Arithmetic expressions are one of the compulsory and most important topics in the course of school mathematics. Insufficient knowledge of this topic will lead to difficulties in studying almost any other material related to algebra, geometry, physics or chemistry.
Features of working with arithmetic expressions in elementary school
In elementary grades, the first arithmetic operations are introduced immediately after learning ordinal counting.
As a rule, the first two operations that are studied almost simultaneously are addition and subtraction. These actions are most needed in the practical life of any person: when going to the store, paying bills, setting deadlines for finishing work, and in many other everyday situations.
The main difficulty that a child may encounter is a sufficiently high level of abstraction of arithmetic. Often, children do noticeably better when it comes to counting specific items, such as apples or candy.
The task of the teacher is to helpmove on to the concept of number, that is, to the addition and subtraction of quantities that are not directly tied to the physical world.
The second goal in the initial study of arithmetic expressions is the assimilation of terminology by students.
Basic arithmetic terms in elementary school
For the addition operation, the basic concepts are the term and the sum.
In the correct equation 10+15=25: 10 and 15 are terms, and 25 is the sum. At the same time, the arithmetic expression itself on the left side of the sign "=" 10+15 is also correctly called the sum.
The numbers 10 and 15 are called by the same word, since their permutation will not affect the sum.
The general rule in the form of a formula is written as follows:
a+c=c+a,
where any numbers can stand in place of a and c. Order independence is preserved not only for two, but also for any number of terms (finite).
The situation is different with subtraction, for which you will have to remember three terms at once: minuend, subtrahend and difference.
In the example 25-10=15:
- decreasing is 25;
- subtractable - 10;
- and the difference is 15 or the expression 25-10.
Addition and subtraction are reverse operations.
The next two inverse steps taught in elementary grades, multiplication and division, have slightly more computational complexity, so they are covered later.
In the multiplication equation 10×15=150: 10 and 15 are the multipliers and 150 or 10×15 is the product.
To rearrange factorsthe same rule applies as for the permutation of terms: the result does not depend on the order in which they appear in the arithmetic expression.
In school, the multiplication sign today is often denoted by a dot, not a cross or an asterisk.
To indicate division, a colon or a fraction sign is used (but this is in higher grades):
15:3=5.
Here 15 is the dividend, 3 is the divisor, 5 is the quotient. The expression 15:3 is also called a ratio or ratio of two numbers.
Procedure of actions
To successfully complete tasks related to arithmetic expressions, you need to remember the order of operations:
- If an operation is enclosed in parentheses, it is executed first.
- Next, multiplication or division is performed.
- Addition and subtraction are the last steps.
- If the expression contains several operations with the same priority, then they are performed in the order in which they are written (from left to right).
Types of tasks
The most common types of arithmetic problems in elementary school are tasks for determining the order of actions, calculating and writing numerical expressions according to a given verbal formulation.
Before calculating expressions of a complex structure, a child should be taught to independently arrange the order of actions, even if the task does not explicitly say so.
Compute means to find the value of an arithmetic expression as a number.
Examples of problems
Task1. Calculate: 3+5×3+(8-1).
Before proceeding to the actual calculation, you need to understand the order of operations.
First action: subtraction is performed because it is in parentheses.
1) 8-1=7.
Second action: the product is found, since this operation has a higher priority than addition.
2) 5×3=15.
It remains to perform the addition twice in the order in which the "+" signs are placed in the example.
3) 3+15=18.
4) 18+7=25.
The result of calculations is written in response: 25.
Many teachers require at the beginning of training to write down each action separately. This allows the child to better navigate the solution, and the teacher to identify the error during the check.
Task 2. Write down an arithmetic expression and find its value: the difference of two and the difference between the quotient of ninety and nine and the product of two triples.
In such tasks, you need to move from expressions consisting only of numbers to more complex ones.
In the above example, the numbers for the quotient and product are explicitly specified in the condition.
The quotient of ninety and nine is written as 90:9, and the product of two triples is 3×3.
It is required to make the difference between the quotient and the product: 90:9-3×3.
Returning to the original difference between the two and the resulting expression: 2-90:9--3×3. As can be seen, the first of the subtractions is performed before the second, which contradicts the condition. The problem is solved by placing parentheses: 2-(90:9--3×3).
The resulting expression is calculated in the same way as in the first example.
- 90:9=10.
- 3×3=9.
- 10-9=1.
- 2-1=1.
Answer: 1.
