### Activity 1: Elevator Operator

Materials: 21 post-it notes for each student, pens/pencils/markers

Format: Whole Group

Plan:

Students imagine that their group has won a crazy contest where they get to design and live together in a mansion — but it’s the world’s 2nd-tallest*, skinniest mansion. Each floor has exactly one room, and they’ll all have to agree on the layout. To design their mansion, they start by each labeling (and draw or describe) 21 floors on a different post-it note, and arranging them to show how they would stack up their floors.

Have each student present their ideas by telling the story of a typical day at their house. What room do they start on? What floors do they visit? How many trips do they make? In what order?

As everyone shares, have the audience consider:

- Who travels farthest? Least far?
- How might you reorganize your rooms to travel the most distance? Least distance?
- Did everyone include bathrooms? How often would you need to visit those floors?
- What about kitchens?
- Is there a “ground floor?” Does everyone come and go by the ground floor or are there heli-pads or underground garages?
- How many people have basements — floors below ground level?

As a group, discuss what you heard and come up with the floor plan that you would submit for your shared house. Make sure it either has some floors below and above ground level, or below and above the bedroom (either the bedroom or ground floor will be “Floor 0″). You might first decide on which 21 levels you definitely want to have and then which order makes the most sense for them. Use the post-it notes to visualize what you’re discussing.

Give each kid some blank paper to draw and decorate their own copy of the house they all agree on. Encourage them to add detail and really think about what the house will look like and what it would be like to live there.

### Activity 2: Using the Elevator

Think of a series of trips you might do in the building elevator. For example, you might start in the bedroom, go down to the bathroom to take a shower, go up to the kitchen to eat, go down to the gym to work out, go up to the movie theater to watch a movie, and then back to the kitchen for lunch. Tell the students what floor you started on, and then give them a series of instructions without naming any more floors. So you might say, “I started in the bedroom and then went down 2 floors, up 4 floors, down 10 floors, up 1 floor, and then up 9 floors.” Have the students say which floors you visited and where you ended up. Ask them, “How did where I end up compare to where I started (the bedroom)?”

Have each student take a turn to think of a day or a series of activities that they would do in their building. What floor do they start on? Where do they go next? Then what? Have them write down the steps of the trip, naming the floor they start on and then using numbers and the words up or down to write everything else, like you modeled.

Each student then shares their trip while the other students try to follow along. See who can tell which floors they visited and where they ended up, and how far it was from where they started.

See how quickly you can give the directions and still have students be able to follow you!

### Activity 3: Labeling the Elevator

Materials: Plastic sleeves and dry-erase markers

It’s kind of inconvenient saying the names of each room all the time, and asking “Where is your location now in terms of the bedroom?” or whatever. Tell the students that you’re going to number the floors, like in an elevator. The ground floor (or bedroom, if the ground floor is on the bottom) should be 0. Label the floors going up, and then ask the students how to label the floors going below. If they don’t think of negatives, show them.

Play the “Show Me” game with the students (at least 10 rounds):

Ask them to *show you* on their elevators and *tell you* with numbers:

“Where would you end up if you went from the -5th floor up 15 floors?”

“Where would you end up if you went from floor -5 down 3 floors?”

“Where would you end up if you went from floor -5 down 12 floors?”

Keep going for at least 7 more rounds. WRITE DOWN THE PROBLEMS YOU GIVE THE STUDENTS!

Walk/look around and quietly indicate “yes” or “try again” as you view students’ elevators.

Now… write on your clear plastic sleeve the first problem you asked the kids to show you in the form of an integer *addition* problem:

-5 + 15

Ask: how would you act that out on your elevator? *Show me*. Look at each kid’s thinking and acknowledge with a “yes” or “try again”. Kids who need to “try again” might want to have a friend who got it right explain.

Repeat with the other *addition* sentences (hopefully someone will blurt out “We already did all of these!”)

-5 + -3

-5 + -12

etc.

DO NOT USE SUBTRACTION FOR GOING DOWN, USE ADDING A NEGATIVE.

Now ask the students to tell you: “How would you use your elevator model to help you explain adding positive and negative numbers?”

Extension: Have each student use their own elevator mansion to make up some moving in the elevator stories to challenge their friends. Have students make up a story to go with the trip (like, I woke up, went down 1 floor to shower, went down 3 floors to get something to eat, decided to be entertained while I ate so I went down 4 floors, I drank too much soda and had to go up 7 floors, decided to work out so I went down 8 floors, then finally went up 9 floors — what floor was I on and why do you think I went there?). Then challenge them to write their trip as a LOOOONG addition sentence.

### Activity 4: Adding positive and negative numbers on a (horizontal) number line

Materials: horizontal number line, plastic sleeve, dry erase marker (for each student)

Write integer addition problems on your white board.

