In this portion of the lesson I call students to the carpet. I want them to understand that numbers can be written in many different formats, including standard notation and expanded notation. I will introduce written form, but it will be used along with place value so that students can fully understand the method of expanded form. To begin, I need to see where my students are in their learning so far. I think working with base-ten materials (MP2- Reason abstractly and quantitatively) will help me determine just how much they can do on their own.
I write three examples of standard notation on the board. I begin explaining what standard notation is and demonstrating what it looks like.
Standard notation is the most common format for writing numbers. The following numbers are all in standard notation.
I ask students if they can think of another way to write these numbers, and whether or not they have ever heard of expanded notation. (I expect that many have not.)
I draw a large place value chart on the board in order to make the connection between expanded notation and the value of each digit.
A number written in expanded notation is broken down into parts, just like it is in a place-value table.
The number 234 written in expanded notation is shown below.
200 + 30 + 4
What place is the 2 in? (hundreds place). And what is its value? (200). What place is the 3 in? (tens place) And what is its value? (30) What place is the 4 in? (ones place) And what is its value? (4)
In this part of the lesson, I want my students to experience writing numbers interactively. This video will help students gain a deeper understanding of how to read and write number in expanded form using place-value charts and base-ten materials.
I give my students place-value charts and base-ten materials. (MP5- Use appropriate tools.)
I want them to work along with the video. As students are working, I will ask guiding questions to focus their attention on the purpose of this lesson. I hope that the work material will allow my students to stay actively engaged by following along and completing the problem solving steps!
Before the video:
To assist students who may be struggling, I briefly go over standard and expanded form. Expanded form is a way of writing numbers so that all that is hidden about them comes out into the open. The simplest way to write expanded form is to first write the number words. I write 456 on the board. Can someone tell me how to write this number using number words? (four hundred fifty-six) This is a good time to remind my students not to use "and" when writing or saying a three-digit number. For example, instead of "four hundred and fifty-six", say "four hundred fifty-six." Where should I insert the four on the place-value chart? (in the hundreds place) What is the value of the "4" in 456? (400) I continue on in this pattern until my students are able to show and tell on their own. After that, I start the video and engage in a facilitator role.
As students are working, I chime in a time or two to check for understanding, and to assist when needed. For instance, I might say: Is their another way to write that number? Can you demonstrate for me? How can place value and base-tens help you understand different ways of writing numbers? I see you have written this number in standard form and expanded form. Are these two numbers the same? Explain. Students start raising their hands high trying to explain why both numbers are the same. One student explains,"The numbers are the same. The only difference is expanded form allows you to see the value of each digit." I decide to probe a bit more. I write 568 on the board. I draw a circle around each digit. I ask students which digit is the largest. Most of my students yell 8 is the largest. So I ask: what place is the 8 in? (The eight is in the ones place) What place is the 5 in? (The five is in the hundreds place.) Which digit has the greatest value? Students seem a bit excited when they discover 5 is the larger digit.
Material: Expanded Notation written
In this activity, I want to see if my students can identify how many hundreds, tens, and ones the number has. I write 768 on the board and ask volunteers to come up to the board and record the answers. Then I ask the value of each digit. Most of my students can determine and identify the value and appropriate place of each digit. Now that you guys fully understand the meaning of expanded form you are more than ready to represent two- and three-digit numbers in expanded form using what you know about place value. As students are working, I continue to support them by asking probing questions. I want them to be able to use base-ten blocks to help them gain a deeper understanding of the value of digits and how to align them for the standard algorithm. (MP5-Use appropriate tools.)
For struggling students:
I allow them to continue to use the base-ten materials to represent their numbers first before writing it in expanded form. I continue to monitor students as they are working to see if we should spend more time exploring expanded form.
Example of expected response:
Question: How is 925 written in expanded notation?
Student reasoning: A number written in expanded notation is broken down by place value.
9 is in the hundreds place: 900
2 is in the tens place: 20
5 is in the ones place: 5
So, 925 = 900 + 20 + 5.
Students continue to work with MP2 and MP5 in the closing part of this lesson.