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What is the key to computational fluency? Practice. Lots and lots of practice. What about reasoning skills? Practice. What about number sense? Practice. What about every important skill I can think of? Lots and lots of practice!
I am a strong believer that none of us have destinies or skills or abilities that are fixed. Our country was built on the belief that if you work hard and do what’s right, you will get ahead. I think this is particularly true when it comes to school and math.
My "Tangy Tuesday" puzzles give students the opportunity to practice and improve their skills in a thoughtful and systematic way. By the end of the year, kids who solve all 5 of my puzzles every week will have done thousands of problems designed to help them become better in math.
But that’s not all. My ultimate goal is for kids to enjoy solving problems – especially challenging ones. Students who solve my puzzles will struggle, learn to persevere, and ultimately become better, more creative thinkers. Through their own hard work, they will become smarter more successful students.
Puzzle 1: DigiCross. For many years, schools and districts have asked me for my scope and sequence for teaching math at each grade level. I have now included them in my DigiCross crossword puzzles. In Q1, we review key concepts from the previous year. In Q2, we build on them and transition to the current year’s standards. In Q3, we focus on more advanced problems, and finally in Q4, we assess, review and strive for mastery. For teachers who want to make sure they are covering and assessing the most important strategies, skills and standards – my DigiCross puzzles can help.
Puzzle 2: Snake. Is there a way to “trick” students into doing thousands of computations in a fun and clever way? Snake puzzles are a student favorite and provide the extensive practice kids need to become fact and procedurally fluent. Puzzles start off easy in the first quarter and become more and more challenging as the year goes on.
Puzzle 3: Numtanga. To help students gain a better understanding of numbers, money, fractions and measurement, Numtanga puzzles use a clever matching algorithm discovered by my son. Quantities are represented in multiple ways and students are challenged to find matches. Sometimes it is easy, but often times it is not!
Numbers are represented by digits, words, ten frames, fingers, expanded form, and base 10 blocks. Money is shown with cents, decimal notation, words, and coins. Fractions are shown as numbers, words, parts of a whole and parts of a set. Lengths, weights, and liquid volumes are given in both customary and metric units.
Puzzle 4: Kakooma. Number bonds – also called fact families or parts of a whole – are the key to great computational skills. What’s 8+6? It’s 8+2+4 = 14. What’s 6x13? It’s 6x10 + 6x3 = 78. What’s 91÷7? It’s 70÷7 + 21÷7 = 13. The secret is knowing the best way to break numbers apart.
I invented Kakooma to give kids a fun and challenging way to develop their number sense. By varying the operation and the number, size and type of numbers, we can create grade-specific puzzles for students of all ages. Kakooma is one of my most popular games and provides many hours of fun and addicting practice.
Puzzle 5: Equato. Is there a self-checking puzzle that gives kids practice with multi-step problems, combines multiple operations in a single equation, teaches order of operations, and develops higher-order thinking and reasoning skills? Equato does all that and more! Our newest puzzle represents a collaboration between my son Greg Jr, my wife Tammy, and me. Its strength is in developing both strong computational and reasoning skills at the same time.
Equato develops strong computational skills by emphasizing the relationships between operations. Each puzzle is loaded with the more challenging “change" and “start" unknown problem types for addition and subtraction, and "group number" and "group size" unknown problem types for multiplication and division. Sums, differences, products and quotients also appear before the equals sign – teaching students that "equals” is a comparative word meaning “is the same as.”
Equato also develops strong reasoning skills by including equations with 2, 3 and 4 unknown numbers. When students first learn to solve these more challenging problems, they can use "guess and check” strategies. Over time, they can be encouraged to instead use higher-order thinking and reasoning skills.
Conclusion. To be good at anything, kids need to practice. In math, this means doing thousands of problems to develop conceptual understanding and fact and procedural fluency. My goal is to make practicing so enjoyable that kids look forward to solving my weekly puzzles and problems. I hope you will give them a try!