Virtual Filing Cabinet

Click on these links to go to the topic
List of Virtual Filing Cabinets
Algebra II
Multivariable Calculus
Algebra I
Good Problems
First Day of School Ideas
Atmosphere Builders/Good Classroom Ideas
Ways To Start Class
(Group) Activities [Not Based On Curricular Topic]
Assessment/Feedback Ideas
Middle School

[Note for Sam: Last updated 1/2/2013]

Virtual Filing Cabinets

Our sporadically updated but rich (if you browse) wiki for our MTBoS community 

For SBG info for beginners, go to the SBG wiki

Take It To The Limit’s Virtual Filing Cabinet for high school courses, techniques, and great classroom ideas, etc.

KFouss’s Precalculus, Algebra II, and Algebra I Virtual Filing Cabinets

Mr. Kraft’s (Many Topics) Virtual Filing Cabinet

Bowman Dickson’s Calculus and Teaching Strategies Virtual Filing Cabinet


Algebra II

Number Lines, Intervals, and Sets

@ffeldon’s use of wolfram alpha to investigate real numbers (solns here)


Ms. Cookie’s Real Life Inequality — Phone Plan & Text Messaging

MathsClass’s exercises on 1D inequalities using Geogebra

Sarah’s inequality bingo!

Polynomials/Polynomial Addition/Subtraction/Multiplication

Kristen Fouss’s awesome Geogebra/Polynomial project

Rational Expressions / Rational Equations

Kate Nowak’s Speed Dating Game with Rational Expressions

Kate Nowak’s Graphical Introduction to Rational Expressions/Equations

Megan Golding’s Solving Rational Equations Project and How Long to Fill The Sink WCYDWT video

Rudy Perez sent me these awesome circuit questions (1, 2) which convert to rational equation questions

@ffeldon’s use of wolfram alpha to investigate rational equations (solns here)

George Woodbury’s little story to help students remember how to add rational expressions

Adam Glesser’s method of adding fractions without like denominators (useful for rational expressions too!)

Mimi’s pointer to NCTM’s worksheet on Rational Equations

Cheesemonkey’s Rational Expression Treasure Hunt


Kate Nowak’s Radical Operations Row Game (read about them here)

Radical Equations / Absolute Value Equations

@ffeldon’s use of wolfram alpha to study radical equations (solns here)

@k8nowak’s use of “error” to draw the absolute value curve, and talk about how it is a distance – gives it meaning

Sam Shah’s worksheet motivating Absolute Value Inequalities

Sam Shah’s method of introducing Absolute Value misconceptions

Kate Nowak’s use of a numberline to give another understanding to absolute value equations

rdkpickle’s way to talk about equations with rational exponents (“is there a shortcut here?”

Factoring / Polynomial Multiplication

Mr. D’s Factoring Quadratics Bingo Game

Mr. D’s Polynomial Multiplication Matching Game

Dan Greene’s Factoring Trinomial’s Game

Math Tales from the Spring’s method of multiplying polynomials: The Claw (is the law)

Maria Andersen’s Factor Pair Block game

Lisa H, at the end of this post, poses a rich question for kids involving factoring (so scroll down already!) — “Find coefficients for x so that you can factor the trinomial x^2 – ?x + 12”

JD2718’s way to help kids remember that (a+b)^2 is not equal to a^2+b^2

Amy’s chart to help students think about a “process” to factoring, rather than think of only a hodgepodge

Simplifying Radical’s game to teach factoring (and the quantitative results of the game)

CalcDave’s awesome way for students to remember the sum/difference of cubes (not SOAP)

Exponent Rules

Social Mathematics’s Mnemonic for an Exponent Rule

Dan Greene’s Error Analysis Worksheet for Power Equations

David Cox’s introduction to fractional exponents — start ’em off guessing and thinking and reasoning based on the rules they know

Kate Nowak’s introduction to the cube root function (careful, though, about how to talk about negative numbers under the cube root function)

*A website which helps kids practice their exponent rules.

Maria Andersen’s Exponent Block “tictactoe-esque” game

Mimi’s gentle introduction to the concept of exponent rules

Paul Solomon’s excursion into the concept of exponents (and their sheer power to make things huge or small)

Mimi’s differentiated around-the-room activity on exponent rules

Simplifying Radical’s exponent rules game

Function Notation / Function Basics / Composition of Functions / Piecewise Functions / Domain Range

Kate Nowak’s Combining Functions Row Game (read about them here)

Ms. Cookie’s Way to Set Up Piecewise Functions

Sean Sweeny’s Cute Way to Drive Home Function Notation

Dan Greene’s Worksheets on Function Notation, Operations, and Multiple Representations

Sam Shah’s Domain and Range Meters

Kristen Fouss’ Piecewise Function Worksheet that goes with using CBLs

Let’s Paly Math’s Function Machine Game

MizT’s Function Dice! (To practice + – * / and composition of functions.)

Mimi’s Piecewise Function worksheets (basic) and Income Tax as Piecewise Function Unit

Sam Shah’s guided worksheet introducing Piecewise Functions

I Hope This Old Train Breaks Down’s word problems for composition of functions

I Hope This Old Train Breaks Down’s introduction to basic operations (+ – * /) on functions and what it does to their domains (focus on multiple representations)

I Hope This Old Train Breaks Down’s use of a Pringle’s Cannon to model quadratics

Bowman’s way to help kids understand the idea of piecewise functions (make the idea “sticky”)

Amy’s use of color coding for piecewise functions

Mrs. H’s baggie of cards to introduce functions

Mr. H’s staple/stapleremover to illustrate the idea of a composition of a function and inverse … that doesn’t quite work (good question for class: why doesn’t it work?)

enzuber’s two ways to introduce functions

Mimi’s method of introduction function notation / the idea of a function as having an input-output relationship

Mimi’s introduction to function composition (using pancakes as a memory/make-it-sticky device)

enzuber’s introduction of inverses using the meat machine!

