Understanding place value is a core concept that should be thouroughly and elaboratively taught to students as they embark onto their life long mathematic journey. Understanding the reasoning behind place value is extrememly important. Place value is a concept that is continuously built upon as students go through their mathematic career, therefore it is extremely important that teachers really make sure that their young students truly do understand the concept of place value and why each number is placed where it is placed/what each number is actually representing. Place value, as the name implies, literally explains the value each digit in a number holds in correlation to where the digit is placed based on the base ten system.
Place value allows students to understand the meaning behind a number. Take for example the number 645. A student should be able to understand that this number symbolizes 6 100's, 4 10's and 5 1's. The understanding of place value allows students not only to understand the reasoning behind a number's value but to also understand the addition and multiplication that represents the number as well as they heighten their mathematic knowledge.
Addition for 645:
The article written by Roger Howe explains that, "Each number is represented as a sum of very special numbers" (Howe).
645 is equal to the sum of 600+40+5.
Hundreds place: 6 represents 6 groups of 100--> 100+100+100+100+100+100=600
Tens place: 4 represents 4 groups of 10--> 10+10+10+10=40
Ones place: 5 represents 5 groups of 1: 1+1+1+1+1=5
Multiplication for 645:
When looking at a number through a mulitiplication aspect, Rowe explains how the digit placed in each place value tells us how many times the digit should be multiplied to its corresponding base 10 value (based on the digits place value).
Hundreds place value: 6 --> 6x100=600
Tens place value: 4--> 4x10=40
Ones place value: 5--> 5x1=5
Rowe explains that the place value system "...provides a unique way to represent each whole number, no matter how large, in compact form" (Rowe). Place value is extremely unique in this way and is a system which allows us to represent extremely large numbers in smaller forms through placing the numerals in their correct "place". We identify which "place" numerals are in so that we can correlate the corresponding base 10 value with where the numeral is placed within the number. Through this, the numerals atual value, and not just digit, is accounted for and understood. This is why when wanting to represent the number 6, we simply put 6. This is showing that we are in the ones place value, therefore there are 6 groups of one and the value of the number 6 is actually 6. We would not want to put a 0 behind the 6 because then there are 0 ones in the ones place value and 6 tens, resulting in the value of 60 and not 6.
Through this unit and intense break down of place value I am actually amazed at how little I understood why I was doing what I was doing for so many years when it came to carrying over in addition, borrowing in subtraction, or simply just what each part of each number truly represented. This unit broke down place value to a whole new level that makes the understanding behind values of numbers and why we borrow when we borrow so much more clear. Before, I simply borrowed from the unit to the left simply because I was trained that that was what to do. I did not even think twice about what place values I was subtracting from when doing subtraction, I would just subtract the digits as they were, not realizing that when in the tens place value you are actually subtracting for example 60-40, not 6-4.
645
-146
Take for example 645-146. I now truly understand that when we cross out the 4 (40) and change it to a 3 (30), this is because the ones place is taking a whole group of 10 from the 4 groups that are present. This 1 group of 10 accounts for the one that is then written in front of the 5, to result in 15-6. Same for the group of 100 that the tens place value will have to borrow from the hundreds place value.
After really grasping an understanding for place value, I realize how important it is for students to truly learn and understand this concept. When students understand the reasoning behind what a number is symbolizing and how each place value directly corresponds to the numbers actual value, it will make the advancement of learning how to carry over and borrow a thousand times more clear. Place value sets the foundation for so many math concepts to come as one continues on their "mathematic journey" so I think that it is incredibly important to make sure students are taught in an extrememly in depth manner about the basics, importance, and longevity of place value.
After reading more on place value in 2.2 of the book, I again just realize that place value is a concept that will follow the children throughout their mathematical career so it is extremely important that they really have a grasp and understanding of the concept. Students who have a better understanding of place value will also see this to benefit them as they answer questions about place value. Questions like "How many tens are in 365" can be answered quickly for children who understand the concept of place value. For those who struggle more however, they will need to solve problems like this through long division or multiplication which is more time consuming. A deep understanding of place value will allow children to thrive and understand other concepts much more quickly as they move on. It will also allow for better time management and quicker answering of questions, instead of having to spend long amounts of time doing multiplication or long division.
Common Core Standards: A.1, A.1.A, A.1.B, A.2, A.3, A.4, B.2, B.2.A, B.2.B, B.2.B.C, B.3, B.5, B.6, B.7, B.8, B.9, C.4, C.5, C.6,
Reflection on Video
*Variation in learning styles is extremely important when working with young children
*When you integrate physical movement, cognitive thinking, change of manipulatives, stations where children work together, and songs where children sing,
-auditory
-kinestheric
-spatial
-collaborative
-visual
-musical
skills are all being established as well.
*It is important to teach children how to get to answers through multiple learning methods
*When teaching young children, you not only are trying to teach them material, but also implement good character skills. By having the students work in groups and collaborate, you are boosting their social skills.