The Purpose of Zero

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SWBAT use zero to hold a place when adding and subtracting money amounts

Big Idea

Zero makes a difference, depending on where it is. It may be worth nothing, but it has a special place in numbers.

Warm Up

10 minutes

I begin today by reviewing smiley face numbers with students. I say a number and ask them to write the smiley face number (round to the nearest 10) on their dry erase mini-boards and hold it up. I do this with 2- and 3-digit numbers. 

Now I ask students if they could make a smiley face number to the nearest hundred? I say 239 and ask them whether it is closer to 200 or 300? I put up a blank number line and mark 200 and 300. I ask for a volunteer to come and show me about where 239 might be. (I am looking for them to put it a little left of the middle.) Now can we see which 239 is closest to?  I do this with 4 or 5 numbers until students begin to understand that we can round numbers to the nearest 10 or nearest hundred.  I tell them that the nearest hundred is like the nearest dollar - because rounding to the nearest dollar is the same as rounding to the nearest 100 cents

I say, if I see the price tag is $4.65, is that closer to $4.00 or to $5.00? We do a few money examples to the nearest dollar.

I ask students what might happen if I had $2.25 and $3.30 and I rounded both to the smiley face numbers 2.00 and 3.00. Would I have enough money if I just asked my mother for $5.00? Why or why not? We can go down to the lower smiley face, but if we go down with both numbers we need to remember that we might come up a few cents short. I tell students to just remember that smiley face numbers get us close to the right number, but they are not exact. 

Now I give them 2 money amounts, $3.57 and $4.91 and ask them if I can buy both items if I have a $10.00 bill. Can they quickly round both numbers to the nearest dollar and answer the question? 

I do another example with $1.38 and $ 6.82 to make sure students are understanding what we are doing.

Purpose of Zero

20 minutes

I hand each child a large paper zero. I ask them what is the value of zero. (0, nothing). So why do we use zero of it's not worth anything? I take responses from the students. I ask them to read the poem with me. I tell them that zero is very important even though it has a value of nothing. I say, here I will show you why it is so important.  I ask them what would happen if I wrote the number 200 with no zeros. Would it be the same number? Why or why not? (I will give another example if needed).

I remind students that the 2 in 200 represents 2 hundreds and the zeros tell us that there are no tens and no ones. I ask them to hold up the zero every time I say a number where there are no tens. I say the following numbers and students hold up the zero if the number has no tens: 307, 468, 610, 704. I write each number on the board after students hold up the zero so they can check if they were correct or not. Great. Now hold up the zero when there are no ones in the numbers I say. I say the following numbers: 459, 380, 102 and 900. We check the same as we did for the tens above. This exercise helps to solidify their grasp of the Common Core Standard 2NBT A.1 that suggests that students should be able to understand that a 3 digit number is made up of so many hundreds, so many tens and so many ones. 

Okay, let's look at money. What would it look like if I had 3 dollars and 9 cents? Can someone come up and write it on the board? If they write it correctly, we will talk about the importance of the 0 in the tens place, if not we will talk about why what they wrote is not exactly how it would look on a price tag.

I make a dollar sign and write $3.09. I ask students if I need to write $3.00 and .09? We agree that we can put them together. Now I ask How I would write three dollars and 90 cents? Again I ask for a volunteer to come up and write the number next to the $3.09. How are they the same (same digits) How are they different? (the placement of the zero). Can I just leave the zero out of either one? (No) Why not? (It represents either the tens or the ones in the amount. Without it I don't know if it is three dollars and nine cents or three dollars and ninety cents. 

What if I had $30 dollars and nine cents. How would I write that? Again notice how the numbers are the same or different. Does the zero have a place?  Can I leave the zero off? 

Zero plays a big role in helping us distinguish different numbers. We can't just leave it out.

With money we always have a place for dimes and pennies after the dot known as the decimal point. If we have no pennies or no dimes, we use the zero to tell us that. The decimal point helps us to know which is the cents and which is the dollars. We use the decimal point to keep the 2 separate and if we are adding, we can add the cents and then the dollars. 

Using The Zero

20 minutes

I tell students that today we will use the zero to create some objects and price tags. They are to draw 2 objects they would like to sell and give each a price of under $35.00 and more than $2.00. I write a reminder $2.00 < price < $35.00.  Your price must include a zero in one of the cents places (tens or ones), but not both places. 

I give students 10 minutes to draw their objects and add a price tag, each on a different piece of paper.

Now I give students some "shopping" money consisting of dollars, dimes and pennies to represent the hundreds, tens and ones as I tell students. I allow half of the students to get up and go around the room to purchase an object using exact change. After shopping students return to their desks and the second round of shoppers can move about the room. 

Each student sells their one or two objects and then they are done. The shopper takes the objects they have purchased. 

If there is time I repeat the process. 

While students are shopping I circulate around the room to observe the counting of money, and to provide support where it is needed.


5 minutes

I tell students that they may take home the pictures of the objects they purchased. 

I also have them repeat the  zero rhyme to help them remember the use of zero in numbers, and money.


Zero is a little thing

It is nothing you might say

But if I leave it out you see

I won't know what to pay.


The zero holds a place, its true

It tells me what to do

Is the number twenty

or is it only two?

Now I ask students to write the two numbers I dictate on the back of their zero paper. I say 405 and 670. I collect the papers to check for understanding of the use of zero as a place holder.