StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...
Free

Multiplication and Addition Relationships - Essay Example

Cite this document
Summary
The essay "Multiplication and Addition Relationships" focuses on the critical analysis of the major issues in the relationship between multiplication and addition. There is a clear relationship between the mathematical processes of multiplication and addition…
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER94.3% of users find it useful
Multiplication and Addition Relationships
Read Text Preview

Extract of sample "Multiplication and Addition Relationships"

There is a clear relationship between the mathematical processes of multiplication and addition. Multiplication, in terms of addition, is the repeated addition of the same number to itself a certain number of times. For every multiplication problem, there is a way to write the equation with the sole use of addition. An illustration of this point can be displayed by showing that the mathematical equation, "5 x 3," is the same as "5 + 5 + 5." Five multiplied by three means that three groups of five are being added together. Understanding the relationship between multiplication and addition can have significant benefits on a student's ability to utilize the skill of multiplying numbers. The relationship between multiplication and addition can also be seen in various mathematical properties. The commutative property is one that applies to both multiplication and addition problems. The implications of this property are that in a multiplication equation, one can multiply the numbers in any order to get the same product, and in an addition equation, one can add the numbers in any order to get the same sum. An example of the commutative property being used in addition is the equation, "10 + 2 = 12." If the numbers 10 and 2 were to be switched (2 + 10), the sum would still be 12. The equation, "2 x 5," can be utilized to demonstrate the commutative property in multiplication. Two times 5 equals 10, and when the numbers switch places, 5 times 2 still yields a product of 10. The commutative property is connected to the thinking strategy of thinking about multiplication in terms of adding groups of numbers. When students see 5 x 2 they may first think that means 5 groups of 2, which is 2 + 2 + 2 + 2 + 2. The commutative property lets them know that it can also mean 2 groups of 5, which is a much simpler 5 + 5. The associative property is similar to the commutative property, but applies to equations that have more than two numbers and have at least two of the numbers grouped. Like the principle of the commutative property, the associative property dictates that the numbers can be multiplied or added in any order, regardless of the groupings. An example of the associative property in addition is the equation, "3 + (2 + 8)." The grouping of 2 + 8 implies that these two numbers must be added first, but the associative property allows the numbers to be added in any order without the sum being changed. Whether you add 2 + 8 + 3 or 3 + 8 + 2 or 8 + 3 + 2, the sum is always 13. The equation, "(4 x 2) x 3," can be utilized to exemplify the associative property as it applies to multiplication. The grouping of 4 x 2 implies that these two numbers must be multiplied first, but the associative property allows the numbers to be added in any order without the product being altered. Whether you multiply 4 x 2 x 3 or 2 x 4 x 3 or 3 x 2 x 4, the product is always 24. Similar to the commutative property, the associative property helps students use the thinking strategy of adding together groups of numbers, because it allows them to solve the problem in the order that is easiest. When students multiply (2 x 6) x 5, which is 12 + 12 + 12 + 12 + 12, it may be easier for them to multiply (5 x 2) x 6, which is 10 + 10 + 10 + 10 + 10 + 10. It is easier to count by 10's than 12's. The distributive property involves breaking down multiplication problems, and it uses addition as a crucial tool. While many students are able to memorize the products of multiplying numbers 1 through 10, numbers greater than 10 that aren't multiples of 10 may begin to pose difficulties. The distributive property makes this sort of multiplication easier, and can be exemplified by the equation, "4 x 56." The distributive property holds that (4 x 50) + (4 x 6) = 4 x 56. To make 56 an easier number to multiply by, 56 can be separated into two numbers that add up to 56, and then each can be multiplied by 4 and added together. Four times 50 is an easy product for students to multiply because it is 50 + 50 + 50 + 50, or 200. Four times 6 is also easy for students because they learn and memorize the products of multiplying the numbers 1 through 10; the product is 24. By adding together 200 and 24, the answer 224 is found, which is the same product found by multiplying 4 x 56 on a calculator. While many students would have trouble counting by 56's, fewer students have trouble counting by 6's and 50's. One common conceptual error of multiplication is that students have trouble understanding the rule that any number multiplied by 0 equals 0. An instructional strategy could be used to help students visualize why this rule is the case, rather than telling them merely that the rule exists. Use an overhead projector to display five chips or markers for the class to see. First, explain that multiplying two numbers, like 5 x 1, means one group of five. Ask them to count how many chips there are and tell you what 5 x 1 equals. Add five more chips, but keep them grouped separately from the first five, and show them that this represents 5 x 2, because it is two groups of five. Ask them to count how many chips there are and tell you what 5 x 2 equals. Now ask them what 5 x 0 equals, considering that this means ZERO groups of five. After a couple of guesses, remove all of the chips and tell them that now there are NO groups of five, so it equals 0. Repeat this process with different numbers and at the end, reiterate the rule that they now understand - that any number times 0 equals 0. Another common conceptual error of multiplication involves students memorizing answers to numeric equations like 3 x 4 without knowing what it really means. A useful strategy in fixing this problem is the use of word problems. Instead of always asking simple number problems, the use of word problems lets students see how multiplication is applied and why it works the way it does. An example of a word problem for 3 x 4 could be the following: Johnny just got allowance and wants to buy candy for his four best friends. If Johnny wants to give three pieces of candy to each of his four friends, how many pieces of candy does Johnny need to buy The students could be asked not only for the answer, but also for the numeric multiplication problem that leads to the answer. This will let students see what multiplication is used for. Read More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Math/Education Essay Example | Topics and Well Written Essays - 750 words”, n.d.)
Math/Education Essay Example | Topics and Well Written Essays - 750 words. Retrieved from https://studentshare.org/miscellaneous/1511252-matheducation
(Math/Education Essay Example | Topics and Well Written Essays - 750 Words)
Math/Education Essay Example | Topics and Well Written Essays - 750 Words. https://studentshare.org/miscellaneous/1511252-matheducation.
“Math/Education Essay Example | Topics and Well Written Essays - 750 Words”, n.d. https://studentshare.org/miscellaneous/1511252-matheducation.
  • Cited: 0 times

