Content explanation Essay
The lesson to be introduced to third graders is simple multiplication and division. This will include the definition, mathematical equation and relationship with one another of the said mathematical processes.
Since multiplication and division have inverse relationships, the method most suitable to introduce these concepts in small and logically organized steps is through comparison relationships. In order to picture the inverse relationship of multiplication and division through comparison, the lesson will formally start by explaining multiplication and division per se.Multiplication, as defined by Kelly and Zeman (1994) in their Everything You Need to Know about Math Homework: a desk reference for students and parents, is a “quick form of addition.
” When numbers are multiplied, the value of one number is added to itself several times.The multiplication sentence is composed of the multiplicand, multiplier and the product. The multiplicand is the first number to appear in the equation while the multiplier is the second number in the equation and multiplies the multiplicand. The product is the answer to the whole equation, the result after the multiplicand and the multiplier have bee multiplied. Both the multiplicand and the multiplier are called factors of the product.For example, in the multiplication sentence 7 x [times] 5 = [is equal to] 35, 7 is the multiplicand, 5 is the multiplier and 35 is the product. This means that the number 7 is multiplied 5 times to itself, arriving at the answer [product] 35.
For a more effective understanding, illustrations are often used. Using the previous equation as reference, the students will draw five (5) sets of seven (7) circles and arrive at thirty-five (35) circles all in all. They will also understand that when they draw seven sets of five circles, they will still be arriving at the same answer and notice that even if they would change the arrangement of the factors in a multiplication sentence, the answer would still be the same.After the lesson proper in multiplication, the teacher will then discuss the whole process of simple division.Reid (n.d.) defines division as the “process of finding out how many times one number, the divisor, will fit into another number, the dividend.” Division is like a quick form subtraction for it is actually a series of subtracting the divisor from the dividend.
The division sentence is composed of the dividend, divisor and quotient. The dividend is the first number to appear and the highest value in the equation. The divisor, on the other hand, is the second number in the equation and is smaller than the dividend. The quotient is the result or answer to the whole division sentence.For example, in the division sentence 35 ÷ [divided by] 7 = [is equal to] 5, 35 is the dividend, 7 is the divisor and 5 is the quotient. This means that the number thirty-five (35) can be divided by seven (7) five (5) times.For further understanding of this division process, illustrations can also be used.
Using the previous equation as reference, the students can draw 35 candies. They will then regroup [divide] these 35 candies into groups of 7, and then identify how many groups of 7 were formed.After thorough explanation of the whole division process, the teacher will now introduce the relationship of multiplication and division with each other. Allowing the students to analyze the multiplication and division processes, the teacher will say that the two has inverse relationship. She will then illustrate this through comparison.The equation previously used in multiplication as an example will be recalled, as well as the previous example for division.
Since both equations used the same numbers, the teacher will ask the students to recite whatever it is they notice in the two equations.To effectively illustrate the comparison, the instructor will then provide the concept that in multiplication the task is to find the product of two factors while in division, the task is to find the missing factor provided that the other factor and the product are known. In numbers, given the equations 7 x 5 = 35 and 35 ÷ 7 = 5, the students will now be able to grasp the idea that multiplication and division work in opposite ways – multiplication provides the product while division uses the product and one factor of that product to find the missing factor.Reference List:Kelly K. & Zeman, A., (1994).
Everything You Need to Know About Math Homework: a desk reference for students and parents. Scholastic Inc., New York.Reid (n.d.
). Multiplication and Division Activities: What is Division? Retrieved April 25, 2009, from http://socrates.acadiau.ca/courses/educ/reid/Elem-math-virtual-Workshops/Multiplication/assortedactivities.htm#multiplication2