Apps, apps, apps!
Solving problems online and on paper is fun. So is using a tablet or smart phone if you have access to one. Below are a few apps you might enjoy trying out.

Math

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Math Doodles
Three different number puzzles with lots of variations.
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Wuzzit Trouble
Use your puzzle-solving skills to unlock the Wuzzits’ cages. It's useful to know your multiplication facts. Thinking ahead helps you succeed!
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Five Dice
Make the target number using only the numbers on the dice.
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Number Pyramid
Use mental math to help you solve these puzzles. Click on the "gear" to increase the level of difficulty. Try using negative numbers!
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Math Lands
Math, logic and puzzle games.
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Mathmateer
Practice your math skills and earn parts to build a rocket.
3, 2, 1... blast off!
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Deep Sea Duel
An addition strategy game that can be played at many levels.
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Motion Math
Move your iPad to play this game! In the process you'll work on fractions, decimals and percents.
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VersaMate
A strategy game and fraction practice all in one. Play the computer or challenge a friend.
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Questimate
By Motion Math
Create, estimate, and learn! Play alone or play with a friend.
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Motion Math: Match
A matching game that builds concentration and mental arithmetic skills.Many levels. Fun!
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Motion Math: Zoom
Practice place value with animals  (amoebas to dinosaurs) on a number line. Race the clock if you like!

Engineering/Physics Puzzle Games and Challenges

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Cargo Bridge
Design and build bridges in a variety of settings. Will they hold weight or will they collapse?!
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World of Goo
Build towers, solve puzzles. It's a gooey world!
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Construction Zone
Design and build in this physics based puzzle game.
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Monster Physics
A building app that lets you play with physics! Build and operate your own car, crane, rocket ship, plane and more!
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Cut the Rope
Wonderfully creative physics-based puzzle game. Lots of variety.
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Feed Me Oil
You'll need a  combination of physics and logic to solve these puzzles.
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Cling Thing
You'll need to think quickly to get out of these sticky situations!

Programming

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Hopscotch
A programming language for kids.
It's a little like Scratch.
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Light-bot
Programming puzzles.
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Cargo-bot
Program a robot to solve the puzzle.