Games are to math as books are to reading! Ways to modify many of these games for younger players are listed here.

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Addition and Subtraction War - addition, subtraction

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Blackjack (21) - addition, numbers up to 21, strategy

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Carcassone - addition, skip counting, puzzle skills, strategy

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Cribbage - addition, multiplication, numbers up to 121

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Cuisenaire Rod Games - addition, awareness of what numbers actually mean through hands-on experience

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Milles Borne - addition, numbers up to 1,000

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Monopoly - addition, subtraction, how to make change, large numbers, financial concepts (such as mortgage, bankruptcy, etc)

Parcheesi - numbers, addition, memory for special rules, sportsmanship

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Poker - strategy, analytical thinking, risk vs. reward (if played with poker chips), 

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Settlers of Catan - addition, strategy, risk management

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Settlers of Catan Dice Game - addition, strategy

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Sorry - numbers, memory for special rules, sportsmanship

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Sum Swamp - addition, subtraction, understanding of math problems and symbols, odd and even

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Uno  - numbers, colors, addition and subtraction (if playing add-and-subtract variant)

Yahtzee - addition, multiplication, strategy, and writing