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Math Worksheet

Get Real Math Mastery of Basic Skills While Building a Mind for Algebra

CLICK to BUY NOW for $4.99

Welcome to the Math Skills Worksheet I created for my kids. This will help your children excel at all basic math functions. To truly excel at math, basic functions must become automatic so the slower conscious thinking gives way to much faster unconscious processing and automaticity takes over. In short, this is an algebra trainer, and mastery tool.

When I was a child, I enjoyed timed math tests. We’d get a sheet of paper with 60 problems and see how many we could complete in 60 seconds. The goal was to finish all 60. I remember feeling awesome the first time I did that. The problems on this program are slightly more complex and require more thought. It isn’t expected that someone complete these sets of 50 problems in under a minute but if that was possible, that would be super awesome. ūüôā

Every Operation at Once

So what is this? It’s a worksheet generator where you are presented with a few columns. Two random numbers within a range you specify (like 0 to 5, or 0 to 12, or -12 to 12) are added and multiplied. The person working the problem out must identify the two numbers. In doing so, they will use all four math operators (+, -, *, /) and learn to hold combinations of possibilities in their mind all at once.

Math Skills worksheet

The one working the problem then has to sort these out mentally. For example, two numbers that add to 10 AND multiply to 25 are 5 and 5. Two numbers that add to 8 and multiply to 15 are 5 and 3, and so on. It’s pretty simple but it really gets the brain working. When my son started doing these a few weeks ago, it took him over 15 minutes to complete a sheet. I wasn’t trying to frustrate him so in the beginning he just worked as many problems as he could for 15 minutes and stopped. Pretty soon he was under 15 minutes to complete the whole sheet and then we started timing him. His scores came down lower and lower with each succeeding sheet (and an occasional increase). Eventually he got under 3 minutes for 50 problems and that was good enough for me to move on.

Introducing: negative numbers…


We talked about the number line and how 1 times any number is itself, so negative 1 times a number is the opposite sign of that number. We discussed this for a bit and the idea that two negatives multiplied times each other will make a positive so you can tell by looking at the multiplication column if both numbers are the same sign and then tell by looking in the addition column if both numbers are positive or negative. Then he started trying out the new worksheet.

math worksheet with negatives

For example, two numbers that add to -17 and multiply to 60 are -12 and -5. Two numbers that add to 0 but multiply to -9 are 3 and -3, and so on.

When my son started this sheet, he could only complete a few problems in 10-15 minutes. It was new thinking. We were patient and just let him build his skills. He worked at it and is now to the point of completing 50 of these problems in 6 minutes. The goal is 3 minutes again (and there’s always a prize involved). This one will cost me so please buy a copy of this worksheet! ūüôā

Adjustable Difficulty


To get children started, you can select a range on one of the spreadsheet tabs for the maximum absolute value used on a worksheet.


The worksheet then adjusts the page title and problems to match your selection.

For example, if I input 5, you’ll see the title change and the problems adjust to the new values.


Start with seeing how many problems they can complete in 5 or 10 minutes. Each day they should get a little better and improve their ability to focus. Help them get used to thinking about combinations that add or multiple to a number. For example, what are all the combinations that add to 10, or numbers that multiply evenly into 24. Maybe one sheet takes a few days of work to finish.

Once they can do the entire sheet without frustration, start timing them and offer a prize when they get under a certain amount of time for completing the sheet. Once they get that prize, offer another prize at a lower figure. Once your child gets down to about 3 minutes with positives, introduce negatives and the time to complete a sheet will reset and probably be more than 15 minutes if they are just learning about negative numbers. Repeat the process of getting them used to it and then build up to see how many they can do in 10 minutes, then once they can complete the sheet time them to get faster.

Getting Started Pages


I also built sheets with answers which are especially helpful for getting started. The column where it says “FOLD BACK” is where you fold back the answer columns A and B so they aren’t visible when doing the worksheet. When they are done they can unfold it to check their answers and see how they did.


Start with positives with answers till they master the math and then you can print without the answer sheets. Then do negatives with answers till they master the math and then you can print sheets without answers (not printing answers lets you print 2 worksheets per page and you could even flip the paper over and use the back side).

Each printable tab on the worksheet will print 10 sheets to use. Pressing F9 will scramble the math values so you can print additional sets with new numbers. If you only want a couple sheets just limit the printout pages accordingly.

Benefits to your Children

Once a child gets these problems down to a low time, they will have transferred a significant load of mental work into their subconscious and will be way ahead of peers that still have to mentally process problems in their conscious mind.

  • Master addition, subtraction, multiplication, and division all at once
  • Your children will grasp quadratic equations when they hit algebra with greater ease and excitement at their ability to know how to separate x^2 -x -12¬† into (x+3)(x-4) without batting an eye.
  • As they lower their time, self-esteem and confidence will increase and they’ll be excited to put their mastery skills to work

 CLICK to BUY NOW for $4.99


License agreement: Purchase of this spreadsheet allows you to print as many physical paper worksheets as you want for your own children. You are not permitted to print pdf copies to distribute to others. This is a personal copy of the math worksheet. Please refer others to the website address above to purchase their own copy of this worksheet. Simple honesty contract.

