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CCSS Math Standard: 4.OA.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Crossing Every Bridge Exactly Once (aka Eulerian Paths)
Crossing Every Bridge Exactly Once (aka Eulerian Paths)
How can you cross each bridge in this city exactly once?
Math Curiosity: Magic Triangles
Math Curiosity: Magic Triangles
Can you make each side of this triangle add up to 9 using the digits 1-6?
How Many Will There Be? Chip Off The Block
How Many Will There Be? Chip Off The Block
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Earthworm
How Many Will There Be? Earthworm
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Courtyard
How Many Will There Be? Courtyard
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Checkerboard
How Many Will There Be? Checkerboard
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Crosses
How Many Will There Be? Crosses
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Squares in Squares
How Many Will There Be? Squares in Squares
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Pyramids
How Many Will There Be? Pyramids
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Sliced Circles
How Many Will There Be? Sliced Circles
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Xs and Os
How Many Will There Be? Xs and Os
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Desks
How Many Will There Be? Desks
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Stairs
How Many Will There Be? Stairs
Give kids a taste of a sequence, let them build an understanding, and then see how far their predictions can take them.
How Many Will There Be? Flowers
How Many Will There Be? Flowers
These flowers sure are getting bigger faster! How large will they be in step 10? What about step 50?
Game: Number Scrabble
Game: Number Scrabble
What if we played Tic-Tac-Toe with numbers and instead of three-in-a-row, we add up to 15? Well… then we’d have Number Scrabble!
How Many Will There Be? Triangles Within Triangles
How Many Will There Be? Triangles Within Triangles
A triangle splits and splits and splits again. How many will there be in step 20?
Math Curiosity: Ulam Spiral
Math Curiosity: Ulam Spiral
What if we make a huge spiral of numbers and then highlight only the primes? Well, a bunch of weird patterns show up!
Math Curiosity: A Pattern Packed Triangle
Math Curiosity: A Pattern Packed Triangle
Pascal’s pattern-packed triangle is a potent puzzle for pupils to ponder.
Math Curiosity: Goldbach’s Conjecture
Math Curiosity: Goldbach’s Conjecture
Can any even number be written as the sum of two primes? Goldbach thought so, but we haven’t proven it… yet!
Evens and Odds – Addition and Subtraction
Evens and Odds – Addition and Subtraction
When we’re adding and subtracting, do evens make odds into evens? Do odds make evens odd? Which one has… more power!?
Math Curiosity: Four Squares
Math Curiosity: Four Squares
Every positive integer can be written as the sum of (at most) four perfect squares!
Math Curiosity: Magic Squares
Math Curiosity: Magic Squares
Imagine a 3×3 square in which every row, column, and diagonal have the same sum. That’s a magic square!
Math Curiosity: Odds & Squares
Math Curiosity: Odds & Squares
Why does the sum of the first 5 odds also equal 5 squared?
Doubling Dollars
Doubling Dollars
Say you have a dollar. Say you can double that dollar each day: $1, $2, $4, and so on. How long will it take to reach… one million dollars? Not as long as you might think!
Math Curiosity: Primes and Squares
Math Curiosity: Primes and Squares
Can any perfect square be written as the sum of two primes?
Math Curiosity: Legendre’s Conjecture
Math Curiosity: Legendre’s Conjecture
It seems like there’s always a prime number between two perfect squares… but is this always the case!?
Math Curiosity: Finding Primes
Math Curiosity: Finding Primes
Prime numbers are unpredictable! How can we possibly find them all? An Ancient Greek mathematician found one way!
Math Curiosity: Twin Primes
Math Curiosity: Twin Primes
What do you call two prime numbers who are very close together?
Math Curiosity: Palindromic Number Conjecture
Math Curiosity: Palindromic Number Conjecture
Using this one weird trick, it seems that you can turn any number into a palindrome!
Math Curiosity: Collatz Conjecture
Math Curiosity: Collatz Conjecture
The Collatz Conjecture: start with any number and get to 1 using just two rules. It seems to always work…