Escape Velocity Education


Math Foundation

Math is largely sequential and is very dependent on a firm knowledge of the items that come before it in studies. Consider the studies of Math as a series of interconnected stair steps where without a good support the upper treads fall off.

For example, it is hard to conceive of adding or subtracting if one does not know reliably how to count. It is impossible to really understand multiplication or division if one cannot add. While the concepts of algebraic abstraction can be explained to any first grader without fear; he or she could not really take advantage of the problem-solving capabilities if he or she cannot solve the underlying addition, subtraction, multiplication, or other numeric operation.

One tread that underlies math school work that is often overlooked, but extremely critical is handwriting skill. The student needs to be able to reliably form letters and numbers neatly so that they can be read by a grader or the student at a point in the future when the memory of the problem has faded. If the handwriting is messy and slips between lines, if the letters are indistinct and hard to read, if plus signs and negative signs are not consistently written then the answers will be wrong. If the figures that accompany the math are not done with a straight edge and compass, mistakes will be made.

On level? How can I tell?

If your child is not starting from the beginning then it is important to be sure that he has mastered all of the concepts. There are many options available to confirm how well or badly your child is doing in mathematics.
If your student is in a public school then you might be most comfortable measuring your student's progress against state and local metrics. Be aware that the state tests do not always test to ensure full mastery, but instead a minimal floor of mastery. To be confident in math as a student continues to later steps on a math journey, full mastery of each earlier step is much preferable!

On Level Checking with state testing

Some examples of state test materials that you can use to measure your child's level:
 Texas STAAR released tests
 Virginia's poorly abbreviated Standards of Learning (SOL) has released tests as well
 Alaska's Sample questions
 Washington State uses a program from Smarter Balanced Assessment Consortium to handle assessments

If you are entirely homeschooling and not supplementing, you might want to have your children take a full version of a test such as the Iowa assessments which can be ordered through  Bob Jones University testing.

On Level Checking with State or Local Curriculum Guides

Almost every school district has a curricula guide at the state or local level that discusses what will be taught in each class.
These guides tend to be worded to prevent any misunderstandings to people that already know what is being discussed which can make them annoying to read.
For example,
 Alabama's Math guideline
 Oklahoma Standards
Your neighborhood school might also have links to the local standards and coverage expected for each grade.

On Level Checking with Curriculum Placement Tests

There are a number of math providers for homeschool and classroom use that are familiar with having students transition between different curriculum programs and between brick and mortar schools and home and have assessments to help determine where the student fits. Even if you decide to pick a different program, working through a variety of assessments is useful to point out any gaps or holes in the student's knowledge.

 Saxon Math (Primary to Highschool)
 Math Mammoth (Grades 1-7)
 Singapore Math (Grades K-6)
 Life of Fred(Primary-College)
 Art of Problem Solving (Pre-algebra and up)

On Level Checking by reviewing a curriculum overview

You can get a feel for placement by looking at an overview such as at the  Khanacademy which shows a list of all of the math by grade.

Suggestion for getting started

While you may want to start looking at an overview and see what you recognize from your child's homework, it is easy to make the mistake that recognizing the content indicates mastery. Also, beware of your child recognizing that they have seen the material and claiming mastery. Please, evaluate carefully to see what your child has actually mastered. Be aware that your child's mastery may be on grade-level, below, or above. It is easiest if the child has holes in their knowledge or is below level if the program is totally different from their prior materials. Then there is no loss of status in starting a bit below where they test and working from there to ensure a solid foundation.
For evaluation of their knowledge and mastery I strongly suggest utilizing either the Saxon math placement or state-level test to get a basic idea and then work in a bit at a time Singapore Math or Math Mammoth or both. Both Singapore Math and Math Mammoth heavily include word problems in the material and this is reflected in the test.

What if my child made a perfect score on the placement test?

Congratulations to your child! Keep doing higher level tests until your child hits an area that needs work or runs out of tests.
If he runs out of tests, try the math section of a practice  SAT(r).
Puzzle and contesting sites can also broaden the interest of a mathematically adept child looking for challenges.

