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Documents to Download



Over time I am committed to compiling and giving away all those documents that have proven helpful to friends and colleagues. Please feel free to download and use the documents on this page for any non-commercial purposes. Also, if there is a document that you would like to see posted here, just let me know so that I can share it with you.

Click on a document title to view a PDF to print or download.

Classical Christian Education



This is my attempt at representing classical Christian education on a single page. The categories appearing on this document also correspond to the Recommended Readings available on my website.

Curriculum Design


Much of my approach to curriculum design has been informed by the principles articulated in Understanding by Design by Grant Wiggins and Jay McTighe. This two-page template has proven to be a simple but effective way to plan units of study in mathematics classes.


I strongly recommend reading all of Wiggins and McTighe's Understanding by Design. This document is a one-page excerpt from chapter five regarding Essential Questions - the foundation of a great unit plan.

Mathematics Samples


This unit is designed for students to develop the following enduring understandings: (1) An equation is a balanced statement that can be manipulated algebraically through the performance of the same operation to both sides of the equation. The most useful operations to perform are those that invert operations already appearing in the equation. When an inverse operation is performed it is common for an identity element, one or zero, to be left behind that simplified the form of the equation and further isolates the unknown; and (2) The same algebraic moves that can be made to solve a linear equation can also be made to isolate a particular algebraic expression in a given equation. For example, the moves you make to solve 5x+9=49 for x are the very same moves you make to isolate the expression (x+4)^3 appearing in the equation 5(x+4)^3+9=49. Click on the unit coversheet link below to view a description of the entire unit then click on the links to the corresponding problem sets and assessments.

Unit Coversheet - Equation Solving

Problem Set 1 - Solving for Boxes Part I

Problem Set 2 - Solving for Boxes Part II

Quiz - Equation Solving

Problem Set 3 - Applications of Equation Solving

Test - Equation Solving

Compare and contrast problem sets 1 and 2 to notice the progression of understanding that develops while students complete these problem sets. Consider the conclusions the students will naturally come to (discover) while they engage in conversations about problems that are similar in form.


In this unit on quadratic equations students wrestle with essential questions like: (1) How are moves used to solve linear equations similar to those used to solve quadratic equations?; (2) What features of a quadratic equation influence the method you choose to solve it?; and (3) Why is the process of completing the square called completing "the square"?Click on the unit coversheet link below to view a description of the entire unit then click on the links to the corresponding problem sets and assessments.

Unit Coversheet - Quadratic Equations

Problem Set 1 - A Re-Introduction to Quadratic Equations

Problem Set 2 - Perfect Square Trinomials

Problem Set 3 - Completing the Square

Problem Set 4 - Completing the Square when the Coefficient of x^2 is Not One

Problem Set 5 - Deriving the Quadratic Formula

Problem Set 6 - The Discriminant

Problem Set 7 - Applications of Quadratic Equations

Problem Set 8 - Mixed Practice Solving Quadratic Equations

Test - Quadratic Equations

Notice that I had trouble composing the Enduring Understandings (EUs) for this unit plan (they are missing in the UbD-based unit plan). While not ideal, I confess that sometimes I compose a unit plan and develop the EU's along the way. Nevertheless, this unit proved to be successful in developing a repertoire of equation solving techniques as students encountered increasingly challenging quadratic equations with features that called for new techniques.


This syllabus includes a content outline with both Essential Questions and Enduring Understandings composed for each unit of study. Beginning a course with a syllabus like this already composed can help you maintain focus and good pacing while also reminding you of the deep understanding you are trying to lead students into.


I created this document to supplement a section titled 1.5, Inverse Functions in Sheldon Axler's marvelous book, Pre-Calculus: A Prelude to Calculus. This has always proven to be a difficult concept to teach within the bounds of a normal class period. I share this document with students as an extra resource that they can read through with the hopes that it will add clarity not confusion. Click on the title in red above to view the PDF.

Professional Development


New teachers should receive a formal observation by their supervisor once each semester for at least the first two years of employment. Thereafter, formal observation should be regular but less frequent. I have been using a template like this one for many years to conduct formal observations of teachers' classrooms. Teachers have appreciated the dynamic and collaborative nature of this documentation process.


A teacher should regularly observe his/her colleagues for the primary purpose of improving his/her own instructional practices but also for the purpose of offering valuable warm and cool feedback to those observed. This two page guide includes a list of questions that a teacher can select from to help focus a classroom observation on just a few items. I suggest that upper school teachers commit to observing one classroom period at least once per month. For lower school teachers, it is best to schedule a half or full-day sub for the teacher so that he/she can observe several teachers on the same day. I suggest that this happens at least once per semester.

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