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Algebraic expressions are the language used in mathematics to relate one or more variables. They are represented with letters, numbers and with the symbols that indicate the mathematical operations. The construction of algebraic expressions means translating the words and phrases that express the combination of these elements into mathematical language. Translate, for example, an idea that involves the sum of different elements into a mathematical expression that represents it. For example, when going shopping at a supermarket, after paying, the cashier will give a receipt with the sum of the amounts of the things purchased, which can be represented by an algebraic expression.
Generating algebraic expressions with sums
Let’s see what series of questions and answers can be posed to a student to generate a reasoning that leads to the construction of an algebraic expression that implies a sum.
- The student could be asked to write seven plus n as an algebraic expression and the answer should be 7 + n . At the same time one could ask: What algebraic expression is used to mathematically express the sum of seven and n? , and the answer should be the same, 7 + n . Then the student could be asked, what algebraic expression is used to express mathematically that any number increases by 8 units? , and the answer should be, 8 + n, or n + 8 . Finally you may be asked, Write an expression for the sum of any number and 22 , and the answer should be 22 + n, or n + 22 .
In this way, the mechanism for generating an idea that contains the addition in an expression that represents an abstract number, a variable that can take any value, and the algebraic symbol for addition or addition: + is induced in the student.
Generating algebraic expressions with subtraction
In a similar way to what was seen before for the generation of an algebraic expression that involves additions, a methodology can be proposed that is the same as another that involves subtraction. Unlike expressions with additions, when registering the concept of subtraction or subtraction, it must be taken into account that the order of the operation is not indifferent, but determining. For example, 4 + 7 and 7 + 4 will result in the same value, but 4 – 7 and 7 – 4 will not.
In the same way, a student can be asked a series of questions and answers to generate a reasoning that leads to the construction of an algebraic expression that involves subtractions. First you would be asked: Write seven minus n as an algebraic expression , and the answer should be 7 – n . Then one could ask, what algebraic expression is used to mathematically express the subtraction of eight minus n? , and the answer should be, 8 – n . The student could also be asked: What algebraic expression is used to express mathematically that 11 units are subtracted from any number?, and the answer should be, n – 11 , in this order. And the mechanics of generating algebraic expressions could be deepened by asking the student: How can you translate into an algebraic expression the idea of twice the subtraction of any number minus five units? , and the answer should be, 2 × (n – 5) .
In the words involved in this dialogue we find the terms minus , subtraction or subtraction , double , any number . And, through dialogue, the student will transform these words into algebraic expressions. Care must be taken to formulate questions or ideas appropriately, as students often have difficulty interpreting subtraction because it must be stated in the correct order.
Generation of other algebraic expressions
Algebraic expressions can include other operations, such as multiplication, division, power, root, and operators such as parentheses at various levels and formats. In their combination there is a pre-established order, fundamental in the translation of a concept that involves these operations and operators in an algebraic expression. Therefore, if you want to induce reasoning in a student so that you can represent an idea that involves these operations and operators in an algebraic expression, you must be very careful in formulating the sequence of questions and answers. As in the case of addition and subtraction, there are several terms that involve the same algebraic operation. Divide , divide , how many times does it fit in, are terms and expressions that are associated with the division operation. In a similar way, multiplication can be considered as an algebraic operation, but the concept of power and root can be more difficult to express in a simple and adequate way so that the student can translate it correctly into the algebraic operation.
Fountain
Samuel Selzer, Algebra and analytical geometry. Second edition. Buenos Aires, 1970.
