Discrete Mathematics
Self-paced online Discrete Mathematics course (Maths 230). NCCRS recommends 4 semester credits; each college decides how it applies them.
See the course →ColoradoTeachers
Which math courses fit the Colorado worksheet
By the team. Checked 15 Nov 2026.
The short answer
CDE's Mathematics 6-12 worksheet needs 24 hours: 6 in number, algebra and modeling, 6 in calculus, 3 each in geometry, statistics, and history or philosophy of math, and 3 in teaching methods or extra content. UPI Study courses line up with four categories; geometry and history of math need another source.
The worksheet category by category
The worksheet dated 11.30.2024 names the categories and gives course examples for each. CDE makes the final call on where a course belongs.
| Category | Hours | UPI Study course that lines up | Gap |
|---|---|---|---|
| Number, algebra and modeling | 6 | Discrete Mathematics (4) | 2 more hours |
| Calculus | 6 | Calculus 1 (4) and Calculus 2 (4) | None |
| Geometry | 3 | None | 3 hours from a college |
| Statistics and probability | 3 | Principles of Statistics (3) | None |
| History or philosophy of math | 3 | None | 3 hours from a college |
| Teaching methods or extra content | 3 | Calculus 3 (4) as extra calculus | None |
Discrete Mathematics and the calculus sequence
The worksheet lists Discrete Mathematics by name as an example under number, algebra and modeling, along with linear algebra, number theory and graph theory. At 4 credits it covers most of the 6 hours.
Courses such as College Algebra or Pre-Calculus are not on the example list. Ask CDE before counting them toward this box.
CDE asks for a two-course calculus sequence, for example Calculus I and Calculus II. UPI Study's Calculus 1 and Calculus 2 are 4 credits each, so together they pass the 6-hour minimum.
Calculus 3 is named on the worksheet as a calculus-based course. It can fill the final 3-hour slot as extra content if you do not have a teaching methods course.
The two categories you need from elsewhere
UPI Study has no geometry course and no history or philosophy of mathematics course. Plan those 6 hours at a college, through a teaching methods course you may already have, or through the up to 6 hours of documented professional development or work experience the worksheet allows.
- Geometry: modern, Euclidean or transformational geometry at a college
- History or philosophy of math: often an upper-level course at a university
- Documented PD or work experience in a category: up to 6 hours
A sample 24-hour plan
Here is one way to reach 24 hours for a teacher starting with no math on a transcript. CDE makes the final reading of each course, so treat this as a plan to check, not a promise.
- Calculus 1 and Calculus 2: 8 hours toward the 6-hour calculus box
- Discrete Mathematics: 4 hours toward number, algebra and modeling
- Principles of Statistics: 3 hours for statistics and probability
- Calculus 3: 4 hours for the final extra-content slot
- Geometry at a college: 3 hours
- History of mathematics at a college: 3 hours
- Number, algebra and modeling: 2 more hours, from a college course or documented professional development
Filling in the worksheet before you apply
Write each course into its category with the semester hours and the grade, as the worksheet asks. Leave the office column blank. Add up each box, then the total. If any box is short, the application will be short, even if the total passes 24.
Send the completed worksheet with official transcripts from every college that holds a course you listed. Keep a copy of the worksheet and of CDE's written answer about transfer grades with your licensing records, so you can point to them if a question comes back during the review.
Grades and transcripts
Every category needs B- or higher, and pass/fail courses do not count. UPI Study courses count only once a college posts them on its transcript. TESU and UoPeople are partner colleges that consider ACE-recommended or NCCRS-recommended credit; ask them how the course and grade will appear, then ask CDE whether that meets the B- rule.
What to ask in writing
Before you enrol
Ask CDE Educator Licensing in writing whether credit posted by a regionally accredited college through transfer of ACE-recommended or NCCRS-recommended courses meets the B- rule and fits the categories you plan to use, before you enrol.
UPI Study is not a college and is not accredited. ACE and NCCRS review our courses and recommend credit; a college decides whether to give that credit and records it on its own transcript.
ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
Questions people ask
Does College Algebra count on the Colorado math endorsement worksheet?
It is not among the examples CDE lists for number, algebra and modeling, which names courses such as discrete math, linear algebra and number theory. Ask CDE in writing before you count College Algebra or Pre-Calculus toward any category on the worksheet.
Does Calculus 3 count for the Colorado worksheet?
The worksheet names Calculus III as a calculus-based course in the calculus category. Once your two-course calculus sequence is in place, Calculus 3 can fill the last 3-hour slot, which allows teaching methods or 3 more hours in one of the content areas.
Where can I take geometry for a Colorado endorsement?
UPI Study does not offer geometry. Look at Colorado community colleges and universities for modern, Euclidean or transformational geometry, and check that the course is college-level with a letter grade. Ask CDE whether a specific course fits before you register.
Courses that fit
ACE-recommended or NCCRS-recommended courses, studied online at your own pace.
Calculus 1
Self-paced online Calculus 1 course (Math 165). NCCRS recommends 4 semester credits; each college decides how it applies them.
See the course →
Calculus 3
Self-paced online Calculus 3 course (Math 365). NCCRS recommends 4 semester credits; each college decides how it applies them.
See the course →Start when you have it in writing
Settle the B- question with CDE first, then use PRO for calculus, discrete math and statistics.
Sources
- CDE: Endorsement Worksheet - Mathematics (Grades 6-12), 11.30.2024 (official)24 semester hours at a regionally accredited college in six categories, B- or higher in each; up to 6 hours from documented PD or work experience; or a math degree; or Praxis 5161/152 or 5165/159. Checked on 15 Nov 2026.
- CDE: Endorsement requirements (content knowledge) (official)24 semester hours as identified on each worksheet; B- or better in each course; professional development courses and pass/fail not used for the coursework route; added endorsements need an existing valid Colorado teacher license. Checked on 15 Nov 2026.