Mr. H’s simple but effective way to have kids see the inverse as the flip over the line y=x

Mathcoach’s introduction to composition of functions via “ESP”

Sarah’s introduction to functions

Lisa’s introduction to piecewise functions

Lines / Systems (some of the lines stuff is good for middle school)

Kate Nowak’s Lines activity

Dan Meyer’s WCYDWT Dan and Chris exploration

Dan Meyer’s WCYDWT Apple iTunes question

Dan Greene’s Method for Students to Remember how to Graph Lines

Jackie B’s Error Analysis in Systems of Equations worksheet

Mr. K’s Slope-Intercept Joke Worksheet

Ms. Cookie’s Trick to Remembering No Slope, Zero Slope, Positive Slope

Sean Sweeny’s Slope Song and Trick to Remembering Undefined Slope

David Cox’s Farming Project (very intensive, would have to seriously commit to doing it) and notes on vertical motion problems (including some applets)

@ffeldon’s use of Wolfram Alpha to investigate linear inequalities and basic lines (solns here)

Dan Greene’s awesome AWESOME worksheets for systems of linear inequalities!

Jackie B.’s systems of equations worksheet which highlights “multiple representations”

David Cox’s geogebra applet with racing cars! to get students thinking about lines as systems

David Cox’s quick check in to see if students “get” lines – by answering the questoin “is the point on the line?”

David Cox’s introduction to the standard form of a line

David Cox’s activity with toy cars to collect data and have students make predictions (data is linear-ish)

Dan Meyer’s Up the Down and Down the Up, and Up the Up and Down the Down,  Stairs — exploit linearity?

Mimi’s use of shapes to make the concepts undergirding substitution and elimination for systems of 3 variables clear

Kate Nowak’s very rich rectangle problem  to have students think about lines, graphs, points.

Kate Nowak’s really simple, really rich line review for students in Algebra II

Mrs. H’s Linear Functions Review Book

I Speak Math’s graphic organizer for lines (useful for Middle School)

Allison Krasnow’s review stations on lines (useful for Middle School)

Math Coach’s post on Slope and the ADA

I Speak Math’s use of foldables for word problems involving lines

I Speak Math’s slope foldable

Fawn Nguyen’s middle school activity on slope (that would be okay for high school too!)

Dave Cox’s awesome, rich question involving lines, boxes, and slope

Mathcoach’s use of bubble wrap (and popping) to get kids to compare slopes/speed of popping (also: related/extension)

Math Tales from the Spring’s simple use of boxes to make systems of equations more “real” and a bit more compelling

Math Tales from the Spring’s Systems of Equations flipbook

I Speak Math’s awesome Barbie Bungee Project (linear equations!)

Infinite Sum’s “What’s the equation of this street on this Google Map?”

yofx’s “Half Your Age Plus 7” dating guide

Math Tales from the Spring’s linear inequality card sort

Optimization Problems

Geogebra applet for the Box Folding Problem

Jackie B.’s contest for who can make the maximum volume for a box class

David Cox’s decision to let kids explore basic optimization problems yields innovative approaches

Fawn Nguyen’s use of popcorn to motivate the box folding problem

Complex Numbers

John and Betty’s story motivating imaginary numbers

Megan Golding’s “Complex Number Blackjack”

ThinkThankThunk has his students programming the Mandelbrot Set


Nick Yate’s Quadratic Equation Puzzle

Sam Shah’s Unit on Completing the Square

Sam Shah’s Unit on Linear and Quadratic Inequalities (1D and 2D)

Dan Meyer’s WCYDWT Basketball In The Hoop? exploration

Dan Meyer’s WCYDWT Projectile Motion exploration

Dan Meyer’s WCYDWT EXIF picture

David Cox’s Quadratics Unit and finishing it off with Vertical Motion

Sean Sweeny’s M&M Catapult Part I and Part II

@ffeldon’s use of wolfram alpha to investigate quadratics (solns here)

Ms. Cookie’s basic quadratic equations review worksheet

David Cox’s use of a golf applet to talk about quadratic (and linear) motion

Riley Lark’s use of pendulums to talk about quadratics

Mr. K’s check in worksheets to see if students understood the basics of the graphs of quadratics

KFouss’s Leprechaun Complete the Square “game”

Sean Sweeny’s use of Angry Birds and Geogebra to play with Quadratics

Mr. Reid’s great pictures of quadratics / center of mass

Kate Nowak’s introduction to Completing the Square

Sam Shah’s revised quadratic stuffs (quadratic inequalities, finding the vertex conceptually, angry birds!)

Mimi’s use of geometry to help kids with completing the square

Regressions (Linear/Quadratic)

Kate Nowak’s Cry for Help on Regressions, and the recommendations

Sam Shah’s Pendulum Lab Part I and Part II

Ms. Cookie’s Linear Regression Poster Project (and her projects)’s reminder that correlation is not causation (for correlation coeffient)

I Speak Math’s use of student collected data and mystery guests to do linear regressions

MathsClass’s toy car for generating data for a linear relationship

Mr. Reid’s use of Anscomb’s Quartet to talk about the correlation coefficient

Faun Nguyen’s barbie jumping!

Use this chart to create a good assessment question about linear regressions (and the meaning of coefficients/constants?)