Have students model the addition challenges using their number line. Look at their work and acknowledge with either “yes” or “try again”. For example they could model -3 + 5 as starting at 0 going left 3 and right 5, or starting at -3 and going right 5. Either way they end up at 2.

Challenge: Add in some simple, verbal problems about temperature, money, and elevation using the number line model. For example: “It was 5 degrees one day and then the sun set and the temperature went down 10 degrees. Show it on your number line and tell the new temperature.” or “I went on a hike that started 10 feet below sea level and then went up 19 feet. What was my elevation at the end of the hike?” or “I owed 13 dollars and then I got 20 dollars for shoveling snow. How much money do I have now that I’ve paid off my debts?”

### Activity 5: Life on the Number Line Game — Addition only

Materials: Game Board, Game Piece for each student, Odd/Even Problem Cards, one +/- die, one number die

Game Play:

Each student takes a turn rolling the dice. They make an addition problem with their starting space as the first number, and whatever they rolled as the second number. They move to the answer and pick a question card based on whether they’re on an odd number or an even number. If they land on 0, in addition to answering an even number question, they also get to pull a special 0 card.

The goal is to race the other advisories to see who can complete the most questions in a term. Special prizes will be awarded at the end!

### Activity 6: Range-Finder Battleship (Less and More on the number line)

Materials: Number Line, Plastic Sleeve, Dry-Erase Markers

Format: Students playing one-on-one

Game Play:

Player A uses the marker to draw 5 “ships” on 5 integers of her choosing, and then announces to Player B that the locations of their ships are all less than ___ and more than ___, or between ___ and ___, on their -10 to 10 number line.

Player B gets 5 guesses to try to sink their ships – but if any guesses are out of range, they lose all remaining turns for that round.

Each hit gets a point… switch roles to finish the round.

### Activity 7: Addition Battleship

Materials: Number Line, Plastic Sleeve, Dry-Erase Markers

Format: Students playing one-on-one

Game Play:

Player A uses the marker to draw the path his ship takes (making at least two stops), and then writes the ship’s trip as an integer addition problem. E.g. if the ship started at -5, and then went to the right 3, to the left -4, and to the right 6, Player A would write -5 + 3 + -4 + 6

Player A reads the addition problem to Player B, who writes it down. Player B solves the addition problem and announces where she wants to “bomb” Player A’s ship.

If Player B is right, it’s a hit. If not, it’s a miss. Each hit gets a point… switch roles to finish the round.

### Activity 8: Subtracting Integers

Materials: Students’ labeled, decorated elevators, plastic sleeves, dry erase markers

Here’s my mansion:

- Bedroom — 7
- Master Bathroom — 6
- Living Room — 5
- Other Bathroom — 4
- Dining Room — 3
- Kitchen — 2
- Den — 1
- Ground Floor — 0
- Gym — -1
- Movie Theater — -2
- Workshop — -3

The location of the Dining Room compared to the location of the Kitchen is up 1 floor.

The location of the Den compared to the location of the Workshop is up 4 floors.

The location of the Gym compared to the location of the Master Bathroom is down 7 floors.

Write some sentences like that for your mansion, and have each student write their own sentence comparing the location of two of their floors.

Play a “Show Me” game using some sentences like this. Have students use their elevators to *show you *their answers to:

The location of the 5^{th} floor compared to the location of the 3^{rd} floor is _up/down_ _____ floors

(do several more big number minus smaller positive number)

The location of the 1st floor compared to the location of the 5th floor is _up/down_ _____ floors

(do several more small positive number minus larger positive number)

(mix in some big – small and some small – big)

The location of the 6^{th} floor compared to the location of the -4^{th} floor is _up/down_ ____ floors

(do some positive – negative and then some negative – positive)

(then mix it up like crazy!)

The location of the -2^{nd} floor compared to the location of the -6^{th} floor is _up/down_ ____ floors

The location of the -8^{th} floor compared to the location of the 6^{th} floor is _____ floors ____

The location of the 7th floor compared to the location of the -3^{rd} floor is _____ floors ____

The location of the -3^{nd} floor compared to the location of the 10^{th} floor is _____ floors ____

Extra Challenge: find all the pairs of floors that give an answer of 3 floors up. Try it again with 3 floors down. And again with 5 floors up.

### Activity 9: Translating Subtraction Problems into Location Comparing Problems:

Write:

5 – 3 = 2

Say:

The location of the 5^{th} floor compared to the location of the 3^{rd} floor is 2 floors up

Show:

On the elevator

Write:

8 – 10 = -2

Say:

The location of the 8^{th} floor compared to the location of the 10^{th} floor is 2 floors down

Show:

On the elevator

Do several for your students, then ask your students to talk through some with you.

