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Arizona Math Standard: 5.OA.B.3

Generate two numerical patterns using two given rules (e.g., generate terms in the resulting sequences). Identify and explain the apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane (e.g., given the rule “add 3” and the starting number 0, and given the rule “add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence).

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.
Gr 3-5
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.
Gr 2-6
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.
Gr 3-5
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.
Gr 1-5
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.
Gr 2-5
Olympics: Winter vs Summer Medal Count
Olympics: Winter vs Summer Medal Count
Which country has a great balance between their summer and winter Olympic medals?
Gr 1, 2, 3, 5, 6
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.
Gr 2-4
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.
Gr 1-5
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.
Gr 2-5
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.
Gr 1-5
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?
Gr 1-6
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!
Gr 1-4
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.
Gr 3-5
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!?
Gr 1, 2, 3, 4, 7
How Many Ways: Times Equals Minus
How Many Ways: Times Equals Minus
How many different ways can you make this math statement true using only the digits one through nine?
Gr 1, 2, 3, 4, 6, 7
Same Perimeter, Different Area For Rectangles
Same Perimeter, Different Area For Rectangles
Can two rectangles have the same perimeter but… different areas!?
Gr 3, 4, 6, 7
Calculators, Patterns, and Multiplying By Decimals
Calculators, Patterns, and Multiplying By Decimals
Before teaching students the procedure for multiplying with decimals, how much can they intuitively glean from a structured play session with calculators?
Gr 3-7
Math Curiosity: Four Squares
Math Curiosity: Four Squares
Every positive integer can be written as the sum of (at most) four perfect squares!
Gr 1, 2, 3, 4, 8
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!
Gr 1, 2, 3, 4, 7
Math Curiosity: Odds & Squares
Math Curiosity: Odds & Squares
Why does the sum of the first 5 odds also equal 5 squared?
Gr 1, 2, 3, 4, 6
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!
Gr 2-8
Math Curiosity: Primes and Squares
Math Curiosity: Primes and Squares
Can any perfect square be written as the sum of two primes?
Gr 1, 2, 3, 4, 5, 6, 8
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!?
Gr 3, 4, 5, 6, 8
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…
Gr 1-6