Function Transformations

Sam Shah’s Function Transformation Unit

Sam Shah’s Cheapest Movers Step Function Question

Dan Greene’s Worksheets on Function Transformations

Megan Golding’s Family Functions Scrapbook

Mr. D’s Parent-Baby Function Mini-Poster assignment

enzuber’s visit to the function zoo (and use of geogebra in the classroom)

Exponential Functions

Kate Nowak’s Exponential Growth and Credit Cards worksheet

Sam Shah’s Exponential Functions Unit

Sam Shah’s Moore’s Law analysis

Sam Shah’s Supreme Court Case which involved Exponential Functions

@ffeldon’s use of wolfram alpha to investigate exponential functions (solns here)

Mr. Anderson’s analysis of Rent-to-Buy

Scott’s use of paper folding to investigate exponential functions

Julia Tsygan’s sorting activity for simple and compound interest

Logarithmic Functions

Kate Nowak’s Logarithm War Cards

Kate Nowak’s use of “Power” to introduce Logs

Sam Shah’s post on Logarithms and the Richter Scale

JD2718’s awesome warm up logic puzzle to get students thinking about logs, before introducing them

@ffeldon’s use of wolfram alpha to investigate logarithms (solns here)

Rebecca Zook’s post on a trick to remember logarithm notation

Riley Lark’s activity involving music/sound to investigate exponentiation and logarithms

Natural Math’s use of family trees to gently introduce the concept and need for logarithms

Mr. Reid’s “loudest sound” analysis (using logarithms)

Julia Tsygan’s method for introducing logs and applications

Kate Nowak’s grounded and concrete introduction to logarithms and log laws

Square Root of Negative One’s logarithm and exponent dominoes game

GL(s,r)’s mnemonic for remembering the log laws

Square Root of Negative One’s “loops” for logs (remembering how to convert between logarithmic and exponential equations)

Brokelyn’s use of logarithms to figure out how loud a concert is going to be (someone make a lesson out of this and post it in your blog!)

Math Mama’s excellent rich task for students who have learned a bit about logs — Building Log Equations

k8nowak and cheesemonkeysf’s translation of Napier’s original text on logarithms

Mr. Reid’s reminder about Logarithmic Scales and why they are useful

Math Teacher Mambo’s list of problems involving logarithm applications

Math Teacher Mambo’s investigation on planet distance and logarithmic scale

Old Math Dog’s update on Kate’s Log Wars

Math Hombre has a twitter discussion on logarithms

How Reddit uses logarithms to calculate how “important” a page is in their page ordering

Direct and Inverse Variation

Matthen’s beautiful illustration of the inverse square law using spheres

Sarah’s introduction to direct variation 


Pat B’s simplistic explanation of standard deviation as the mean distance

Sam Shah’s use of digital cameras to talk about histograms

Pat noticed that the Normal Distribution can visualized by use of a door!

I Speak Math’s A Human Box and Whisker Plot (good for Middle School)

Bowman Dickson’s list of where he gets his favorite data from


CalcDave’s most awesome Calculus Questionnaire, for all students starting calculus

Study of Change’s way to get kids to remember ideas/concepts from precalculus on the first day

Broken Airplane’s Android App for collecting motion data (need to find a lesson plan around this! so cool!)

Andrew A.H. Alexander has a way with explanations, and this is his set of pdfs for Precalc and Calc handouts

A beyond eminently decent free calculus textbook with some good problems/short activities


Sam Shah’s Who Invented Calculus: A Webquest

SquareCircleZ’s transcription of Newton’s original text on integration


Sam Shah’s excursion on sin(1/x)

Mr. H’s Comic Guide to when Limits Exist

Think Thank Thunk’s intro to the need for limits (basically, starting fresh with derivatives to motivate limits)

Think Thank Thunk’s use of a radar speed gun to talk about limits and infinitessimals

Sam Shah’s use of limits (and systems of equations) to find all points on a funny looking curve (idea: maybe  have students make this drawing first with a few lines… then add more… then add more… then add more… until they see that they need two “infinitely close together” lines to get a point on the curve)

Irrational Cube’s writing prompt for a limiting geometry problem

Bowman Dickson’s class to identify and cure misconceptions on limits and holes (and Cheesemonkey’s analysis of it)


Sam Shah’s post on the Intermediate Value Theorem

Kate Nowak’s post on the Intermediate Value Theorem

Bowman Dickson’s post on the Intermediate Value Theorem

Basic Derivatives and Meaning of Derivatives

Built on Number’s story of how the decay of Radium can be used to detect forgeries

Robert Talbert’s investigative packet using Wolfram Alpha to discover basic derivative rules

Think Thank Thunk’s use of Logger Pro to motivate the power rule

Jason Dyer’s Q-bert based lesson on the binomial theorem (needed for the derivation of the Power Rule)

Maria Andersen’s Power Rule Format and Multiple Derivatives card games (page here)

Sean Sweeny’s geogebra applet and investigation on what a derivative is (leading up to limit definition)

I Hope This Old Train Breaks Down’s introduction to average speed (need to have video to analyze)

Sam Shah and Bowman’s backward planned unit on the relationship between limits and rates of change

Bowman’s memory modeling project (deals more with modeling that derivatives, but it gets students think at least a little about rates of change of memory loss)

Spiked Math’s comic reminder that the zero function is also it’s own derivative!

Bownman Dickson’s “Folding Stories” activity for derivatives

Ashli’s use of polynomial long division to show a connection between a polynomial and tangent lines

Dave’s use of angry birds and the fact that yellow birds (when tapped) shoot of a tangent — so students come up with a piecewise function that has continuity!