Text Materials

Cost Item Description
Free digital / $ text
 Ray's Arithmetic First Book
 Ray's New Intellectual Arithmetic
 Ray's New Practical Arithmetic
 Ray's New Higher Arithmetic
 Ray's New Test Examples

 Ray's New Elementary Algebra
 Ray's New Higher Algebra

 Ray's Plane and Solid Geometry

 Rays Arithmetic blog

 Ray's arithmetic series in print

Ray's Arithmetic Series

The phrasing can be quaint, but the price is right and the books are formatted to largely have the student help themselves.
Ray's Arithmetic series can be found multiple places online as the series has moved out of copyright. The math topics covered have not changed since these books were written and they can still provide thoughtful and complete coverage of the material. One advantage of a text that can be downloaded is that if there is limited internet availability then these materials can be used easily once obtained.
I will mention two places these are currently, although you may find alternative locations as well. On the books can be read online or downloaded in many formats including PDF, EPUB, text, and kindle.
Ray's Arithmetic blog hosts PDFs of most of the texts as an alternative download location and has added some videos to accompany the book. I have not reviewed the videos, but feel free to comment in the blog about these or other resources and I will make notes as time allows.
  Program Link

Centre for Innovation in Mathematics Teaching program

Centre for Innovation in Mathematics Teaching program for and following the UK school years, but including texts workbooks and review materials presented in an organized fashion. Year 1-4 materials are also available in Spanish.
  Libros de Texto

Mexico Libros de Texto SEP - primer-sexto

PDFs of the Mexican first-sixth grade textbooks are available. This is a complete curriculum and can be helpful for Spanish learners or Spanish speaking parents who want to review.
  Oxford Owl Link

Oxford Owl

Another UK resource including, math and reading activities for 5-11 year olds (Year 1-6)
  Siyavula Link


A spin off of the Free High School Science Texts project. Siyavula provides open math and science texts in English & Afrikaans.
  CK-12 Elementary
  CK-12 Grades 6-12

CK12 Digital Textbooks

An open textbook progect. These can also be found by searching on Amazon for "CK12 math" for books formatted for the Kindle.

Comprehensive School Mathematics Program

This material was originally archived off by Buffalo State and then saved by It has many resources including lesson plans and worksheets, but not all presentations are the ones that will help the most people understand the topics.
  Phillips Exeter Academy

Problem Sets from Phillips Exeter Academy

This material is developed by and for Phillips Exeter Academy and has numerous problems. No solutions are provided to these problem sets.
and low cost

  Contemporary Calculus

Free Online Caluculs book

Online calculus book comprised in part of materials from the Open Course Library Project of the Washington State Colleges.
Even if you decide on a different math text the author please take the time to read the author's suggestions on  How to succeed at Beginning Calculus
and low cost

  AIM Reviewed Texts

American Institute of Mathematics Reviewed Text books

For a number of years members of the American Institue of Mathematics have been reviewing free and low-cost math texts to select ones suitable for a standard college level class. As there is considerable overlap between the lower level college courses and the high school courses, these materials merit consideration.

Texts have been reviewed and recommended in the following groups:
Liberal Arts Math, Elementary Algebra, College Algebra and Precalculus,
Trigonometry, Calculus, Differential Equations, Linear Algebra,
Introduction to Proofs, Discrete Math, Combinatorics,
Computing and Numerical Analysis, Number Theory, Abstract Algebra,
Real Analysis, Complex Analysis, Geometry and Topology,
Probability, Statistics, and Logic

Math Website Resources

Item Description

  Khan Academy

Khan Academy

KhanAcademy allows the creation of a user account to progress through levels of math from kindergarten to beyond calculus. For an elementary student it is often suggested that the user begin at kindergarten and review and test out of the earlier material. This allows students who have previously been hesitant or un-successful in math at their grade level to back track and have math that is fully in their grasp. When the math is suddenly easy, they find that what had been scary is fun. As the review fills in holes in their knowledge the challenges are manageable and often they discover that they like math after all. For a math wiz who has mastered these concepts, point out that as they test out of sections that they can move on to a continuum of challenges at their own pace.
If you want a single resource for math, pick this one. Although nothing is a fit for all students, the adaptive nature and ability to go at your own speed above or below your grade level make this a flexible choice.

  Purplemath tutorials
  Purplemath guidelines


Purplemath provides middle school and high school math review materials. It also has a nice guideline for doing math homework.
To summarize --- neatness matters. Messy math makes mistakes.

  Math is fun

Math is Fun

Math games and activites with translations into several languages.

  Oxford Owl Math

Oxford Owl Math

Activities, hints, and videos to learn math.

  UC Scout

UC Scout

UC Scout provides subscription high school classes with various price plans, many plans free to residents of California.



