Lauren's Class: The Teachers' Lounge

Dear Families,

The Teachers’ Lounge is a problem that pushes students to think deeply and carefully about division situations. It highlights the two types of division situations, quotative and partitive, or grouping and sharing.

In a quotative, or grouping division situation, the number in each group is known and the number of groups is unknown: 24 fourth graders are playing soccer. The coaches want to make teams of 6. How many teams can they make? 6 is the number in each group, and the unknown is how many groups will be made with 24 kids.

In a partitive, or sharing division situation, the number of groups is known and the number in each group is unknown: I have 24 cookies to share with 6 friends. How many cookies can I give to each friend? 6 is the number of groups, and the unknown is how many cookies will be in each group.

In the classroom, we talk about whether a division situation is asking “How many groups?” or “How many in each group?” When you look at the student work below, that is one place your conversation might go. When you read the juice and water machine situations, think about which problem is a quotative situation and which problem is a partitive situation.

Please start by reading the problem, and involve your child in viewing his or her work. You'll find some questions below that will guide your conversation.

Please bear in mind that each pair of students saw these problems differently and therefore solved them differently. Each partnership’s work is valid. There was no “right way” to go about this.

We started working on this problem last week. Working with their math partners, students solved the problem and showed their thinking on a poster using equations, pictures and words. They worked hard to make their work both accurate and clear. Today, math teams switched posters and left notes for each other about what could make the posters better. Revisions were made, and then we had a math meeting on the rug where several students shared their work. After the meeting, each student wrote about how he or she felt The Teachers’ Lounge problem helped them grow as mathematicians (That might be a good way to begin your conversations.).

I love this problem. As I told the class today, it's like a washing machine. They go in grass-stained 3rd grade mathematicians and come out clean and shiny 4th grade mathematicians. This work sets the bar for the level of deep mathematical thinking they'll be doing all year. I hope you are as moved by the sophisticated thinking you'll see in their work as I was.

Happy thinking,

Lauren

The Teachers’ Lounge

Yesterday in the teacher’s lounge, I bumped into the woman that fills the vending machines. One vending machine holds water, and the other vending machine holds juice. I was curious about how many bottles the machines each held, and she told me that each machine holds 156 bottles!

The Water Machine

I noticed that there were a bunch of six packs next to the water vending machine—the woman had to tear the packs open in order to fill the machine. That got me thinking. I wonder how many six packs the machine will hold?

The Juice Machine

The other vending machine holds juice. It also holds 156 bottles. There are six different flavors of juice—apple, cranberry, lemonade, grapefruit, grape and orange. The machine holds an equal amount of each kind of juice. I was wondering how many bottles of each flavor fit in the juice machine when it is full?

Questions to Discuss While You Read This Work

What was your first step? Why did you start that way?

What do the numbers in the equations represent? What do they mean in terms of the problem (Is that 20 six packs? 20 bottles? 20 of each flavor?)?

What does this picture show? Where in this picture are the 26 bottles per flavor? Where are the 26 6-packs?

What is the relationship between the Juice Problem and the Water Problem? How are they

similar? How are they different?