Bowman Dickson’s use of drawing to help kids understand conceptually/visually the idea of rates of change (graphs and numbers have concrete instantiations using this idea)

Exuberant’s use of Polly the Parrot to talk about calculus and polynomials

Bowman Dickson’s use of graphing to “discover” the power rule (but not prove it)

MathClass’s foldable for rules of differentiation (including product/quotient/chain rule)


Bowman Dickson’s use of stock market graphs to make predictions in the near future (using linearity)

Emily hits upon the notion of error … and how error propagates through equations… this is calculus!

Product / Quotient Rule for Derivatives

Think Thank Thunk’s activity motivating the product rule (answering: when will you ever have the product of two functions?)

Think Thank Thunk’s note that showing the quotient rule as a consequence of the product rule (he teaches product rule, chain rule, THEN quotient rule

Dave’s introduction to tangent at a point using a video of car dashboard

Bowman Dickson’s way to have kids countenance and full on recognize the product rule misconception

Chain Rule

Sam Shah’s “box method” way to teach the chain rule (scroll down)

Think Thank Thunk’s use of gears to teach the chain rule (I’ve never seen this before! Awesome.)

CalcDave’s Inception Chain Rule

Infinigon’s Chain Rule musings

Sean Sweeny’s song about the chain rule, product rule, and quotient rule to the tune of Cee Lo’s Forget U

exzuberant writes about calculus, and links to a powerful visualization of the chain rule in action


Dan Meyer’s Graphing Stories

Frank Noschese’s use of 5 representations to understand a velocity/distance problem

Megan Golding’s activity relating position and velocity graphs with linear and quadratics

Dave’s use of Kobe Bryant video to determine whether a video is a fake (going from position to measuring acceleration!)

Julia Tsygan’s use of graphing stories to start the year in calculus

Implicit Differentiation

Think Thank Thunk’s use of conic sections (and rice krispie treat cones) to motivate implicit differentiation

Sam Shah’s packet which helps kids remember that implicit differentiation has a graphical meaning

Related Rates

Sam Shah’s “Dos Mocas” related rates problem

Think Thank Thunk’s post on motivating related rates using Torricelli’s Theorem

Sam Shah’s (stolen) Related Rates investigation using Logger Pro and a martini glass

Bowman Dickson’s way to really get kids to visualize (and organize their work) with Related Rates problems

Kate Nowak’s extension work on Bowman’s work on Related Rates problems

CalcDave’s use of beakers to talk about related rates conceptually

Dave Martin’s use of related rates to talk about a speed trap

Newton’s Method

Think Thank Thunk’s post on Newton’s Method (via Computer Programming)

Shape of a Graph

SquareCircleZ’s Absorption of Drugs in the Body post

SquareCircleZ’s H1N1 and the Logistic Curve post

Nikki Graziano’s beautiful  “Found Function” photographs and the equations accompanying them

Bowman’s way of helping kids write sign analyses so they make sense and remember meaning

Bowman Dickson’s use of an infection model and the logistic curve to introduce concavity

Sam Shah’s formalizing Bowman’s infection model to analyze the shape of a graph

Bowman Dickson’s project on concavity and population

Optimization Problems

Think Thank Thunk’s motivation for Optimization Problems (Lord of the Rings)

A nice but involved optimization problem from I Hope This Old Train Breaks Down (Sam Shah also blogged about the problem here)

Think Thank Thunk’s excoriation of most standard Optimization problems, but he also promotes the use of graphing technologies (because why the heck not?)

Riley Lark’s beautiful starting place for introducing optimization problems in calculus

Sam Shah’s introductory class on the idea of optimization (without calculus)


Sam Shah’s Worksheets on Introducing Anti-Derivatives

Maria Andersen’s game called “Antiderivative Block!”

Riemann Sums

Sam Shah’s way of organizing information so that the Riemann Sum is easily calculated

Sam Shah’s analyzing error from Riemann Sum worksheet

Think Thank Thunk’s regular but good way to relate Riemann Sums to integrals

Basic Integrals

Think Thank Thunk’s awesome Race Car game to get students to relate integrals and velocity

Maria Andersen’s way of Teaching Basic Integration using Wolfram Alpha

SquareCircleZ’s use of integration when investigating wealth distribution (and the Gini coefficient)

SquareCircleZ’s Tanzalin Method for easier Integration by Parts (in Stand and Deliver?)

Think Thank Thunk’s introduction of the integral of 1/x

Think Thank Thunk’s introduction to the integral of e^x

Mr. H’s graph from Starcraft 2 on the collection rates of resources for Player 1 and Player 2 (update here)

Think Thank Thunk’s trigonometric substitution

Think Thank Thunk’s parabolic arch question (area under a parabola)

Bowman’s awesome project to help kids understand limits of integration and calculate areas between curves

Dave’s very real way to introduce integration with a speeding question (and the post prompting it)

Bowman Dickson’s integration drawing project using Geogebra (and Dave’s assignment for the same project)

Bowman Dickson’s methods to help kids with the trials and tribulations of integration

Sam Shah’s investigation (from NCSSM) on wealth inequality — highlighting the calculus concepts of the trapezoidal rule and the area between two curves [exzuberant does the same!]

Exzuberant’s pictures of things being sliced and diced and more (the hallmark of integration)

Cosmic Latte’s “color of the universe” picture — if you integrate the function to find the average height, you’d get the color!

