Math II

PROBABILITY AND STATISTICS

	In Edward Einhorn’s A Very Improbable Story (Charlesbridge, 2008),  Ethan wakes up one morning with a talking cat on his head – who absolutely refuses to move until Ethan wins a game of probability. Ethan then struggles with challenges involving socks, coins, cereal shapes, and marbles, gradually learning how best to judge odds and predict outcomes. (The cat’s name, incidentally, is Odds.) For ages 7-10.
	By Sheila Dolgowich and colleagues, Chances Are (Libraries Unlimited, 1995) is a 125-page collection of hands-on activities in probability and statistics. For ages 8-13.
	Carla Mooney’s Big Data (Nomad, 2018) is a catchily designed explanation of what big data is, and how we store, manage, and analyze it. All about information in the digital world, with many activities for ages 10 and up.
	Darrell Huff’s 144-page How to Lie With Statistics (W.W. Norton, 1993) is a funny, friendly, and informative overview of statistics and the way in which – if we’re not on the ball – they can fool us into drawing the wrong conclusions. Learn all about sampling and bias, deceptive averages, “gee-whiz” graphs, and more. Illustrated with vintage-style cartoons. For teenagers and up.
	Larry Gonick’s The Cartoon Guide to Statistics (HarperPerennial, 1993) covers everything from data display and analysis to distribution, confidence intervals, hypothesis testing, and experimental design through the medium of clever (and highly intelligent) cartoons. For teenagers and adults.
	Charles Wheelan’s Naked Statistics (W.W. Norton, 2014), subtitled “Stripping the Dread from Data,” is an overview of what makes numbers meaningful, dealing – in reader-friendly fashion – with such questions as “How does Netflix know what movies you like?” “What’s a batting average?” and “How useful is a GPA?” Various chapters cover correlation, basic probability, the importance of data, the Central Limit Theorem, polling, and regression analysis. For teenagers and adults.
	From the New Jersey Mathematics Curriculum Framework, Probability and Statistics is a detailed and useful overview of what kids should know and do at each grade level (K-12), with suggestions for activities and resources.
	TeacherVision’s Resources for Teachers has a selection of printables and lesson plans for probability and statistics studies. Lesson plan titles include Heads or Tails: Penny Math; Using Scatterplots; Range, Median, and Mode; Baseball Fun; and U.S. Immigration. For ages 7-12.
	The BBC’s Handling Data has videos, written tutorials, and quizzes on frequency diagrams, mode, median, mean, and range, and probability.
	Rock, Paper, Scissors: The Study of Chance is a lesson in probability involving paper, pencil, two players, and a pair of hands.
	Try Rock, Paper, Scissors against a computer.
	Up for a challenge? Try Rock, Paper, Scissors, Lizard, Spock.
	From Science Buddies, Probability and Playing Cards has several probability projects and activities aimed at family groups, variously using playing cards, M&Ms, and dice.
	Also see Scientific American’s Suited Science: What Are the Odds of Drawing That Card?
	From Cut the Knot, Probability Problems has a detailed tutorial with definitions, explanations, and a long list of challenging problems. For older students.
	From the extensive Core Knowledge website, What’s Math Got to Do with It? is a multi-lesson study targeted at grade 5.
	From Annenberg Learner, Against All Odds: Inside Statistics, consists of 32 video modules plus coordinated guides. Available online or on DVD. For high-school-level students and up.

 SUPER-GOOD GAMES

	Set, “the family game of visual perception,” is a diabolically clever exercise in mathematical thinking. It’s a (deceptively) simple card game, consisting of 81 cards, each printed with one of three basic shapes: a diamond, a lozenge, or a fat squiggle. On each card, the shapes appear in different numbers, colors, and shadings. To play, the dealer lays out 12 cards, face up, and all players attempt to identify three cards that make a set: that is, three cards in which each feature (shape, number, color, shading) is either exactly the same or completely different. When you’ve managed to do so, you yell “Set!” and remove those three cards from the board; the dealer then adds three new cards and the set-search begins again. Everybody plays at once, which means that nobody has a chance to get bored, and the game is considerably more challenging than it first appears. It is appropriate for persons aged 5 through adult, and adults – believe me – have no advantages over younger players.
	Chess might be the ideal teaching tool. It’s all about strategy and patterns, lines and angles, spatial analyses, weighing options and making decisions.  Research shows it boosts academic achievement, but it’s also challenging and fun. Also Harry Potter played it.
	Doubtless one reason that it’s so successful is that it’s self-empowering – players figure a lot of it out on their own – and it provides a range of intellectual benefits without overtly trying to do so. Recommended age for introducing chess to kids is around 8 or 9, but there are no hard and fast rules.
	ChessKid has a tutorial on playing chess targeted at kids; young players can also sign up (safely) to play with others online.
	Sudoku puzzles are applied logic puzzles, played on a 9×9 grid, with nothing more than a pencil (eraser also highly recommended) and brains. The puzzle grid is subdivided into nine 3×3 blocks or regions; the trick is to enter the numbers 1 through nine (with no repetition) in each horizontal row, vertical column, and block. (“Sudoku” or “su doku” means “numbers singly” in Japanese.) In each puzzle, a few number clues are present on the grid – these cannot be changed and players must work with and around them while solving the puzzle. Sudoku puzzles range in difficulty from the easy to the fiendish; and all are excellent and mind-expanding exercises in the art of logical thinking. (This isn’t arithmetic. It’s more like chess.)
	There are many books of sudoku available, including some specifically for children – see, for example, Alastair Chisholm’s The Kids’ Book of Sudoku 1 (Simon & Schuster, 2005).
	Web Sudoku offers zillions of puzzles – variously classified as easy, medium, hard, and evil – that can be printed or played online. Also see Gamehouse Sudoku, which has online puzzles at five levels of difficulty.
	In Proof, an award-winning game of mental math for 2-6 players ages 9 and up, kids race to identify equations in a grid of number cards. Fast, fun, and easy – it’s like Set, but with numbers.
	Equate (Conceptual Math Media) is a board game for ages 8 and up. Basically, it’s Scrabble with addition, subtraction, multiplication, and division instead of spelling.
	Coolmath4Kids, in bright flashy colors, has dozens of categorized math games, geometry/art projects, printable flash cards, dozens of online calculators, cool apps, and more.
	Math Playground has dozens of online math games, variously involving numbers, logic, math manipulatives, and word problems, along with interactive projects, worksheets and flashcards, and more. Click on “Common Core Math” to find grade-by-grade games and challenges aligned to the Common Core.
	PBSKids’ selection of Math Games includes dozens, among them Juggling George, Send in the Trolls, Star Swiper, Vegetable Planting, the Great Shape Race, and many more. Experiment.
	Calculation Nation has math-based games for upper elementary- and middle-school-level students, in which kids can challenge themselves or play against others.