Master Nines Years 4 - 8

Summary If the title of the activity sounds a little like the well known game of Master Mind, it's supposed to. The activity is modelled on reasoning similar to that game. The objective is for one player, who never knows all of what's on the calculator screen, to give instructions that eventually change the screen display to 999. To assist with framing the instructions, the other player gives clues. The only clues allowed are the number of nines on the screen and one other digit. Suitable for threading. Materials One calculator

Procedure Player A, The Hider, secretly enters any number less than 1000 into the calculator and keeps the display secret throughout the round. Player B tells The Hider what to add and in which column. For example: Add on 6 ones (or 5 tens or 7 hundreds) or add on 6 (or 60 or 700). Player B must keep a record of the instructions they give. The Hider does the addition on the calculator and tells Player B the number of 9s on screen and one other digit. The Hider only reveals the digit, not its place value. If an instruction would cause the screen to go over 999, The Hider says Too big, please try again. The 'too big' instruction does count in Player B's score. Player B continues giving instructions until they are told 999 is showing on the screen. Player B's score for the round is the number of instructions they have given. (The Hider may keep a tally of the number of instructions.) When a round is finished, players swap roles. The winner of the game is the player with the smaller score when each player has been The Hider for three rounds.

Content addition facts beyond 10 addition facts to 10 complementary addition decimal calculations decimal interpretation place value problem solving properties of number properties of zero recording - written subtraction

Here is a sample of one round. Of course we don't know what Player B actually thought. Use the 'thinking column' to record what you would think at each step.

Turn No.	Instruction (Add ... )	Display (Secret)	Player B Told	Player B Thinks
		123
1	5	128	Zero 9s and a 2	~~~~~~~~~~~~
2	1	129	One 9 and a 1	~~~~~~~~~~~~
3	700	829	One 9 and an 8	~~~~~~~~~~~~
4	300	829	Too big, please try again	~~~~~~~~~~~~
5	100	929	Two 9s and a 2	~~~~~~~~~~~~
6	70	999	That's it!

Player B's score for this round is six. But perhaps they could have got it in less (see below).

Variations

• What happens if we increase the target to 9,999 or 99,999 or larger?
• What happens if the target is 1000 (or 10,000 or larger) and it's zeros that have to be revealed?
• What information should be revealed on each turn for these larger targets?
• What happens if we play the game with decimal place columns, for example with The Hider secretly entering between 0·01 and 10 with a target of 9·99, or between 0·001 and 1·0 and a target of 0·999?

Could Player B have done better?

• Step 1: If adding 5 didn't make a carry figure, I might be quite near 9 in that column.
• Step 2: Good guess, and there couldn't have been a carry figure, so the screen is either 129 or 219.
• Step 3: Must have been 129 or I wouldn't get the second, so now it's 829. First add 100 and then add 70.

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