Fundamental Theorem of Calculus

Amber Caldwell’s awesome calculus wedding, marrying Intragroom with Deriva

Rectilinear Motion (with integration)

Dave’s simple but good project on getting students to grapple with rectlinear motion

Volumes (of Revolution/Cross Section)

Ms. Cookie’s Volume of Revolution Project

Ms. Ashton’s Volumes by Cross Section using play-doh and dental floss

Ms. Ashton’s delicious Diet Coke way of setting the stage for Volumes of Revolution

Amy G’s use of cakes to visualize (yummy!) and measure volumes of revolution

Mr. H’s video of paper stacking, but more importantly, he throws up an idea about giving students two paper squares from a pyramid built from squares (say #30 and #180 out of 200 sheets) and have them calculate the volume of the pyramid. Love the simple idea – and wouldn’t take too much to convert into an activity.

Bowman’s method of drawing pictures of volumes of revolutions so kids understand and remember what’s going on

Bowman Dickson’s use of paper cutouts to help kids visualize volume of integration / cross sections

Surface Areas of Revolution

Differential Equations

Think Thank Thunk’s introduction of differential equations via resistance

Taylor and other Series

Avery’s awesome yet oh so simple way of getting students to understand Maclauren series

Differential Equations

SquareCircleZ’s use of differential equations to study fish population

End of Year Projects

Dave’s Open Ended Project in Calculus

Infinigon’s Calculus Projects for the Festival del Sol

Bowman Dickson’s end of year projects (and his rubric and reflections after they were over) — examples: packing consultant, math of the pilgrimage, twitter followers, 3D solid modeling (and his awesome geogebra instructions)

Multivariable Calculus

Dave Richeson using skewers and rubber bands to make a hyperboloid model

Adam Glesser’s cute way to remember curl and div

Built on Fact’s short exposition on the Mercator Map and Jacobians

Sam Shah’s Multivariable Calculus Projects for 2010/11

Mr. Reid’s lovely center of mass / parabola pictures

Michael Lugo’s probability problem on the expected distance between two points randomly chosen on a sphere

Robert Talbert’s exposition on the origin of the Nabla symbol

Dave Richeson’s small project for students to use parametric curves to make pretty pictures

Mimi’s way to get students to see 3D on a 2D graph (using color)

Andy Rundquist’s lissajous curve maker! using a record player!

Dave Richeson’s nice counterexample with partial derivatives/maxs/mins

Mr. Honner’s vector fields illustration and wind current illustration site

Pictures of Math’s illustration of a magetetic vector field

Mr. Honner’s slice forms to visualize graphs in 3D


Translating the graphs of Sine and Cosine using a Geogebra applet

Kristen Fouss’ applications of trigonometry problems

Riley Lark’s way to introduce unit circle trigonometry without all the abstraction (and Kate Nowak’s accompanying Geometer’s Sketchpad and Excel files)

SquareCircleZ’s use of the “equations of time” to motivate the addition of two trig functions

zshiner’s word problems for Law of Sines and Law of Cosines

Square Root of Negative One’s use of clinometers and trigonometry to measure the height of the ceiling

Ms. Fouss’ story of Sinbad and Cosette to remind students the sum of angles formulae

Pat’s beautiful trigonometric relationship with 30 – 60 – 90 triangles

squareCircleZ’s method on how to find the sine of 1degree exactly (good problem for advanced students once they learn sum and difference formulas)

Mimi’s Unit Circle and Wave Function Project (Part I, Part II)

SquareCircleZ’s posting of the movie “two dots” which illustrate trigonometry using triangles using a really classy song (classy with a c, not a k)

Kate Nowak’s simple question on radians (which I should put on an assessment!)

Fouss’s trig stations for review (war, dice, row game, etc.)

Ms. Cookie’s Law of Sines/Cosines/Triangle challenge problem for PreCalculus students

Ms. Cookie’s challenging clock problem for Precalculus

Mimi’s organizing sheet for sin/cos transformations

Fouss’s story of Sinbad & Cosette to help sum and difference of angle identities

Mr. Honner’s simple but conceptually deep trigonometry question

enzuber’s analogies and other “sticky” ways to think about trigonometry

Fouss’s simple way for students to find the area of triangles via trig

Infinite Sum’s Inverse Trig War

Tina Cardone’s introduction to the law of sines and cosines

FracTad reminds us to use trigonometry outside — to make it memorable (with clinometers)

Mr. Reid’s use of sonic booms and angle of “cone” to measure speed (inverse trig function)

Square Circle Z’s gentle overview of Fourier Series! (click on Fourier Series Graph)

f(t)’s awesome use of moon data to model and analyze a sine curve

Kate Nowak reminds us to derive the angle sum identities


Andrew A.H. Alexander has a way with explanations, and this is his set of pdfs for Precalc and Calc handouts

Probability and Combinatorics

Mr. D’s use of a dartboard to introduce basic probability

Riley Lark’s activity to get students to question the assumptions implicit in standard probability questions

Sarcasymptote’s use of Applebee’s advertisement to talk about combinations

Riley Lark’s introduction of the Monty Hall problem to talk about probability

John Scammell’s use of Mozart’s Dice Game to hook kids into combinatorics and counting

Adam Glesser’s alternative way to represent three intersecting Venn diagrams

matthen’s nice applet illustrating the pigeonhole principle (kids get it intuitively, but having an illustration helps makes thing “sticky” methinks)

Dave Richeson’s  visualization on False Positives

CalcDave’s reminder that we can study the hunger games with probability (two more articles about it here and here)

Mr. Reid’s Russian Roulette probability question

John Berray’s awesome “Shot at Glory” way to start out a probability unit!

Mathcoach’s introduction to probability, with a brown paper bag

Avery has students analyze games with guiding questions after a unit on probability (and also: yahtzee with two dice!)

