: it is easier to add a smaller number to a larger number than to add a larger one to a smaller one, and you can always rearrange numbers when adding - the sum does not change.

Then they show how to use the permutation technique to solve examples and problems involving addition within 10 (add 5, 6, 7, 8, 9). During the exercises, children develop the ability to use the technique of rearranging terms. After this, a short table of addition within 10 is compiled, knowing which you can solve all examples of addition within the first ten:

6+2=8 5+3=8 4+4=8

7+2=9 6+3=9 5+4=9

8+2=10 7+3=10 6+4=10 5+5=10

After looking at the table, children themselves can explain why only these cases are included and why the rest are not included.

At this stage, work continues on mastering the composition of numbers from terms. Students are systematically offered tasks to replace each of the numbers of the second heel with the sum of terms, to add these numbers to a specified number (for example, to 10, to 9), to select coins (for example, which two coins can pay 6 kopecks, 7 kopecks, 8 kopecks, 10 kopecks?). This prepares children to learn subtraction in the next stage.

At the fourth stage, the subtraction technique is studied, based on the relationship between the sum and the terms to find the results in the cases of “subtract 5, 6, 7, 8, 9.” To solve, say, example 10 - 8, you need to replace the number 10 with the sum of the numbers 8 and 2 and subtract one term from it - 8, we get another term - 2. To use this technique, you need to know the composition of the numbers from the terms, and also know how the sum and the terms are related.

Preparation for learning connections between components and the result of an action addition is carried out from the very beginning of work on addition and subtraction. For this purpose, special exercises are provided: using a given picture (1 large ball and 2 small balls), make up examples of addition and subtraction, or use the same picture to make up an addition problem and a subtraction problem; solve and compare pairs of examples of the form: 4+3 n 7-3.

A special lesson is given to familiarize yourself with the connection between the components and the result of the addition action. You can work on new material like this.

The teacher invites the children to illustrate with red and blue circles an example of addition (5+4=9). The example is read with the name of the numbers when adding. Then they offer to remove (move aside) the red circles from all the circles, find out which circles remain and how many there are. Write down a new example: 9-5 = 4 and read, calling the numbers as they were called in the first example (subtract the first term from the sum 9, get the second term 4).

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The example is considered similarly: 9-4=5.

A sufficient number of such exercises must be completed so that, based on their observations, children can draw their own conclusion: if you subtract the first term from the sum, you get the second term; If you subtract the second term from the sum, you get the first term.

To consolidate knowledge of the connection between the sum and the terms, students perform the following exercises: for this example, for addition, they make up two examples for subtraction and solve them (2+4=6, 6-4=, 6-2==), with three data Using numbers (4, 3, 7) they make up and solve four examples (4+3,3+4, 7-4, 7-3).

Knowledge of the relationship between the components and the result of the addition action is used to find the results of subtraction (cases “subtract 5, 6, 7, 8, 9”). In a lesson dedicated to introducing children to this method of subtraction, first of all, they repeat the composition of the numbers 6, 7, 8, etc., and also consolidate knowledge of the studied relationship.

Then they begin to reveal a new subtraction technique. The teacher invites the children to explain how example 10 - 8 can be solved (elastic circles are attached to the board, with which it is convenient to carry out the explanation). Students, as a rule, first name the counting technique (subtract 5 and another 3, subtract 4 and 4, etc.). After listening to the children's suggestions, the teacher sets the task of finding a more convenient method of calculation.

“Here we have written down the composition of the number 10 from various terms. 10 is 8 and how many more? (10 is 8 and 2. Indicates the composition of the number 10 on the circles.) This example will be our assistant. If you subtract 8 from the sum of 8 and 2, how much do you get? (It turns out 2, writes down the answer, shows on the circles, repeats the reasoning.) Now we need to solve example 10 - 6. Who guessed what terms should be used to replace the number 10 in order to subtract the number b? Give an example - assistant.

Other examples are considered similarly.

In the following lessons, a variety of exercises are included to develop calculation skills.

In the process of learning addition and subtraction, exercises with zero are performed: 2 – 2, 4 – 4, 6 + 0, 5 – 0.

Work on the “Ten” ends with repetition and consolidation. It is important to achieve computational fluency.

Questions and tasks for independent work

1. What is the meaning of addition and subtraction in a set-theoretic approach to studying mathematics?

2. List the groups of computational techniques and indicate the theoretical basis for their study in the “Ten” concentration.

3. Indicate the types of exercises with the number “zero”.