You are welcome to purchase copies of the worksheet for others and send it to them. If you need bulk pricing please contact me.

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Students are not College Math Ready

Someone sent me a link to this graph which comes from pg. 74 of a PARCC document¬†and shows exactly what‚Äôs happening in public education. 89% of high school math instructors believe their students are ready for college level work, yet only 26% of college instructors think they are ready. What’s the disconnect here? Are high school math teachers in a bubble thinking they’ve imparted “higher order thinking skills” through constructivism but reality is otherwise?

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The UVU Remedial Math Situation

Most universities have remedial math courses for students who have had difficulty getting to university math levels. However, few universities have remedial math DEPARTMENTS. UVU is one such university that has been forced to do this because of the low quality math skills of students who arrive at the university.

For years the Utah State Department of Education has maintained that the high remedial math class percentage at UVU is the result of returning missionaries who haven’t had math for a period of 2-3 years and then need help getting back up to speed. This is a myth which can now be fully corrected.

UVU generated the following information after a request by Dr. David Wright, math professor at BYU, and Senator Margaret Dayton.

Click to enlarge

This chart shows that these remediation rates (as high as 72% in the past few years) are for first time college students. Many people who go on missions squeeze in a semester or two before they leave, and when they return from their mission they are no longer counted as a first time college student. The percentage of students prepared for college level algebra, is a pitiful 16-24%. How can this be? Constructivist math promoted by BYU’s Math Education department has made the rounds of all the surrounding school districts and it’s killing us. There has not been a single study showing constructivist math programs as effective. Yet we continue doing this injustice to our children making them non-competitive with the rest of the world. When will our schools change? They won’t until school board members quit listening to the so-called “expert” educators within their districts and from schools of education. It’s obvious these folks don’t value actual scientific facts or else they would drop these programs and just use something that works like Singapore math.

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A Letter to U.S. Secretary of Education Arne Duncan

This letter was posted, in August, 2009, to the RACE TO THE TOP comments section of the federal government website.   (

Underlining is mine. Signatures have been removed to shorten the post. You can view them at the link above. It’s a who’s-who of math professionals.


A Letter to U.S. Secretary of Education Arne Duncan


If a first grade teacher read at the fifth grade level, we’d be outraged. But what if she had only third or fourth grade mathematics skills and lacked the conceptual understanding needed for teaching mathematics?¬† Unfortunately, this is the reality for all too many licensed K ‚Äď 8 teachers in this country.¬†¬† According to a recent report by the National Council on Teacher Quality, the current training that prospective K-8 teachers receive in the vast majority of this country’s education¬†schools assures that this appalling situation will continue unchanged.

We agree with U.S. Secretary of Education Arne Duncan’s statement:¬† “… it is hard to teach what you don’t know. When we get to 6th, 7th, and 8th grades, we see a lot of students start to lose interest in math and science … because their teachers don’t know math and science”.¬† For the United States to remain competitive, every part of K-12 mathematics education in this country must be strengthened: curriculum, textbooks, instruction, assessments, and, above all, the preparation and continuing professional development of those who teach mathematics and science, regardless of grade level and the kind of school in which they teach.

Teachers’ mathematical knowledge is particularly important in K-8, since students’ mathematical foundations are built there. The first priority must be rigorous mathematics courses for prospective teachers of elementary and middle school children, followed by state-approved licensing tests that fully assess their knowledge and conceptual understanding of elementary mathematics.  We must radically upgrade the mathematical content of their professional development programs as well.

Recommendation 1. The United States Department of Education should fund only those states that present a plan to implement the recommendations of the National Mathematics Advisory Panel in mathematics courses or programs¬†for prospective or current teachers of mathematics and science in K-8 and on their licensing (certification) tests. The rigorously researched Panel’s 2008 report advises that teacher preparation programs and licensing tests for all K-8 mathematics teachers should fully address the foundational topics in arithmetic (including fractions, decimals, and percents), geometry, measurement, and algebra that are spelled out in the Panel’s report. Middle school teachers should know more than teachers in early grades.¬† Other professions have state licensing requirements, whose purpose is to protect the public from practitioners without entry-level knowledge and skills.¬† Good grades from law school do not exempt aspiring lawyers from having to pass state bar exams. Clearly the education of K-12 students should be considered as important to safeguard as the interests of a lawyer’s clients.

What are needed are serious college mathematics courses. The Massachusetts Department of Education’s guidelines for the mathematical preparation of elementary and special education teachers are a step toward describing the content of such courses. The courses must cover the core material that we should expect teachers to know in order to prepare our children to compete successfully in the world economy and to help their students avoid remedial coursework if and when they enter college.

Recommendation 2. The programs funded by the U.S.D.E. should require instructors of the mathematics courses for aspiring or current K-8 mathematics and science teachers, coaches, and supervisors to hold a Ph.D. in mathematics or a mathematics-dependent field (or at least be closely supervised by someone holding such a degree).  All prospective K-8 mathematics and science teachers, coaches, and supervisors should be required to pass a solid test on the core mathematical material (especially arithmetic) for licensing.  Mathematics supervisors and coaches should be required to have at least the mathematics qualifications of those they supervise.