CHECK THESE SAMPLES OF Multiplication and Addition Relationships

Error Patterns in Computation. Whole Numbers: Addition and Subtraction

One of the error patterns I have encountered is that students forget basic addition, especially for additions involving whole number 1 to 9.... Some even make up a new rule in addition by adding all the numbers in the ones position then placing the sum under the tens.... However, this is not easy to observe since, just like in addition, this is only apparent when renaming is required in the equation.... It is interesting to note that students who demonstrate a certain error pattern in subtraction is more likely to have the same error pattern in addition....
4 Pages (1000 words) Book Report/Review

Mathematical Concepts

It explores algorithms of basic operations, addition, subtraction, multiplication and division, with respect to decimals and fractions.... The basis of ratios, percentages, and proportions as expression of relationship between variables, and understanding of their concepts is important in solving real life problems such as interest and interest rates among other practical relationships (Billstein, Libeskind and Lott, 2010) Relevance of the learnt... The course also covers concepts of operation of whole numbers that includes addition, subtraction, multiplication, and division with stepwise procedures for carrying out the operations....
3 Pages (750 words) Essay

Related Work on XML Labelling Schemes

), multiplication-based schemes (Section 3.... In the introductory chapter, there are specific objectives that defined motivation.... The 1st area of literature relevant to this goal is an overview of labeling schemes.... The 2nd part of the literature review presents others labeling schemes that have commonly been used with XML documents....
42 Pages (10500 words) Literature review

Matlab SimMechanics: Double Mass Spring Damper

The design method assumed second-order relationships between open-loop frequency and closed-loop time response measures.... In addition, it addresses operations and development of monumental products, as well as the development and functionality of evolving programs.... It is thus important to note that since each complex variable consists of two numbers, the multiplication of these variables must involve the combination of the four individual components in order to form a single product that is also made up of two components just like the initial variables....
3 Pages (750 words) Essay

How to Define Place Value, Where Does It Sit within Number Sense and Numeracy

If the mental images and relationships to which the student is trying to connect new knowledge are poorly developed, future constructs are weak and confused, and misconceptions may arise.... Relational understanding is the process of connecting mathematical concepts and relationships (conceptual knowledge) with the symbols, rules, and procedures that are used to represent and work with mathematics (procedural knowledge).... Students require a thorough understanding of place value when learning the formal processes of addition, subtraction, multiplication, and division....
10 Pages (2500 words) Coursework

Philosophy of Mathematics Learning and Teaching

.... ... ... The paper 'Philosophy of Mathematics Learning and Teaching' is an excellent variant of an essay on mathematics.... Over time, I have developed a philosophy on Mathematics learning and teaching, it encompasses my beliefs regarding mathematics and why it is important, as well as my, believes on what the best approach to teaching the subject is....
10 Pages (2500 words) Essay

Mathematical Thinking in Children: Number Sense

The factoring phase is also characterized by the ability of children to connect with groups of numbers as well as the ability to conduct mathematical operations such as multiplication and division.... For instance, a teacher may use a family situation to teach basic numeracy operations such as addition and subtraction.... he quantifying phase allows a child to possess more sense of numbers in such a way that he or she may understand that numbers remain constant unless an addition or subtraction is done....
5 Pages (1250 words) Literature review

Teaching Mathematics

raction relationships: they can be changed back and forth into decimals, for example, 0.... A couple of operations can be done to fractions, like addition, subtraction, multiplication, and division.... (Multiplication) ½ x ½ = ¼ (division) ½ / 1/2 = 2 (addition) ½ + ½ = 1 (subtraction) ½- ½ = 0....
16 Pages (4000 words) Term Paper
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us