Activity Instructions: 
1. The aim of the game is to wipe out the five alien spaceships in the least number of hits. Each spaceship represents one digit in a five digit number.

2. The teacher or a player enters a starting number into the calculator. The starting number for each game must be composed of 5 different digits, excluding zero, as well as a decimal point. E.g. The alien number is 12.453

3. Spaceships (digits) must be shot down in order from the lowest digit to the highest digit.

4. The laser gun is always targeted on the spaceship in the ones column. To shoot down the spaceship (subtract the digit), it must be moved to the ones column first. This can only be done by using the multiply or divide buttons with powers of 10. (Later, let students work out why you use powers of ten by trying other numbers instead.)
E.g. 12.453 ÷ 10 = 1.2453

5. The subtraction to shoot does not count as a turn and is done by whichever player has moved the spaceship (digit) into position.
E.g. 1.2543 - 1 = 0.2543

6. The player whose turn it is states what their move will be (e.g. "multiply by 10"). All players fill in the row of their recording sheet, including their own prediction. The original player then presses the keys on the calculator and shows all players the display which is then recorded. Students tick their prediction if it was correct.

7. Play continues with the calculator passing to the player on the right.

8. Game is completed when calculator display is zero, meaning that the alien ships have all been destroyed.

Comments: 
Using the recording sheet encourages all the children to be actively involved throughout the game and helps children reflect on what has happened. Without this record, children are unlikely to make the necessary generalisations.

Variations:
For beginners, aim to improve prediction skills in each successive game in a session. Questions which prove helpful:

• Can you see a pattern for what happens when you multiply? divide?
• What happens when you multiply by 10 compared to 1000?
• Can you write some helpful hints for someone new to the game?

For experienced players, write a number on the board and have teams compete to see who can complete the game in the fewest number of steps. Later, play without recording sheet.

• New Rule: If you fail to move digit into position on first try, the alien shoots back and all students have to start a new game. The challenge then becomes to complete a game.
• New Rule: Only multiplication can be used (hence multiplication by decimals like 0.001 may be required).
• New Rule: Only division can be used (hence division by decimals like 0.001 may be required).

Teaching Notes:
It is possible for experienced players to play without thinking. It is good to ask them the question, "Why do the rules they've discovered for manipulating numbers work?" This is a good opportunity to bring in the LAB model.

Unfortunately, the display on some calculators may reinforce the idea that it is the decimal point which moves rather than the digits moving into new columns. It would therefore be an appropriate time to demonstrate the effect of multiplication and division by powers of ten on a number slide. Appreciating the reason for the movement of the digits between the columns may reduce the reliance on, and misuse of, rules about moving a decimal point.

Reference: Jill Cheeseman (1994) describes a calculator game called "Alien Invaders", which is very similar and also suggests other activities.