Math
When A Math Puzzle Isn’t Very Puzzling
It looks like a fun puzzle. But it’s actually just a low-level worksheet in disguise!
Fixing my “Think Like A Statistician” Frame
I used a Depth and Complexity Frame like this with my math students. Let’s look at how we could improve this. Some problems: It asks four unrelated questions. I want to build a sequence of questions that climbs Bloom’s Taxonomy. Most of the questions are naturally answered with “yes” or “no” or a list. Questions […]
Updating Old Questions: Addition With Missing Pieces
How can I go beyond asking 20 variations of 622 + 77 = ___?
Updating Old Questions: A math question that’s TOO high level?!
What happens when we ask a math level that scares off 83% of our students? Don’t lower the ceiling! Lower the floor through scaffolding.
A Math Question That Moves Around on Bloom’s
I was aiming for engagement rather than higher-level thinking.
Healthy Donuts!? Framing a Math Project with a Big Idea
Instead of jumping straight to calculations, what if we framed this math concept with a big idea?
High Level Thinking in Math
When differentiating for my most brilliant mathematicians, there are two traps I fell into: Just making it harder. (Use more numbers or more steps.) Turning it into an art project. (Design a bedroom!) On Bloom’s Taxonomy, my math tasks always maxed out at Apply or would leap away to a fluffy creative task. I think […]
Strategy Game: Sprouts
With Sprouts, students draw a small set of dots and then connect those dots with lines. The first person who can’t make a connection loses.
Math Game: Heaps
Heaps is a lovely math-y strategy game that requires no more than paper and pencil to play.
Just How Much Pasta Could I Cook…
So, just how much pasta could I cook in an Olympic-sized pool?
Which is longer: a Ray or a Line?
Let’s move beyond memorizing definitions and get kids grappling with the fascinating concept of infinity!
Universal Themes in Math? With Fractions!?
What if we used a universal theme to guide our study of fractions? These very big ideas get students thinking about fractions in a new way.
Using a Classic in Math!?
According to Costello, 7 × 13 = 28. In fact, watch him prove it…
Could we fit 1,000 kids on the playground? 10,000?
If your students can find the area of a square then, armed with Google Earth, they can also figure out how many students you could pack into your school’s playground.
Fizz Buzz – A Divisibility Game
Here’s a quick to learn but difficult to master math game. Start with some basic divisibility rules, but then feel free to extend it to any math topic.
The Coloring Problem
How few colors can you use to fill in a map so that no neighboring regions are the same color?
Thinking Like Equivalent Fractions
Go across disciplines by asking students to write a story about fraction equivalence.
Calculating the Volume of Laptops
So once your students can calculate volume… what do you have them do next? In this math project, kids will look up historic laptops, calculate their volumes, and note how technology has changed over time.
Fill ‘er up with Clam Chowder!
Sure gasoline seems expensive. Until you try to fill your car up with other liquids!
Making Awful Graphs
Sometimes we can learn a lot by doing something the wrong way. Here are six ways your students can purposefully design awful, misleading graphs.
Creating A New Mathematical Operation
Do your students realize that addition, subtraction, multiplication, and division are all examples of the same idea: an operation? And that it’s quite possible to create a brand new operation? Let’s do it!
The Surprises Within a Triangle’s Angles
Discovering what is interesting and unexpected about a triangle’s angles. What twists have I unintentionally spoiled for my students over the years?
Make A *Better* Calendar!
The calendar is a source of fantastic factoring problems with many social studies add-ons. Why 12 months? Why 30 (or 31 or 28) days? Why are weeks 7 days long? Why don’t they fit into the months (or the year!)? Why did we do this to ourselves!?
Differentiate Math: Getting Started
Working with a student who is bored in math? Quickly finishing lessons? Needs something more? Here are three ways you can get started differentiating in math.
Depth and Complexity: Ethics… In Math!?
The Ethics prompt of depth and complexity fits so easily into the humanities… but what about ethics in math?!
What if you lived in Vegas but worked in San Francisco?
Is it possible to save money by commuting to San Francisco from Las Vegas?
Prime Number Explorations
Students learn about prime numbers early in their careers, but the true, quirky nature of these numbers isn’t really explored unless kids go on to become math majors. Here are three fun prime explorations suitable for even young students.
Encourage Curiosity With Calculators
It’s easy to fall in love with chasing the newest technology to use in the classroom. But sometimes, the perfect tool is a plain old calculator. We’ll be using this tool to develop curiosity about math.
Exploring Palindromes in ELA and Math
Palindromes are one of those fun ideas that some gifted kids just latch onto. We’ll check out palindromic words, phrases, and even numbers in this article.
A Millionaire By Doubling Pennies
How long will it take to get a million dollars if you start with a penny and double it?
Olympic Medal Math Project
In the paper, I read about Norway’s dominance of the Winter Olympics, despite being a tiny country. I love this juxtaposition of unexpected data! Let’s turn it into a math project. Here are some questions I thought of…
Math Project: Shrinking Airline Seats
What kind of math project could you build based on the shrinking dimensions of seats on the Boeing 777?
Goldbach’s Conjecture
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.
The Collatz Conjecture
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…
Why Pi?
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.
Big Gifts, Small Prices
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!
Mathematical Curiosities
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.
Conflict and Quadrilaterals
Rather than merely asking “what patterns are there in these quadrilaterals” we’ll set up an exploration of conflict and quadrilaterals.
Math Project: Box Office Totals
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.
Math Project: Disneyland Parking Structure
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!
Math Game: The Game of 100
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.
Differentiate Math with Inductive Learning
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.
Constructing Meaningful Math Projects
Here are four key attributes I look for when developing math projects: juicy data, interesting conflict, an expert’s lens, and a final product.
Explore Geometry: Area and Perimeter
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.
Math Project: Furnish A Hotel
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.
An Inductive Exploration of Linear Graphs
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.
Exploring Circumference With Famous Circles
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!
Math and Novelty: What if we didn’t have 10 numerals?
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.
To Show Or Not To Show Work In 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.
An Apple Stock Math Project
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?”
Solving An Authentic Classroom Problem: The Desk Arrangement
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.