Raw lesson plans without accompanying reflections:
* Not a blog post, but this link to all my lessons for Grades 7 through 12 from SY2011-2012 from Dropbox might be helpful to someone out there. Also, a link to all my lessons (Alg 2, Precalc, and Calculus) from SY2013-2014.
* Working on CCSS lesson compilation, starting with elementary grades.
General Courses Organization:
* Precalculus organization and two very different ways of organizing Calculus topics. Note: This is only a first-pass brainstorm prior to 2013-2014 year. (Plus, an update on teaching Calculus backwards.)
* IB MYP and IB SL brainstorm of topics and activities on how to teach them. Note: This was only a first-pass brainstorm prior to 2011-2012 year.
* A more general organization of middle-school math topics and what I think is a logical progression of middle-school skills
* An organization of geometry topics by themes, rather than by content.
IB or MYP:
* Introducing internal assessments
* Choosing internal assessment topics
* Making effort transparent to help kids self-select for their own correct IB Math classes
* Successful elements of test-prep, benefits of creating flashcards, how I structure test-prep quizzes, and overview of long-term test prep strategies.
* Giving realistic MYP grades and how I structure grading and assessment
* Video for introducing Type 1 portfolio and other accompanying resources
* Introducing Type 2 portfolio and other accompanying resources
* (Cross-listed with Algebra below) A collection of teaching tips on various algebra topics such as solving equations, proportions, fractions, sequences, and parts of Calculus.
* Geometry magazine assignment and student work!
* 3-D project: description, how it went, photos of student projects, and student calculation work samples. Also, some additional 3-D problems to use for practice or assessments after the project.
* How I scaffolded kids up to doing a quadrilateral trigonometry project. See also here, here, and here for earlier trigonometry word problems lessons that led up to this.
* Mini-golf project and string art project
* Tangram projects
* tessellation example work from my kids, plus why tessellations are geometrically educational and my own examples of artistic tessellations
* Architecture project for finding irregular area and perimeter
* A middle-school fractions project (involving also some geometry)
* Daily activities
* Making a Spiral of Theodorus and tying it into square root algebra practice
* A collection of various proof problems; a coordinate proof project with student work sample; and my general approach to teaching proofs.
* Balancing triangles using centroids
* Scaffolding circumcenter and perpendicular bisector algebra
* Using a walk-around demo to illustrate locus of equidistant points
* A "tried-and-true" kinesthetic method for teaching opposite vs. adjacent sides in right-triangle trigonometry.
* Pringles cannon activity report, and here are instructions on how to assemble it.
* Some nice geometry puzzles
* A reading about tri-lateration and inclinometers or "sextants" and GPSs
* (Cross-listed with Algebra below) Applying algebra to a prism
* (Cross-listed with Probability below) A Salvadoran application of geometry to dividing up cakes evenly
* Open-ended geometric construction explorations
* A bunch of worksheets on angle relationships, parallel lines, transversal, etc.
* Applying parallel and perpendicular slopes to drawing polygons in the coordinate plane. Or, if your students are learning those slopey relationships for the first time, they can explore perpendicular and parallel slopes using the Geoboard.
* Learning orthocenter properties the tactile way
* An alternative to teaching p's and q's
* Some handy tools for tying geometric transformations to music
* Letting kids develop their own way of describing a transformation in the coordinate plane, using a "blind-folded" activity
* Scaffolded snowflakes predictions worksheet for teaching symmetry
* Always, Sometimes, Never True? questions involving points, lines, and planes.
* Using Geoboard and rubberbands to introduce/explore areas inside a coordinate plane
* (Cross-listed with Algebra below) Geogebra lab for exploring midpoint formula and Segment Addition Postulate
* Activity of reading instructions (besides geometric origami)
* First-week geometry activities to get the kids thinking and remembering geometry basics
* Introducing geometry in a kid-friendly way, then visualizing composite areas, estimating circular areas as a way to introduce circular formulas, and thinking about what info we NEED in order to calculate areas.
Geoboard activities and why I think Geoboard is a nice transition between the concrete and the abstract.
* Japanese Geometry problem sets one and two.
