# MAA AMC Curriculum Inspirations

I believe in good and deep math, and good math appears in all sorts of places. Here are some essays and videos showing how to take some math from the competition world and bring it to the classroom in a way that a) is relevant and connected to the curriculum, and b) revels in deep, joyous, mulling and flailing, and reflection, and intellectual play and extension, and insight, and grand mathematical delight!

Big plans are afoot for this ever-growing contebt! STAY TUNED!

** CURRICULUM BURSTS VIDEOS**

These short videos get us going on an individual MAA AMC queries. They each have an accompanying essay. (See below).

CB001_Two Trees

CB002_Angles in a Star

** CURRICULUM BURSTS **

These short one-page pieces each present one interesting MAA AMC query, and follow it with a discussion towards its solution and the thinking process behind that journey to its solution. A sampler…

CB001_Two Trees

CB002_Angles in a Star

CB003_Elite Players and Logarithms

CB005_Focus and Directrix

CB006_Areas in Triangles

CB008_Stacking Coins

CB009_Differences of Four Numbers

CB014_Town Population

CB015_Units Digit

CB016_Quadratic Values

CB017_Distributive Rules

CB018_Sums of Powers of Ten

CB020_Two Digit Means

CB024_Frog LeapingCB025_Intersecting Tetrahedra

CB029_Three-digit Reversal

CB031_Coloring a Pentagon

CB033_A Trigonometric Length

**THE TEN PROBLEM-SOLVING STRATEGIES**

These TEN essays each give a detailed description of a problem-solving strategy, illustrated through the process of actually solving an MAA AMC problem. All the supporting videos mentioned in the essays are linked here.

MAA_AMC_Inspiration_Letter 1_2012

TOPIC: A 12th-grade question about incircles to triangles.

PROBLEM SOLVING TECHNIQUE: Successful flailing. Go with what you know.

TANTON’S TAKE-AWAY: How to go beyond what the author suggests. Be in charge of your own mathematics!

LINKS TO CURRICULUM VIDEOS:

Incircles and Circumcircles for Triangles

Tangent Lines to Circles

Pythagoras Galore!

MAA_AMC_Inspiration_Letter 2_ 2012

TOPIC: A scary-looking 12th-grade question about algebra and equations and biggest values.

PROBLEM SOLVING TECHNIQUE: Do something!

TANTON’S TAKE-AWAY: How to see the “big picture” of things.

LINKS TO CURRICULUM VIDEOS:

Proving the Reflection Property of an Ellipse

MAA_AMC_Inspiration_Letter 3_ 2012

TOPIC: An 8th-grade question about numbers raised to integer powers.

PROBLEM SOLVING TECHNIQUE: Go for “wishful thinking!”

TANTON’S TAKE-AWAY: Let go of the need for speed.

LINKS TO CURRICULUM VIDEOS:

Explaining Tricky Exponents

MAA_AMC_Inspiration_Letter 4_ 2012

TOPIC: An 8th-grade question about ratios and fractions.

PROBLEM SOLVING TECHNIQUE: The power of drawing a picture.

TANTON’S TAKE-AWAY: Think visually, even in mathematics. (Many mathematicians do!)

MAA_AMC_Inspiration_Letter 5_ 2012

TOPIC: An 10th-grade combinations question

PROBLEM SOLVING TECHNIQUE: Solve a smaller version of the same problem.

TANTON’S TAKE-AWAY: Let’s think about the mathematics education culture we have.

Prototype VIDEO: Technique_Solve a smaller version

LINKS TO CURRICULUM VIDEOS:

On Teaching Permutations and Combinations

MAA_AMC_Inspiration_Letter 6

TOPIC: An 8th-grade distance/time graph problem with connections to 9th to 12th grade topics too!

PROBLEM SOLVING TECHNIQUE: Eliminate incorrect possibilities.

TANTON’S TAKE-AWAY: To model problem-solving… let go of being the expert!

LINKS TO CURRICULUM VIDEOS:

A Brief Introduction to Parametric Equations

MAA_AMC_Inspiration_Letter 7

TOPIC: A 10th-grade geometry question, making good use of area formulas and algebra.

PROBLEM SOLVING TECHNIQUE: Perseverence is key.

TANTON’S TAKE-AWAY: We can model the multi-week research process in the classroom!

LINKS TO CURRICULUM VIDEOS:

Do you believe the area formula for a triangle?

MAA_AMC_Inspiration_Letter 8

TOPIC: A 10th-grade question about factoring.

PROBLEM SOLVING TECHNIQUE: Can we second-guess the author of the question?

TANTON’S TAKE-AWAY: It is okay to be honest and open when parts of the curriculum are contrived.

LINKS TO CURRICULUM VIDEOS:

Divisibility Rules Galore!

A serious question: Are Factor Trees Unique?

Polynomials and the Reverse Galley Method

MAA_AMC_Inspiration_Letter 9

TOPIC: An ALGEBRA II question to explore after factoring polynomials.

PROBLEM SOLVING TECHNIQUE: Avoid Hard Work!

TANTON’S TAKE-AWAY: We can actively teach the art of “Thinking Berfore you Leap”

LINKS TO CURRICULUM ESSAYS:

A Few Assessment Thoughts

MAA_AMC_Inspiration_Letter 10_ 2013

TOPIC: A 10th-grade question about average counts of birth months.

PROBLEM SOLVING TECHNIQUE: Go to extremes! Ask something absurd!

TANTON’S TAKE-AWAY: “Passive” mathematical concepts can take an active role in discovering real-world results!

LINKS TO CURRICULUM ESSAYS:

The Pigeon-Hole Principle