Think Thank Thunk’s drake equation!

John Scammell’s use of The Amazing Race and a challenge to talk about possible combinations of flags

Mr. Honner posts Birthday Frequency Distribution… I wonder how a student would go about solving the probability of there being at least 2 people in a room having the same birthday with the actual distribution.

misscalcul8’s better way to introduce pascal’s triangle rather than just throwing it at them

Mathing’s use of Jeremy Lin (basketball) to talk about probability

Delta Scape using Pass the Pigs for probability

Series and Sequences

Dave’s great video introducing the concept of geometric sequences

JD2718’s post introducing geometric series via tax

@ffeldon’s use of wolfram alpha to investigate sequences and series (solns here)

Jason Dyer’s Q-bert based lesson on the binomial theorem

Pat B’s beautiful problem that involves special right triangles with infinite series and geometry

Sol’s beautiful proof without words of an infinite sum – rich for class discussion (and what constitutes a proof)

BrainOpenNow’s “box” activity for sequences (linear, non-linear, etc.)

Dan Meyer’s use of a photocopier to introduce the idea of a sequence (geometric!)

Dan Meyer’s skyscraper/domino problem

Mimi’s fractal introduction to sequences and series

John Berray’s use of a 1792 penny to introduce geometric sequences!

Faun Nguyen’s use of shaded circles in circles (pretty!) to introduce series

Math Hombre’s use of box-figures to introduce sequences (any level)

James Dunseith’s use of excel to teach sequences (see explorations #1 and #2)

Fawn Nguyen’s awesome new site on patterns for sequences/series (also good for any visual pattern questions)


Kate Nowak’s Systems and Matrices Row Game (read about them here)

Sam Shah’s Matrices & Social Networking Worksheet

CalcDave’s awesome method for multiplying matrices


f(t)’s videos bringing vector summation to life

Dave’s activities and a project on vectors

Proof’s beautiful dynamic illustration of the conversion from rectangular to polar coordinates

Polynomial Analysis and Theorems

Riley Lark’s “Painting with Functions” introduction to polynomials and zeros using Geogebra and play

KFouss’s Polynomials Photo Project

KFouss’s wonderful “maximize the volume of a box” activity (complete with building the boxes!)


Sam Alexander’s post on Conic Sections using Lampshades

Square Root of Negative One’s use of Conic Cards to teach Conics! (and follow up)

Math Coach’s use of conics to have students draw pictures (and part II)

Zachary Abel’s way to prove light shining from one focus of an ellipse will end up at the other focus

exzuberant’s use of Miss Anna Parabola to talk about parabolas (in conic form)

Apollonius’s Conics

Rational Functions

Jackie’s investigation of the End Behavior of Rational Functions

zshiner’s mnemonic to remember the important information about a graph


Math Teacher Mambo’s Introductory Matching Game activity for Prisms and Polyhedra

Kate Nowak’s “Example-Not an Example” worksheet on circle vocabulary

Dave Richardson’s relationship between hat size and \pi

Megan Golding’s introduction to converse, inverse, contrapositive using Alice in Wonderland clip

Mimi’s Tangram Project for basic angles, areas, and perimeters

A video on parallel lines cut by a transverse – and learning vocabulary

Math Teacher Mambo’s introductory excursion into Spherical Geometry

Mimi’s Mini Golf Project

Mr. Anderson’s virtual scavenger hunt for Triangles

Mimi’s many worksheets on Angles!

Ms. Cookie’s worksheets on parallel lines and transversals

Kate Nowak’s use of the US Dollar to talk about Special Right Triangles

Mimi’s Slopes and Parallellographs

Mimi’s Angle Pair worksheets

Mimi’s Orthocenter Activity/Cutout

f(t)’s Counterexamples in Geometry

Dan M.’s Geometry (parallel lines and angle bisectors) using Origami

Miss Calcul8’s process of getting students to generate formal definition of geometric shapes

Megan Golding’s schoolwide treasurehunt using school blueprints, Geometer’s Sketchpad, and a triangle

Ms. Cookie’s power of CPCTC worksheets

Ms. Cookie’s worksheet on congruent triangles (or not!)

Maria Andersen’s Polygon Capture game

I Hope This Old Train Breaks Down’s post on proofs in Geometry (and a concrete way to teach them)

Math Teacher Mambo’s introduction to basic right triangle trigonometry

Square Root of Negative One’s SOHCAHTOA’s scavenger hunt activity and Proportional scavenger hunt activity

I Hope This Old Train Breaks Down’s worksheet on the algebra behind finding the circumcenter

I Hope This Old Train Breaks Down’s worksheet on the Law of Sines and Cosines

Math Teacher Mambo’s Is this a Parallelogram?

Mimi’s Volume and Surface Area of 3d shapes project

John Scammel’s use of right triangles to make a radical ruler (cool!) – good way to visualize and compare radicals

Mimi’s Unit Circle cardboard toy that she uses with yarn to illustrate arc length, angles, sectors, etc.

Ms. Cookie’s worksheet on basic geometry notation/terminology

Ms. Cookie’s worksheet on drawing basic geometric figures given basic geometry terminology

Kate Nowak’s short but sweet “if you were a geometric object which one would you be and why?” activity

Justin Lanier’s genius method of introducing the idea of “squareness” and interrogating it (which gets kids to investigate perimeter, area, ratios, etc.)

dy/dan’s (well Malcom Swan’s) activity of having students understand the relationship between perimeter, area, and the impossible… probably for a good advanced class?