* Holiday geometry activities
* An overview of the Hands-On Measurement Unit
* Measurement Unit Lessons 1 to 3 on basic conversions and using similarity concepts and strings+weights to measure heights
* Measurement Unit Lesson 4 on volume formula and conversion between cm^3 and liters
* Measurement Unit Lessons 5 and 6 on Volume conversion practice, plus solid density of regular and irregular objects, plus volume of an irregular container
* Measurement Unit Lessons 7 and 8 on liquid density and net weight
Algebra / Precalculus:
* Projects and Labs:
* GeoGebra unit circle project: Description, how it went, and how it ties into solving simple trig equations.
* Applying rational equations in a resistors lab
* Using the NCTM Laser activity for teaching rational functions
* A parametric equations project in GeoGebra that brought out lots of interesting functions! Examples of student-made math animations and my initial project brainstorm/reasoning.
* Functions pictures project (for Algebra 2) with a writing component
* A buttons sale project for modeling linear patterns
* A socioeconomic research project about indicator statistics.* An idea about an exponential project linking to sustainability (not implemented b/c of time)
* Math pop-up books project for reviewing algebra skills
* Three-variable relationships and how they appear in the real world. Plus, a three-variable investigation project for middle-schoolers, and an in-action update! Set the bar high! Also, a somewhat challenging 3-variable pattern depending on row r and column n.
* Analyzing quadratic motion using Logger Pro
* Retirement project (which went well, by the way! even though I didn't blog an update)
* Daily Activities:
* Using a toy wheel to visually illustrate circular relationships.* Thinking flexibly about the exponential form
* Composition function word problems and an analogy for composed functions .
* (Same link as above) Telephone game for introducing inverse functions
* Using diagrams to visualize function relationships and effects on domain
* Thinking about how to break down function transformations
* Letting kids develop their own graphical analysis vocabulary using a "blind-folded" activity
* Piecewise function and income tax units!! Links to entire units are available.
* Scaffolding piecewise functions so that they're kid-proof!
* Mandatory Salvadoran Christmas bonuses as a piecewise function
* (Cross-listed with Geometry above) Applying algebra to a prism
* A kid-friendly analogy for recursion
* Algebra 1-level activity for teaching the meaning of slope (also good to use as review material in later grades)
* Geometric series word problems
* Interactive Geogebra demo for the beauty of geometric sequence in nature (spiral)
* The beauty and math behind cyclically rotating figures, and my previous ruminations here, here, and here.
* Middle school-level introduction to algebra substitution using visual puzzles and my whole (fairly unique) unit on systems of equations; plus, in response, a clever substitution method developed by my students!
* Using trig to figure out how to maximize viewing angle in a movie theater
* Connect the dots activity for practicing how to graph points
* Quadratic links to other math topics and a fun visual pattern comparison between linear and quadratic growth (and here are the relevant preceding exercises)
* Singing Solo and Quadratic Formula
* Thinking of quadratic factorization flexibly and an exploration of quadratic graphs in terms of flexible factorization.
* Tools for teaching the "sense" of ratios and lines and a profit/revenue application on quadratics.
* Some visual sequences and series problems based on fractals.
* Slowing down on exponent rules in order to help kids make sense of them, and a sneak peek of what it looked like.
* Some super scaffolded lessons on lines, designed for a high-needs, low-confidence student population
* A visual approach to finding linear equations and more follow-up material on using this approach.
* Re-introducing wave equations to students who have seen them before
* Introducing Calculus in the IB and introducing limits .
* Teaching complete the square using geometric visualization, or completing the square backwards .
* Modeling the input-output nature of functions with some dramatic flair
* Using visual organization to increase student understanding of relationships between algebraic concepts such as transformed vs. original functions and derivative vs. integral.
*Introducing equations , focusing on the process of solving equations, moving around while practicing , and finding ways to make introductory algebra fun.
* Some of my favorite Exeter 3 questions and a cute log problem .
* A nice hook when re-introducing wave functions.
* A trick to help struggling kids visualize order of operations .
* (Cross-listed with Numerical Concepts below) Teaching number definitions meaningfully.
* (Cross-listed with Numerical Concepts below) Giving geometric meaning to complex number operations.
* A non-flashy secret for teaching logs
* (Cross-listed with MYP/IB above) A collection of teaching tips on various algebra topics such as solving equations, proportions, fractions, sequences, and parts of Calculus. Plus, some visualization techniques my students find useful.
