# The game of Left-Overs

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## Objective

SWBAT divide quantities into equal groups and make sense of remainders.

#### Big Idea

In this lesson, students write division equations and work with identifying remainders in an engaging partner game.

## Number Hook

5 minutes

This is a fun trick I start today's lesson with.  My students always like to use calculators, so this is a treat for them.

We discovered that this trick is one number off each time, giving a persons age one year lower than they actually are.  This was a good talking point, though. I was able to ask my class where the error could have occurred and what we could do to fix it. Most of my students were able to identify that when adding 1762 or 1761 that could be where the number error occurs.

I love that my students are becoming more critical thinkers and analyzing my magic tricks.  In reflection, I'm glad this had an error which allowed for a great discussion and teaching point.

## Warm Up

5 minutes

I begin this lesson by asking students to model an array on their whiteboard which shows an array with a remainder of one if they could match it to a division situation. I remind them about the book the read, Remainder of One, in which they did the same thing.

I then ask students to talk with their learning partner about what a remainder is.

## Concept Development

45 minutes
In this lesson, students spend time continuing to explore remainders through a game called The Game of Left Overs. Students also write equations to go with situation in this game.
To play the game, you will need:  one dice per partner, about 40 unifix cubes per partner, paper and pencil.
I begin by telling student that they will work with their learning partner to play a game today.  I tell students that the object of this game is to accumulate the most leftovers.
Next I tell students how to play:
The first player rolls a die. The number rolled tells how many groups the student will divide 40 cubes among. If there are leftover cubes, the first player keeps the cubes. Both players record equations in their math notebooks to match the situation. For example, if student A rolled a 6, both students would record 40 / 6 = 6 R4.
Then, the second player begins his or her turn with 36 cubes because player one kept
the remainder.  The second player rolls the dice to determine how many groups he or she is dividing 36 in to. Again, this player will keep any remainders and return the equally divided cubes. Students write an equation to match the division situation. Students take turns and continue until there are not any cubes left.
You can see two students playing the game in the video below. Notice how I use words like "dividend, and remainder" so students get used to using and hearing this vocabulary.

## Student Wrap Up

10 minutes

Students will participate in a formative assessment I call Write, Pass, and Read for this lesson's wrap up.  Students will write on a small piece of paper for this activity.  Students finish this sentence:

A remainder is ___________________________.

After students complete the sentence, they form a circle in the room, holding onto their paper.  When everyone is finished, I review the procedure for Write, Pass, and Read.  Students will always pass their paper to the left when they hear me say, "pass."  When I say, "Read," they stop passing the paper and read the one they are holding.  Students are not allowed to make comments or questions at this time.  They are to think about questions or comments they would like to make when the activity is over.

In this video, you can see a small clip of the Write, Pass, and Read happening.

This is an important formative assessment.  In the next lesson, students will explore remainders and experiment with various ways to record remainders, as decimals, fractions, and whole numbers. It is important for me to connect with students who do not understand what a remainder is before they can be successful with different remainder forms.