Math
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 problemsolving
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 17)
Singapore Math (Grades K6)
Life of Fred(PrimaryCollege)
Art of Problem Solving (Prealgebra 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 gradelevel, 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 statelevel 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 
Arithmetic: 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 Algebra: Ray's New Elementary Algebra Ray's New Higher Algebra Geometry: Ray's Plane and Solid Geometry Rays Arithmetic blog Ray's arithmetic series in print 

Free 
Program Link 

Free 
Libros de Texto 

Free 
Oxford Owl Link 
Another UK resource including, math and reading activities for 511 year olds (Year 16)

Free 
Siyavula Link 
A spin off of the Free High School Science Texts project. Siyavula provides open math and science texts in English & Afrikaans.

Free 
CK12 Elementary CK12 Grades 612 
An open textbook progect. These can also be found by searching on Amazon for "CK12 math" for books formatted for the Kindle.

Free 
CSMP 
This material was originally archived off by Buffalo State and then saved by archive.org. 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.

Free 
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.

Free
and low cost 
Contemporary Calculus 
Online calculus book comprised in part of materials from the Open Course Library Project of the Washington State Colleges. 
Free
and low cost 
AIM Reviewed Texts 
For a number of years members of the American Institue of Mathematics have been reviewing free and lowcost 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.

Math Website Resources  
Item  Description  
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 unsuccessful 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.


Purplemath tutorials Purplemath guidelines 
Purplemath provides middle school and high school math review materials. It also has a nice guideline for doing math homework. 

Math is fun 
Math games and activites with translations into several languages.


Oxford Owl Math 
Activities, hints, and videos to learn math.


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


Hippocampus 
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


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


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 
Freely available review materials provided by West Texas University.


AoPS Resources Alcumus Art of Problem Solving Vol 1 & 2 on Amazon 
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 
Animations and games for learning math.


Lure of the Labyrinth 
Math activity for middle schoolers.


Cyberchase 
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 halfhour of low key fun with math included.


Upper Level Course resources  
MIT OCW 
MIT generously has a large collection of course materials available for independent learners.


AP Courses 
The archive.org 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


Coursera Edx Modern States 
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.
 
SAS 
This resource is going away after August 31, 2020, but till then it is worth a look.
 
Wolfram 
While not explicitly a teaching site, Wolfram Alpha has a ton of mathematical material.
 
Math Curricula  
$ 
DK Math
DK Math PreK DK Math Kindergarten Math Made Easy: 1st Math Made Easy: Second Math Made Easy: Third Math Made Easy: Fourth Math Made Easy: Fifth 
DK has a series of workbooks for grades K5 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 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 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 
Both online and print curricula for 813 year olds.

$$ 
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.
 
$ 
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 
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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