* Graphically analyzing inequalities and equations to improve algebra-graph connections.
* Discussing with students why choice of function model needs to be sensible
* Two very different ways of organizing Calculus topics. Note: This is only a first-pass brainstorm prior to 2013-2014 year and an update while implementing backwards Calculus.
* A collection of Calculus projects I found on the web.
* Creative problem-solving on rollercoaster project with samples of student work (and more here).
* Daily Activities:
* Introducing derivative of e^x
* Organizing info for related rates problems
* Exploring sine and cosine derivatives based on graphical intuition
Probability / Combinatorics / Discrete Math:
* (Cross-listed with Geometry) Salvadoran lottery system
* How the Allies Used Math Against the Germans with an awesome link in the comments for explaining the math!
* Using student art to motivate combinatorics
* A tactile activity to lead in to combinatorics
* Random entrance fee and expected values
* Math in psychology
* Mathematics of scheduling classes
* A middle-school fractions project (involving also some geometry)
* A middle-school percents project.
* A middle-school survey project, involving proportions, measurement of angles, communication, and making predictions.
* Important elementary concepts from the perspective of a Middle School teacher
* Reasoning about percents using proportional concepts
* Ken-Ken puzzles and math processes in the classroom
* (Cross-listed with Algebra above) A trick to help struggling kids visualize order of operations
* (Cross-listed with Algebra above) Teaching number definitions meaningfully
General Teaching Strategies, Resources, etc.:
* Despite my worry of being presumptuous, I decided to write down my 11 recommendations for middle-ish grade teachers .
* A presentation I put together for AGIS 2013 on using projects as a means to letting kids self-differentiate. (Here are notes about other interesting things I learned at AGIS 2013, such as flexible math grouping.)
* Letter to new teachers and How to keep kids on your side while addressing their misbehavior
* Providing a rubric to help students assess their own depth of understanding (broken down by topics) for the semester.
* Creating videos as review material, with "meh" updates here.
* Playing around with pencasts.
* Getting kids to make their own review videos, with successful updates here.
* On goal-less problems in math
* Structuring lessons as stories
* The impact of incorporating physical gestures into an explanation.
* Incorporating reading into the math class, explicitly addressing weak verbal skills in math, and a great writing project in math. Also, an "average" writing sample from my Grade 8 class (of non-native English speakers).
* Why I still like traditional resource books and a list of recommended resource books, plus a fractals video recommendation.
* About having faith in what you do, not giving up, student apathy, why the work is not really just about the work, remembering that you cannot do it all yourself, making effort transparent, what makes a great teacher, modeling adult reactions, and how to raise effectiveness in the classroom. Also, why exploratory learning matters and ideas on how to help kids transition from lecture-based to constructivist learning.
* What teaching looks like in my classroom, things that I consider, my 3 core classroom values, and how I communicate my teaching philosophy to student parents.
* Conducting course surveys using Google Forms.
* Integrity, more about integrity, choices, resourcefulness, building confidence, meta-cognition, student accountability, persistence, creativity, differentiation, racial identity development in children, and handling conflicts.
* Experiment with letting kids have more say in homework and giving categorical feedback on errors (based on these categories) and assessing by criteria.
* More strategies on building students' confidence with math, an unusual game format and my version of speed games, and a walk-around review activity.
* (Cross-listed with Geometry above) On how to teach a complicated algorithm
* new changes for my classroom in 2011-2012, based on my learnings at Klingenstein Summer Institute (June 2011) and Park City Summer Institute (July 2011).
* A draft of a rubric for assessing a teacher's implementation of the Common Core's 8 Mathematical Practices, as well as a draft of supporting documentation. Also related: a reflection on process vs. content in developing these resources.
* Using mini whiteboards to institute accountability/focus on accuracy and, on the other hand, how to focus on process and normalizing errors.
* Pro-tip: Organizing important handouts by color .
Department Head Considerations:
* People relationship tips, tips on motivating people and leading people .
* Benefits of shared assessments
* Issues of differentiation within a particularly diverse population
* Use of portal
* PD topics that would be useful to our department
* Other possible improvements
* What can we do to support elementary math?
* The process is not easy, but the outcome is worth it!