This was at one time a robust and complete site, but some of the content was pulled back and is no longer available. It is interesting, but would not be the first place that I would look for content. The site does include a list of other collections such as The Art of Problem Solving and the  University of Colorado's Interactive simulations


Science and Math Simulations at the University of Colorado

Numerous Science and Math simulations in HTML5, JAVA, and Adobe Flash.

 Paul's Online Math

Paul's Online Math

This provides review resources and notes for all of the classes that were taught by the author at Lamar.

 West Texas College University

West Texas University Algebra Review

Freely available review materials provided by West Texas University.

  AoPS Resources
  Art of Problem Solving Vol 1 & 2 on Amazon

Art Of Problem Solving

Resources and online learning experience for avid math problem solvers.

  PBS Math


Videos and interactive materials for many subjects including math are available on PBS.

  Math Snacks

Math snacks

Animations and games for learning math.

  Lure of the Labyrinth

Lure of the Labyrinth

Math activity for middle schoolers.



Cyberchase is a math cartoon that presents surprising complex math topics in a kid's cartoon. Episodes are available in English and Spanish. A limited subset is available on the PBS site, but sometimes your local library will have DVDs to check out. This is a great half-hour of low key fun with math included.

Upper Level Course resources


MIT Open Courseware

MIT generously has a large collection of course materials available for independent learners.

  AP Courses

AP Course materials on

The description is "this library of open educational resources features course materials for seven Advanced Placement (AP) courses. These high school level materials are available for free download." These include materials for Calculus AB and Calculus BC

 Modern States

Open Education Initiatives

These sites provide both free and purchased coursework in many subjects. Modernstates is targeted with helping students review during high school material in order to test out of introductory college classes.
iTunesU can also provide interesting materials.


SAS Curriculum Pathways -- going away August 31, 2020.

This resource is going away after August 31, 2020, but till then it is worth a look.


Wolfram Alpha

While not explicitly a teaching site, Wolfram Alpha has a ton of mathematical material.

Math Curricula

$ DK Math
 DK Math Pre-K
  DK Math Kindergarten
  Math Made Easy: 1st
  Math Made Easy: Second
 Math Made Easy: Third
  Math Made Easy: Fourth
 Math Made Easy: Fifth

Dorling Kindersley Math

DK has a series of workbooks for grades K-5 that are colorful and well presented. The only complaint that I have against these workbooks is that the pages of the workbook are slick which causes frustration to a child writing with a pencil. This is offset by an entire page of gold stars to excite your younger student.
$$ Singapore Math
 Primary Level 1
 Primary Level 2
 Primary Level 3
 Primary Level 4
 Primary Level 5
 Singapore Math Inc Site

Singapore Math

Singapore Mathematics have extremely well organized materials with a textbook and workbook and optional teachers guides. The problems include multiple steps from early levels. Do not pick this option if you feel unsure of math without having a math friend on tap or purchasing the instructor guides.
$$ Math Mammoth

Math Mammoth

Math Mammoth provides word problems and multiple step solutions from early levels and progresses up to 6th grade. The best deal for this program is found in the discounted  packages If after taking the placement tests, you are unsure what the appropriate level is, customized help is provided.
 Beast Academy Level 2
 Beast Academy Level 3
 Beast Academy Level 4
 Beast Academy Level 5
 Beast Academy site

Beast Academy && Art of Problem Solving

Both online and print curricula for 8-13 year olds.

Life of Fred

When it was February before the Advanced Placement test in calculus and all texts were deemed boring, what brought success but Life of Fred: Calculus.
The high school materials for Life of Fred put learning in a story as a precocious tot discovers the usefulness of calculus.
This does not have enough problems for many students to become proficient, but it is an excellent resource. The story aspect can make remembering calculus easier for some people.


Barron's review books for SAT Subject Test Math Level 1, Math Level 2, and the Calculus AP are excellent review materials. While the coverage might not be enough for a student who has not seen the material, the review books are more than adequate for students to find deficiencies.
Free & $ SparkNotes


Sparknotes review materials for many subjects are available online. Print copies are also available for purchase.  Sparknotes math link
  Free CLEP Prep

Free CLEP Prep

This site provides study guides to prepare for various CLEP tests to get credit for previously learning college material. Sometimes the guides are links to material that you may see here or elsewhere. If you are studying any CLEP covered course and looking for review material this is not a bad place to check out.

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