Our look at math conjectures continues with Goldbach’s Conjecture, which states that all even integers greater than 2 can be written as the sum of two primes. Is this true for all cases? Another authentic, unsolved question.
Content Area: Math
A “conjecture” is an idea that is believed to be true, but has not yet been proven. They are authentic unanswered questions for students to explore. The Collatz Conjecture uses two simple rules to get from any number to 1. It seems to work for all numbers…
Pi Day is just around the corner, but the typical fare include π art projects, memorization challenges, or other activities that separate π from its real uses. But π is such a fascinating topic that it should inspire curiosity and wonder on its own.
What if you want to buy a big gift that’s cheap for its size? By calculating the volume of the object, we can find how much each cubic inch costs. Measured by price per volume, Thomas is 250 times more expensive than a big outdoor slide!
Sometimes you encounter that math student who is simply interested in numbers. Here are some famous (and not so famous) sets of numbers that have curious properties.
Struggling math students shut down when they’re smacked with a mouthful of academic vocabulary right away. So lower the barrier of entry. Ask students to identify the conflict between two shapes, rather than defining “congruent sides” and “bisected diagonals.”
As a teenager, I loved monitoring the weekend’s box office results. This kind of data is exciting, oozing with built in conflict. It sets up questions that require math to answer.
Let’s develop a math project to challenge students who have demonstrated a mastery of multiplication and are ready to explore its applications. We’ll count the parking spaces in the Disneyland parking structure!
The Game of 100 is a simple game requiring no supplies, yet it opens up a rich world of exploring strategy and a little mental math.
With inductive learning, we still define terms, explain rules, and practice, but the order is different. We’re harnessing gifted students’ natural abilities to enhance our lessons.
Here are four key attributes I look for when developing math projects: juicy data, interesting conflict, an expert’s lens, and a final product.
The problem is that we dive in with formulae before students have their bearings. Let your students get their hands dirty with geometry. They’ve got to play with the shapes and explore. Beginning adders and subtractors work with manipulatives before they delve into abstract arithmetic. Older students are still beginning geometers. Give them a chance to touch the math and have some fun.
Starting with an IKEA catalog, a hotel furnishing math project was born. Use this project as a tool to differentiate your math instruction and impart some practical knowledge on your students.
Let’s play with linear graphing! First, don’t set this up as a direct instruction lesson. That wouldn’t be playing. Instead, capitalize on your students’ ability to think inductively and recognize patterns. Set up a situation where they can construct their own meaning.
Remembering the formulae for area and circumference of a circle is often a challenge for students due to their surface similarities as well as the additional confusion of radius and diameter. I like to tackle them one at a time and give students a chance to explore the origin of each formula. Let’s look at circumference today by utilizing some famous circles from around the world… and beyond!
Looking for some ways to challenge your advanced mathematicians? If you’d like to keep them on the same topic as the rest of your class, consider increasing the complexity of your current unit. If they’re in need of more advanced curriculum to keep their creativity flowing, try to bring in novel ways of looking at math.
We must be careful not to admonish our intuitive learners for being intuitive. As teachers of the gifted, we must set up learning environments that are best for our students. And if they’re doing it all in their heads (and getting it right!), then the environment needs to change.
Entice your gifted mathematicians with real world data and an authentic problem such as: “Let’s say that instead of buying the original iPod, you spent the same amount of money on Apple stock. How much would that stock be worth now?”
How often do you give your gifted students the opportunity to solve authentic, relevant problems? What is more authentic to a student than solving classroom problems? And what excites students more than having ownership over the classroom seating? Here’s an authentic problem solving idea that ties in public speaking skills, group work, and classroom ownership.