As I planned how to get kids to master writing multi-digit numbers in expanded form, I really wanted some sort of model that stretched out. I thought of a Slinky! I used it throughout this lesson stretching it out as we "stretched out" multi-digit numbers in expanded form.
I wrote the word "EXPANDED" on the white board and asked my students what it meant to them? I asked them if they had ever heard it as a math term before. They responded that yes, in third grade, they had worked with expanded form.
I asked them to give me a synonym for the word "expanded". One student came up with "stretched". I had been playing with the Slinky in my hands back and forth and everyone was watching me as we talked. I finally dropped the Slinky from about my head height so that it stretched to the floor. I said " I just expanded the Slinky and I can do that to numbers that are really large...numbers up to one million."Expanded form and the slinky. shows how I elaborated using the Slinky. Yes, that is a mustache you see on my face. It was mustache day... :) Fun!
I wrote the goal on the board: I can write numbers as high as one million in expanded form. I told them that by the end of this lesson they would be able to expand numbers like I expanded the Slinky.
I asked my students: Does the slinky model stretch farther out as numbers get larger? Do you think numbers written in expanded form make larger equations? Students shared their thinking and affirmed that they thought as numbers got larger, the slinky would stretch out farther and the equations would be longer.
To help them understand that expanded form doesn't change the value of the number, I asked:
When the Slinky is stretched out or expanded, is it still the same Slinky? They acknowledged that indeed it was. I explained that when we expand numbers, they are still the same number, just written differently and the larger the number, the more values would be represented in the equation.
Whole Class Lesson: I used Learnzillion.com LZ13 written by Amber Smith as a resource to instruct a whole class lesson because my pretest had shown me that expanded form needed to be taught to all of my students. Write Numbers in Expanded Form is a good quick resource because I would have taken time to use the place value blocks in the manner she does to instruct. This video allows me the opportunity to instruct and stop when I need to to bring out certain points, answer questions and then monitor student notes and progress. In order for CCSS Standard 4.NBA.A.2 to be fully mastered, my students needed practice and exposure to different examples of multi-digit numbers.
Students sat on the floor and took notes as the video was shown on the SB. I noticed that she makes errors in reading her numbers by using the word "and". I was sure to point out that it is important to reserve 'and' for numbers with decimal points. We then paused the video and re-read the numbers, using 'and' correctly.
* Connection to Hook: I pointed out that each number when written in expanded form needs to be thought about like the Slinky...it stretches it out.
After the video I wrote on the whiteboard, 63,709 = 63,000 + 700+9. I asked them if this number had been "stretched out" completely. They noticed right away that the thousands place had not been included. I asked a student to correct the mistake. He wrote: 60,000 + 3,000 + 700+ 00 + 9 ( including the zeros in the tens place.) We discussed if the zeros in the tens place were supposed to be there. I asked for a vote for those who thought it was important. Every student raised their hand. I could see from this informal assessment that they were attentive to showing each place value in the equation.
I talked about how the zeros in the tens place were not wrong, but generally, if there is a zero in a place value, we usually omit it. I told them it was a common mistake, however, to leave two numbers together accidentally and that they needed to be extra careful to be sure each place value was separated.
To help boost students' number sense and help them apply their understanding and connection to the real world, I looked for texts that displayed large numbers that would be connected to something interesting. I really like the idea of shifting the responsibility of finding numbers to them and then have them convert to expanded form, rather than just taking numbers out of a text book resource. This develops Math Practice Standard 7 as they strive to look for and make use of structure. They become aware of large digit numbers in the real world.
I modeled the assignment by dropping down my classroom map of the United States. I used the populations of cities, being sure not to go over one million. I chose Madison, Wisconsin at 240,323 people. I read the number aloud and modeled how I wrote it in the chart resource.Place Value Chart for Expanded Form should help them place numbers in the right places. My most advanced students were given this chart too, but I allowed them to write it on notebook paper if they could show me they were mastering the skill and thinking about why they were writing each number in the expanded equation.
200,000 + 40,000 + 300 + 20 +3 = 240,323
I told them that starting from the right would help them not skip a value. I asked them: What value is in the thousands place? One student responded with 40,000. I pointed to the place value and asked him to read the thousands place value to me. He soon knew that the zero in the thousands place meant there was no value in that place. I reminded them that a common mistake was to forget about the place value. On their chart, I explained they should include it using zero for its place. I did this because I wanted them to become more fluent and comfortable recognizing that zero is a number and serves as a placeholder.
Before I assigned them their assignment, we went through writing numbers in expanded form once more. Writing in expanded form- Mastering the Standard shows students working on the board and expanding the number. They used the strategy of starting from the right and working left to the highest value. After we had written the equation, Reading it out loud shows how we went over the number and read it aloud using the equation to check our work. I had the slinky stretched out once more to re-enforce visual understanding. Expanded Form Introductory Movie.
Assign: Number Hunt!: I gave students some time to look at different sources of media to find numbers up to the thousands place to create an expanded form example of that number. (I suggest they find them in 3-5 different resources. Do this so that they understand that numbers are in all sorts of types of reading material.)
I told them that they could use their samples from a number written in word form or standard
( numerical) form as well as standard form. I wanted the chart completely filled out for homework. They could use any resource at home to complete the whole chart. I told them that often even junk mail will contain large numbers. I also told them they could take any classroom resource home that they had started to use in class.
I expected that they write down the source of where the number was found, write the number as they found it on the right of the chart ( there is plenty of space there), and then create an expanded notation of that number. I told them to use any notes from class. Place Value Chart Discussion is a discussion with students about how the chart is working for them.
* For my lowest level students, I reduced the size of the numbers they should look for. I assigned automobile ads from a local newspaper. The ad has the photo and then a clear number written below. They really enjoyed looking at the cars and the ads. I had them read the number aloud into their iPad movie ap and then listen to themselves as another reinforcement.
* For higher students who did well on the quiz, I assigned numbers up to one million or higher. They had the choice to write their numbers onto a loose leaf paper rather than filling in the chart because they are mastering this skill easily as I assessed their classroom work.