Kate Nowak’s activity on tilings and polygons

Math Teacher Mambo’s Magic Hand with Transversals

Justin Lanier’s Introduction to Proofs using Formal Systems

Kate Nowak’s plan for teaching Volume/Surface Area

Ms. Cookie’s special quadrilateral “categorization” sheet

Mimi’s “proof in a bag” activity to help students get started on understanding proofs

misscalcul8’s activity on sorting the types of lines that are in triangles (median, angle bisector, etc.)

Kate Nowak’s introduction to if/then statements (logic statements)

Mimi’s enriching circle/triangle/tangency problems from Japan

Shireen D’s way to help kids remember the properties/angles of the special triangles

Faun Nguyen’s way of investigating area using origami

Proof’s the Spiral of Theodorus (pythagorean theorem and triangles)

Proof’s accounting of how the golden ratio is NOT everywhere

Fawn Nguyen’s geometry project (photographs)

Fawn Nguyen’s activity with a person describing a complex geometric shape to another verbally and trying to get the other person to draw it (and her discovery that geometer’s sketchpad would make it go better)

Mimi’s reminder that estimation is really important for conceptual development (and this was estimation with the area of a circle using a rectangle)

Fawn Nguyen’s dissecting polygons activity

Fawn Nguyen’s awesome use of estimation when talking about volume!

Tina Cardone’s unit on lines and angles and work on parallel lines and transversals

Fawn Nguyen’s “how would we rate/judge if a triangle is equilateral?” class

Proof’s visual “proof” of the pythagorean theorem… could lead to a good discussion of whether this truly is a proof or not

Dan Meyer leads us to an interactive applet which gets kids to think about SAS and AAA

Sarah’s use of color when introducing parallel lines and tranversals

Sam Shah’s logic statements (converse, inverse, etc.) introduction

Sarah’s way to organize information about points/lines/planes and intersections

misscalcul8’s popsicle stick proofs

Dan Meyer has a beautiful 3 Act on area of sectors 

Algebra I

Sean Sweeny’s “adding like terms” is like adding bananas technique

dy/dan’s method of introducing scientific notation

David Cox’s method of getting students to understand and learn the name of basic addition/multiplication properties (e.g. associative)

cheesemonkey’s activities to help students gain numbersense

David Cox’s “unlecture” on having students understand the Standard Form for a line

Molly’s Evaluating Expressions row game

Mr. D’s “alphabet slope” activity (to test understanding of positive, negative, zero, undefined, or nonlinear slope)

Faun Nguyen’s Always Sometimes Never questions (useful for middle school too)

I Speak Math’s graphic organizer’s way to introduce square roots (with cheesits!)

Mimi’s cute pop-up math book project for the end of the year


Good Problems (that don’t fit)

Justin Lanier’s grid problems

Anand Thakkar’s Bridges of Konigsburg problem (also good for Parent Night or first day of school)

Dan Meyer’s problems on rectangles/areas/perimeters (etc.)

Dan Meyer’s problem to start class (game theory/strategy)

JD2718’s really neat equation (useful for precalculus or calculus) to have students analyze/investigate implicitly defined functions (maybe do before conics?)

Brent’s No Monochromatic Rectangles image

Aperiodical’s “Where should we live?” problem

Brent’s disquisition on the divisibility of Fibonacci numbers (and solution)

Fawn Nguyen’s use of making boxes, cutting a cake, etc., for rich problems for varying grades

Epsilon Delta’s good problem on temperature and change in temperature

John Cook’s teaching of Euler’s Characteristics using Dice

mathrecreation’s fascinating investigation into the multiplication table… so simple yet so rich

Tina Cardone’s Fiddle Toy!

Bowman Dickson’s dragon curves

First Day of School Ideas

Kate Nowak’s “snowball” activity

Bowman Dickson’s way to introduce SBG (using Angry Birds)

BrainOpenNow’s first day of class analyzing data


Megan Hayes-Golding’s first day scavenger hunt

Mathy McMatherson’s first day live-blog

Sarah’s first day activity using cards / problem solving

Amber Caldwell’s second day calculator boot camp

MrKent’s first day of school (be different)

Good Atmosphere Builders/Good Ideas

Bowman Dickson’s belief in normalizing and celebrating mistakes/errors

Kate Nowak’s reminder to tell parents something good, randomly!

Cheesemonkey’s use of buttons to promote class atmosphere

Dave’s vow to “Make More Mistakes”

John Berray’s Friday slide on an “outstanding student” 

enzuber’s error monster!

Riley Lark’s 6 ways of showing respect (and of showing disrespect)

Amy Gruen’s use of spoons to ensure kids have pencils!

Math Teacher Mambo’s idea for things to have kids write something positive before the start of an exam (final)

Mathy McMatherson’s Wall of Remediation

Epsilon-Delta’s way to introduce interesting math history in her classroom

I Speak Math’s method of dealing with kids when they don’t have their homework

misscalcul8’s ingenious way to help kids turn words into math (cheesemonkey too)

Bowman Dickson’s Geogebra tutorials

Teaching Statistic’s awesome way to get kids to stop saying “I don’t get it”

Cheesemonkey’s way to help kids with words and math

Bell Ringers/Ways to Start Class

Ashli Black’s most amazing way to start class and activate prior knowledge, get students to talk, and laugh [genius! genius!]

Amy’s recollections of a chant that was used to start class, which I love but don’t think I could pull off (or could I???)

