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Students will try to find a path across this city which crosses each bridge exactly once.
First, students will cross five bridges exactly once.
Next, they’ll try to cross seven bridges one time each. ⚠️ Note: This is impossible.
Students create three maps connecting four cities with seven bridges, aiming for a solution that allows crossing each bridge once.
Students mark the number of bridges connected to each city on their maps to identify patterns that indicate possible solutions.
Students identify which networks allow crossing each edge exactly once, determining the presence of an Eulerian path.
Students will find several solutions for magic triangles of various sizes.
First, students find a solution that adds up to 9 for an order-3 magic triangle.
Next, they find a solution that equals 17 for an order-4 magic triangle.
They revisit the order-3 triangle and find the remaining three solutions.
Students describe four solutions to the magic triangle that add up to nine, ten, eleven, and twelve using specific numbers.
Students will search for patterns of prime numbers within a triangle made famous by Laurence Klauber.
Students build their own Klauber triangle.
Then they highlight all of the prime numbers, looking for patterns.
I reveal a giant triangle and then challenge them to create their own shape to look for prime patterns.
Students will generate an Ulam Spiral, highlight the primes, and note what patterns they see.
Students arrange the first 100 (or so) integers into a spiral.
They will highlight (or circle) only the primes in their spiral, looking for patterns.
Finally, they will either extend their spiral or try to create a new shape or spiral and look for patterns.
Students will search for patterns, patterns, and more patterns within the fascinating Pascal’s Triangle.
Students will look for one pattern in this triangle and then use that pattern to add another row.
After I build out the triangle a bit more, students will search for even more patterns.
I show one set of interesting patterns, reveal the triangle’s name, and then point students towards more resources.
Goldbach’s Conjecture states that, “Any even number can be written as the sum of two primes.” Is it true?
Students will see that any positive integer is also the sum of four or fewer perfect squares.
Students find another solution for 10.
They see how many solutions they can find for 50 – and look for patterns along the way.
They work with 99 and any other number they’d like to explore.
Students arrange integers into squares so that each row, column, and diagonal will add up to the same sum.
Students arrange 1–9 in a 3×3 magic square so every row, column, and diagonal has the same sum.
As an extra hint, I reveal that the sums must all equal 15.
Finally, I reveal the solution and challenge your students to try a 4×4 magic square!
How few colors do you need to color in any map so that no two neighboring regions are the same color?
Students learn how to color maps using different colors for neighboring regions to avoid confusion and reduce printing costs.
Next, students will determine the fewest number of colors needed to fill in a more complex map.
Finally, students are challenged to color a complex map using only four colors or to create a map needing more.
Students will try to explain why the first X odds add up to the same number as X2.
Students find the sum of selected odd numbers and compare it to the square of how many numbers they chose.
Students add odd numbers to show how they form perfect squares and illustrate this relationship with drawings and examples.
Students will explore the unproven Waring’s Conjecture.
Students test Waring’s conjecture by expressing odd numbers as the sum of three primes.
Students search for odd numbers that cannot be written as the sum of three primes.
Students will determine if all perfect squares can be written as the sum of two primes.
Students list perfect squares and attempt to find two prime numbers that add up to each square.
Students color primes and perfect squares in different colors to find unexpected patterns between these two types of numbers.
Students will work with primes and perfect squares to investigate Legendre’s Conjecture.
Students will use the prime sieve to find primes up to 150.
Students will search for special primes and look for patterns along the way.
First, students search for twin primes: prime numbers with a difference of two.
Then, they look for cousin primes: prime numbers with a difference of four.
Finally, they look for prime quintuplets: five primes in which the difference between the largest and smallest is 12.
Turn any number into a palindrome by following these steps…
Students reverse the digits of given numbers and add them to find palindromes.
Students add numbers and their reverses to find palindromes, noting how many steps it takes to reach each one.
Start with any number and get to 1 using just two rules. It seems to always work…