Place value - another look and Arrays
I wanted to look again at place value. I think this is at the core of a lot of mathematics and want to make sure I fully get what we are talking about.
In some sense I feel I am over complicating things because I am pretty good at math and I am feeling a bit confused, but I have to understand in order to move on.
So, what exactly is place value???
PLACE: The position of a digit in a number
what??
It's simple. I am definitely over thinking this. All this means is is it in the tens, the hundreds, the thousands, then thousands, etc.
What is the place of the underlined number?
90,000 - ten thousands
252,875 - hundreds
VALUE: What is the value of the digit in it's place?
Again, this is so simple.
What is the value of the underlined number?
90,000 - 90,000
252,875 - 8 hundred
This is simple. But, for 3rd graders this is a concept they have to grasp in order to move on. Different ways to go a bout this is to do examples like the above where you underline a number and ask for the place and value, write out the words of the number (ex eight hundred forty two) and have the write the number numerically, ask how many hundreds are in the hundreds place, and finally write out a number using words. All of these will help the student understand that 842 means there are eight 100s in the hundreds place and 4 tens in the tens place. They can also use tools to show this using base ten or base 100 blocks.
Given that this was pretty simple I am going to look at arrays as well.
This is also a 3rd grade Common Core Standard
First of all, what is an array? An array is an arrangement of objects, pictures or numbers in columns and rows.
This is a 5x4 array. There are equal groups in each row (4) or each column (5)
Using arrays is a good way to show students multiplication. It also can show the communicative property by showing an array and then just turning it over onto it's side!
This array can be put into this number sentence:
And then, if you turn it around like this:
Still the same product of 18, but the number sentence changes to:
This shows that as long as the factors are the same, they can be in any order and still come up with the same product. This is the same as they have heard about in addition.
It is also good to remind students that if they know 6x3 they also know 3x6. They know two times as many multiplication problems!
In some sense I feel I am over complicating things because I am pretty good at math and I am feeling a bit confused, but I have to understand in order to move on.
So, what exactly is place value???
PLACE: The position of a digit in a number
what??
It's simple. I am definitely over thinking this. All this means is is it in the tens, the hundreds, the thousands, then thousands, etc.
What is the place of the underlined number?
90,000 - ten thousands
252,875 - hundreds
VALUE: What is the value of the digit in it's place?
Again, this is so simple.
What is the value of the underlined number?
90,000 - 90,000
252,875 - 8 hundred
This is simple. But, for 3rd graders this is a concept they have to grasp in order to move on. Different ways to go a bout this is to do examples like the above where you underline a number and ask for the place and value, write out the words of the number (ex eight hundred forty two) and have the write the number numerically, ask how many hundreds are in the hundreds place, and finally write out a number using words. All of these will help the student understand that 842 means there are eight 100s in the hundreds place and 4 tens in the tens place. They can also use tools to show this using base ten or base 100 blocks.
Given that this was pretty simple I am going to look at arrays as well.
This is also a 3rd grade Common Core Standard
First of all, what is an array? An array is an arrangement of objects, pictures or numbers in columns and rows.
This is a 5x4 array. There are equal groups in each row (4) or each column (5)
Using arrays is a good way to show students multiplication. It also can show the communicative property by showing an array and then just turning it over onto it's side!
This array can be put into this number sentence:
And then, if you turn it around like this:
Still the same product of 18, but the number sentence changes to:
This shows that as long as the factors are the same, they can be in any order and still come up with the same product. This is the same as they have heard about in addition.
It is also good to remind students that if they know 6x3 they also know 3x6. They know two times as many multiplication problems!
Hey Bonnie,
ReplyDeleteI liked the exercise that students could do, in order to better understand place value! I think that it was pretty straight forward, and they would be able to understand it easily. Regarding arrays, I actually love this part of math! I am learning as my daughter was sent home with homework the last two weeks regarding arrays! So I am actually enjoying completing her homework with her, because I actually know what I am doing, lol. I like some of the steps to arrays. In her homework they had the word problem, then had her draw out the array, and then had her write out an equation, and then they had her turn it around! I believe factors of numbers are an important part of the mathematical process too. I love how each step is broke down. At first, it seems like a lot, or like "the long way" but it actually is like Professor Cho used to tell us, task breakdown. I like the step by step! Good job.
Bonnie Jeanne, it's Erin. This is awesome! I love that you talk through the ways to describe place value clearly and succinctly. Your presentation is elegant and simple, too, which makes it easy to follow.
ReplyDeleteThe arrays are cool, right? I really enjoyed that part of class. It almost felt like magic to see that each side of the array is a factor and that the area is the product. In fact, now that I think about it, this concept is going to help in geometry, too--something I really hated in high school (or middle school, or whenever that was!). I continue to find myself wishing they had Common Core when I was in school. . . .
Thanks for the peer feedback everyone.
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