My Favorite No activity (to normalize mistakes and misconceptions)

Bowman’s use of whiteboards with problems clipped to them to start class (here again)

(Group) Activities (not based around specific topic)

The Resolute Instructor’s Exam Prep Activities: post 1, post 2, post 3, post 4, post 5

Ms. Cookie’s Blank Math Joke Sheet

Mr. D’s Jenga test prep activity (suggestion: put #s on each Jenga tile, and have packets with questions numbered to match the Jenga tiles)

Ann Gregson’s group-based accountability-for-all review activity

Kristen Fouss’ trasketball game (played by others too!)

Miss Cal.Q.L8’s group activities to break up the monotony (love the balloon pop activity!)

Riley Lark’s roles for students when they are doing group work

Math Tales From the Spring Star Chain review activity

Math Mama’s Risk Your Knowledge Game

zshiner’s Pair Check activity

Amy G.’s Math Dominos game (and here)

f(t)’s Add ‘Em Up game (and Amy G.’s extension)

Miss Calcul8’s 4 color “game” on calling students in a group activity

Amy G.’s Station Review

Sue Van Hattum’s method of getting kids to decide how confident they are when doing problems

I Speak Math’s Math Hunt review activity

Maria Andersen’s Trinomial Activity Game

Math Hombre’s Linear War game (emphasizing comparing slopes, x-intercepts, and y-intercepts)

Kate Nowak’s use of GoodQuestions and clickers/poormanclickers to generate discussion/debate/instigate ARGUMENTS in her classroom

zShiner’s “math hospital” worksheet idea (to illustrate and correct common errors) — not really a group activity but a good activity

I Speak Math’s MATHO (like BINGO) review game

Bowman Dickson’s Math Taboo game (learning vocabulary words, communicating in math)

Amber Caldwell’s great activities using notecards, like having problems of different levels to get students to practice problems, by playing “52 card pickup.” Also, a wonderful activity where students intentionally solve a problem incorrectly on a notecard at the start of class, and then at the end of class, students get a random card and have to correct the mistake.

Bowman Dickson’s use of mini-white boards to facilitate understanding and groupwork

Fouss’s activity where students made a game as a final project!

Jason Buell’s use of exit tickets in the middle of class (instead of the end)

I Speak Math’s use of picture frames to “spice up” review stations

I Speak Math’s use of differentiated (colorful) review stations

Teaching Statistics’s list of great classroom activities (getting kids to practice practice practice! in class)

Old Math Dog’s review worksheet with a twist!

Megan Hayes-Golding’s end of year vocabulary task to have kids organize the course in their own way

Fouss’s use of geogebra and google forms TOGETHER!

John Berray’s “You can count” all class activity! For fun, and/or to talk about functions and relations

Sarah’s use of foldables for when it makes sense

Tina Cardone’s favorite review games (bingo, basketball, checksum, sequence, smartboard toss, taboo)

Bowman Dickson’s 3 favorite whiteboarding modes (and his thoughts on why it’s good to whiteboard)

BorschtWithAnna’s use of whiteboards (and a second post!)

Fouss’s use of 140 character tweets to get kids to summarize what they took away from a unit

Assessment/Feedback Ideas

Ashli Black’s format for writing quizzes, so she can give good feedback

Cheesemonkey’s first day “grade via this rubric” activity, to show students what you expect

Justin Lanier’s 4 part “extension” to basic skill learnin’

Sam Shah’s formative assessment slips

Megan Golding’s Interactive Notebooks (and part II on grading)

misscalcul8’s use of “summary sheets” at the end of a class

Teaching Statistics’s Algebra II Interactive Notebooks

John Scammell’s core beliefs about assessments

Old Math Dog’s proposed use of homework for meaningful feedback

Julia Tsygan’s summary of scaffolded questions

Sarah’s way to grade interactive notebooks (and how interactive notebooks changed her teaching) (and how to set them up)

Middle School

Approaching Infinity’s Multiplying and Dividing by 10 mnemonic

Sean Sweeny’s “Rainbow Trick” to dividing fractions by fractions (actually, good all the way up to calculus!)

I Speak Math’s method for “Solving for Y” (in 2 step equations)

Math Teacher Mambo’s worksheets on adding and subtracting integers

David Cox’s method for setting up work problems

I Speak Math’s song and dance to solving multi-step equations

Sarah’s use of floorplans for measuring areas… And then using different flooring tiles to take things a bit further.

Fawn’s fraction work using rectangles

John Berray’s “Marshmallow Minute” to teach rates of change and graphing. Awesome idea.

Sarah’s use of messy sorting to talk about how to combine like terms… to make the idea “sticky”

Embracing the Drawing Board’s awesome use of mad-libs to talk about variables and their meaning

Cheesemonkey’s helping kids develop numbersense using an awesome numberline boardgame

Sarah’s use of diagrams/balances for equations (focusing on special case equations with no solutions or all solutions)



  1. I am so happy that my mneumonic device for logarithms made it into your virtual filing cabinet! I’m looking forward into checking out more of these ideas. Thanks so much for gathering them all in one place. I totally know what you mean about trying to find links… ;)

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  3. Hi Sam, you have a lot of great resources here, thank you!! I’m looking or more mathy blogs to follow (came here from Math Teacher Mambo). You have quite a blogroll yourself — I could fit in between f(t) and fuck :-) Will have to check out yours after I finish Ms. Cookie’s list. Cheers!

  4. I was directed to this page from a commenter on my blog. This is AWESOME! Thanks for compiling it, looking forward to starting my own “virtual filing cabinet” and adding to it as well. =)

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  6. This design is steller! You most certainly know
    how to keep a reader entertained. Between your wit and your videos,
    I was almost moved to start my own blog (well, almost…HaHa!) Fantastic job.

    I really enjoyed what you had to say, and more than that, how you presented it.
    Too cool!

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