RTI Expanded Form: All Hands on Deck!

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SWBAT create numbers in expanded form and then write the standard form of the number.

Big Idea

Students manipulate this great card game to strengthen their skills in creating and understanding expanded form better. They use a slinky to help them check and understand if their whole number is stretched out!

Create the Game from Note Cards and a little auditory warm up.

10 minutes

Finding the Place Value to match the Value

Another Way of Going About It

Rationale: In order for all of my students to master the standard of reading expanded form as expected in standard 4.NBT.A.2, I needed to find a new way of going about it! I know these children to be very hands-on. So, it was fitting that I find something tactile and simple to get expanded form mastered. I came up with just the thing!

 I found that some of my students keep writing expanded form like this: 325, 789 = 300+25,000 + 700+ 80+9. It is a common problem. They just don't think that ten thousands place should come apart! Or, they write like this: 300 + 25 + 700+ 80+9. Sometimes they just aren't grasping the idea about the value of each digit in the number. I am hoping this card game will help them reason quantitatively (MP2), strengthen their place value knowledge, talk about and read large numbers.This little game helps students make use of structure MP7, model with mathematics, MP4 and MP5 as they manipulate the cards (tools) correctly to show their understanding as we master that standard and have fun doing it!


Preparation of materials: About 15 minutes ahead of time:

I grabbed a pile of note cards and wrote values for each place value. (I love using note cards!)

Ones: 0-9

Tens: 10-90

Hundreds: 100-900

Thousands: 1000-9000

Ten thousands: 10,000- 90,000

Hundred thousands: 100,000 - 900,000

And one card reading 1,000,000 since the standard expects them to read only to 1,000,000 and not beyond.

I also drew two commas on cards to help them separate the periods. 

I wrote place value names to one million on cards and laid them down on the floor as a heading to guide  them where to place their cards. 

Warm up: 10 minutes

I gathered the small group of students together that I needed to work with and asked them to explain the number, 2,345 by telling me each place value word from left to right. I had written it on a small white board and had sat them in a circle around me.

We said the place values out loud together to just practice the place value words of each number and to hear it. I erased the board and did this about 4 times, increasing the place value. They seem to get stuck on the ten thousands place and it is very apparent that if there is a zero in the tens place, this really hangs them up.

This little auditory warm up got them ready to pull apart numbers as they strengthened their skills in learning to write expanded form.



Let's Play!

30 minutes


I told my students we were going to play a game that would help them master the expanded form expectations of their learning goals ( Standard 4.NBT.) I have been using a slinky for a mental model ( I keep one on hand).  The slinky is an excellent model to stretch out to show that the equations have to be stretched and some are longer than others.They were excited to hear the word "game."! I love teaching with games. 

All Hands on Deck!

Players: 2-3

To play: Shuffle the deck making sure the cards are mixed up well.

I chose to start with lower number place values and increase the place values as I saw mastery. So, I suggest that you start where you think your students will be at a level of mastery so they play the game confidently. The Equation Derived from the Cards

 Each child draws a card from the pile and places it in its proper place value. If they can't place it because  there is a card there, then they must keep it. After all place values are filled with a card, they write their expanded form expression in their notebook. I noticed that this transference can be difficult.

After that, I stopped and worked with them to see if they could see how the equation was like a slinky and had them stretch the slinky out above the cards. It is a good time to address a common mistake . I got lots of smiles and "ohs!" as they realized what was going on.

After they have their expression written down correctly, I asked them to write it in standard form by underlining the first digit of each value in the expression. They wrote each digit down in order and then went back, said their place values and put in the commas.


As the students played the game, I thought about how I could differentiate it and suggested some do the following as I saw need.

* Have them trade out larger or smaller values to make goals of largest or smallest number created: i.e. If a card is drawn for the 10's place as 30 and the next draw is 60, trade it out for the larger value.Deciding on the larger value and trading it out...

* Have them write the new number in standard form to drill this more thoroughly.

* Have them reverse the process by rewriting the expanded form again from the standard or word form. This solved some worries I have about them being able to do both processes.

It is my hope that this differentiation fits the needs of all of my RTI learners. It's really fun and they caught on really fast with this very tactile way of creating expanded form.