Finally, write solved subtraction problems on your white board and play the “Show Me” game. Have students say what the subtraction sentence means for the elevator, and then show you on the elevator:

4 – 3 = 1

8 – -2 = 10

7 – 10 = -3

-3 – -5 = 2

-6 – 4 = 10

Once students are confident translators, give them some independent subtraction practice problems to do, writing them on your whiteboard, or their whiteboards if you need to mix it up for kids of different skill levels.

### Activity 10: Life on the Number Line — Addition AND Subtraction

Play Life on the Number Line again, introducing the second +/- die. This time, students roll both +/- die. The first tells them whether they are adding or subtracting from their current position, and the second tells them whether they are adding a subtracting a positive or negative (of whatever number they roll with the number dice).

Mix in some of the Activity 10 cards into their Even and Odd problem piles.

### Activity 11: Integer War Addition

Materials: Deck of regular cards with face cards and jokers removed, recording sheets

Game Play:

- Divide the deck evenly between the 2 players. Players don’t look at their cards.
- Each student turns over the top
*two*cards. Red cards are negative and black cards are positive. - The player with the greatest sum (remember, furthest to the right is always bigger) will win that round and collect that set of cards. If students aren’t sure, they model the problem with their number line.
- If two players have sums with the same value (even if they look different, e.g. -4 + 5 and -9 + 10), then a round of “Declare War” must be played.
- Players in a war round must take three cards and place them face down from the top of their decks. A fourth and fifth card should be taken from the deck and placed face up.
- The highest value sum wins and that player may take all of the cards used in the declare war round, as well as the cards that created the “Declare War” round.

- Winning the game:
- Short version: Play each round as usual; however, keep the cards won from others in a separate pile. After the last round, determine a winner by picking the player with the most cards.
- Long version: Play each round as usual, but add the cards won from each round to the bottom of your face down deck. Play until one player has all of the cards.

Students use their recording sheet to record sentences: e.g. black 5, red 7 “starting at 5 and traveling down 7 puts you at -2” or “starting at -7 and traveling up 5 puts you at -2”

### Activity 12: Integer War Subtraction

Materials: Deck of regular cards with face cards and jokers removed, recording sheets

Game Play:

- Divide the deck evenly between the 2 players. Players don’t look at their cards.
- Each student turns over the top
*two*cards, and lay them from left to right. Red cards are negative and black cards are positive. - The player with the greatest difference, reading from left to right, will win that round and collect that set of cards. If students aren’t sure, they model the problem with their number line.
- If two players have subtraction problems with the same value (even if they look different, e.g. -4 – 5 and -10 – -1), then a round of “Declare War” must be played.
- Players in a war round must take three cards and place them face down from the top of their decks. A fourth and fifth card should be taken from the deck and placed face up.
- The highest value difference wins and that player may take all of the cards used in the declare war round, as well as the cards that created the “Declare War” round.

- Winning the game:
- Short version: Play each round as usual; however, keep the cards won from others in a separate pile. After the last round, determine a winner by picking the player with the most cards.
- Long version: Play each round as usual, but add the cards won from each round to the bottom of your face down deck. Play until one player has all of the cards.

Students use their recording sheet to record sentences: e.g. black 5, red 7 “location of 5 compared to location of -7 is up 12”

### Activity 13: Name That Integer

Materials: Standard deck with face cards removed. Red cards are negative.

Format: 3 or 4 players per deck (s0 split larger advisories in half)

A player shuffles the deck and places five cards face-up on the playing surface. This player leaves the rest of the deck facedown and then turns over and lays down the top card from the deck. The number on this card is the number to be named.

In turn, players try to (re)name the number on the set-apart top card by adding or subtracting the numbers on two (or more!) of the five face-up cards.

A successful player takes both the two face-up cards and the number-named top card. A successful player also replaces those three cards by drawing from the top of the facedown deck. Unsuccessful players lose their turns. But they turn over and lay down the top card from the facedown deck, and the number on this card becomes the new number to be named.

Play continues until all facedown cards have been turned over. The player who has taken the most cards at the end wins.

*Example:*

Mae’s turn:

The number to be named is 6. It may be named with 4+2, 8-2, or 10-4.

Mae selects 4+2. She takes the 4, 2, and 6 cards. She replaces the 4 and 2 cards with the top two cards from the facedown deck and then turns over and lays down the next card to replace the 6.

Mike’s Turn:

The new number to be named is 16. Mike can’t find two cards with which to name 16, so he loses his turn. He also turns over the next card from the facedown deck and places it on top of 16, and the number on this card becomes the new number to be named.

Play continues as before.

**Game Variations:** If children are finding the game difficult, increase the number of face-up cards.

Use any combinations of two or more numbers and all operations. For example, Mike could have named 16 as follows:

10+7-1

10+12-7+1

8+12-10+7-1

Children can experiment by using different numbers of face-up cards.