SWBAT break apart a number to count the correct change from $1.00

Breaking apart numbers is one way to approach making change and relates to an understanding of how numbers can be manipulated.

10 minutes

Today's warm up is a review of coins and values. This is something that students worked on earlier in the year, but we have not revisited it lately.

I put pictures of the coins on the Smart Board. I ask students to write in their math journals what each coin is worth. I ask, "what is the value of each coin?" to reinforce the term value that students have seen used in place value questions.

I walk around to check that all students remember the values of the coins.

Next I ask what would the value of 3 dimes be? How about 3 quarters? 5 nickels, etc. Before moving on to making change, I want to be sure that students know the value of the coins. I am asking students to use quantitative reasoning here, by asking them to figure out the value without using the actual coins.

30 minutes

I invite students to come to the rung. I bring out several small objects such as bouncy balls, baseball cards, toy cars etc. and put a price tag of less than $1.00 on each one. I ask if anyone has ever been to a yard sale. Next I ask if they have ever had to pay for something but not had the exact coins? What happens when you don't have the exact change? I hold up a dollar and say, "this is all I have but I want to buy something at the yard sale. What can I do?" I let students suggest what I might do. I acknowledge each idea, and possibly demonstrate some of them, hopefully landing with making change. If no one suggests this, I will say, "I bet I could pay with my dollar and someone would give me something back. Would that be possible?"

I tell students that at first we will rely on dimes and pennies. This is important because I want to reinforce the concept of place value with tens and ones. I also know that students count more easily by tens from a number ending in zero, so I help students to learn to count on with pennies until they get to a smiley face number (one we have talked about as ending in zero) and then counting on by dimes (tens) until they get to the next dollar. I want the price and the change to equal my dollar. I write Price ____________ + Change _________ = $1.00 on the easel. (Here I am reinforcing place value counting which is a big part of 2NBT5).

I pick up an object that is 89 cents ($0.89). I ask if anyone could count on from the price ($0.89) to make change for me? I take a volunteer and have them count out with the pennies and the dimes to equal 100 or 1 dollar.

I repeat this process with the other objects on the rug, letting other students count back the change. I am hoping that students will begin to see the structure of counting to the nearest 10 and then counting on by 10s to get to $1.00. (MP7)

Next I hold up a new object and price tag. I hand every other student a $1.00 bill and pass out dimes and pennies to the other partner. I ask the person with the dollar to pay for the item, and the partner to count out the change by counting up from the price to $1.00. I remind them to start with the pennies and count to the next smiley face (zero) number and then on by 10s to get to $1.00.

When they are done, we check together to see if everyone gave the right amount of change. We count together starting with the pennies and then adding the dimes with each group checking their own change pile.

The partners switch roles and we repeat the process with another object.

Some students will find it easier to count on by 10s first such as from $0.66 they will count 76,86, 96 and the count by ones from 97,98, 99 , 100 and then counting what they have to see 3 dimes and 4 pennies or $.034.

If students seem secure at this point, I ask partners to go off together and practice shopping for items I hand them. If they are not secure, I keep some students with me to practice counting up together.

For some students this is too simple, and I give them a ten dollar bill, higher price tags and enough ones to make change.

Students practice at their level for about 15 minutes taking turns being the shopper and the cashier.

5 minutes

I invite 2 volunteers to come to the front of the room and show us how they make change for an object. I write .16 on the board. I put out a stuffed animal and hand the buyer $1.00. We watch as the student counts out the change.

I ask students what they notice about making change (counting up to the next ten, counting down, etc.) I am hoping that they will connect to the idea of tens and ones and their understanding of place value. I also want reinforce for students that they can use dimes to represent counting by tens. I hope that students gain a better understanding of the idea that price + change should equal the amount paid (in this case $1.00). All of these things are reinforcing the Common Core standards for place value understanding.

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