Recommendation 3. The U.S.D.E., as part of the provision in Title II of the Higher Education Act, should require each state to report publicly by institution the pass/fail rates for all prospective elementary and special education teachers on a mathematics licensure test as demanding as the 40-item test now required in Massachusetts. This recommendation is fully supported by the report of the National Council on Teacher Quality documenting the inadequate preparation in mathematics of future elementary school teachers in 67 of the 77 colleges/universities surveyed.

Recommendation 4. The states funded by the U.S.D.E. should be required to align the courses in mathematics pedagogy taken by prospective K-5 teachers with the new mathematics coursework, as outlined in Recommendation 1.  Current methods courses too often focus only on demonstrating how to teach very low level mathematics content.

Recommendation 5. The U.S.D.E. should fund content-rich professional development programs for current K-8 mathematics and science teachers, coaches, and supervisors, and for elementary and middle school principals.  It should not fund professional development programs that do not have a significant arithmetic component.

Close cooperation between teachers in the field, mathematicians having an active interest in K-12 mathematics education, and mathematics educators, together with the active help of government and the business community, can turn our mathematics outcomes around, but time is of the essence.


National Council on Teacher Quality. (2008).  No common denominator: The preparation of elementary teachers in mathematics by America’s education schools.  NCTQ: Washington, DC:

National Mathematics Advisory Panel. (2008).  Foundations for Success: Final Report of the National Mathematics Advisory Panel. U.S. Department of Education: Washington, D.C.

We, the undersigned, support this letter: (see link at top)

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Math Update

Howdy folks,

I’ve been buried with projects, one of which is getting Mathino ready for purchase as quickly as possible so those of you that want it for Christmas can get it. It’s really a fantastic game (since I didn’t create it I can say that :)).

There’s been a bit of stuff lately that has come out, some more important than others and where my time is short I will just summarize the highlights and give you links to the information.



This first piece would be great to share with board members, teachers, and principles.
Who Needs Mathematicians for Math, Anyway?
The ed schools’ pedagogy adds up to trouble.
by Sandra Stotsky, former Assistant Commissioner of Education in MA, and now professor of education reform in Arkansas.
“The math wars, which started in debates about pedagogy, may end in questions about the long-term prospects for American prosperity.”


In this classic “news” report by The Onion, just substitute “reform” for “Montessori” and “math” for “dentisty” and you’ll get a good laugh over the insanity of constructivism.

Montessori School Of Dentistry Lets Students Discover Their Own Root Canal Procedures


A couple weeks ago, the U.S. Chamber of Commerce released a new report on educational innovations in each state entitled “Leaders and Laggards”. Not many states faired well, but Utah was near the bottom of the heap with poor school management, staffing (removing ineffective teachers), pipeline to postsecondary, and technology.¬† We did get an ‘A’ for data and a ‘B’ for finance, but overall a ‘D’ rating.


NCTQ report recommends Colorado adopt Singapore Math


Latest outrages:

Achtung! Prosecutor says only jail deters homeschooling

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Impressive Math Lesson Videos

Someone recently sent me a link to the Khan Academy’s site. This person has over 800 videos on YouTube teaching various math courses. The videos aren’t too long, but the amount of them is quite impressive. If your child is struggling with a concept, see if there isn’t something on this page they can review to get up to speed.

Not only does he cover tons of math subjects, he also has a lot on finance including some analysis on the Geithner and Paulson plans.

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National Standards are Dangerous

There are certain appealing aspects to having national standards, such as looking at a country like Singapore or Japan that has very high standards and achieves great things through them. However, within the United States, we have already seen tendencies from those in power to dictate down to the local level things that are “best” for us when in fact they’ve been proven wrong over and over again. ¬†This article by Laurie Rogers is an excellent summary of some of the issues.

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“No Common Denominator”

Two reports by the National Council on Teacher Quality (NCTQ) do a fantastic job of showing just where education colleges are failing students who want to become teachers, and then our children who are taught by these teachers.¬† One report was released in June 2008 for mathematics preparation of teachers entitled “No Common Denominator–The Preparation of Elementary Teachers in Mathematics by America’s Education Schools.” The second, released in May 2006, is on reading and is titled “What Educations Schools Aren’t Teaching About Reading and What Elementary Teachers Aren’t Learning.”

The math report examined 77 schools around the country and Utah State University was the only college in Utah that was examined, and also received a failing mark for teacher preparation.

This August, thanks to a grant by a generous donor, a report will be revealed that examines all 8 major colleges in Utah. I understand that only 1 college has received a passing mark, while 3 would pass if they required more courses of elementary education students, and 4 fail completely.

The links below will take you to the math and reading reports, but the gist of them was to give a few standards for teachers and development of a proper education base before they go off to teach impressionable minds.  The math report details 5 standards as follows:

1) Teachers must acquire a deep conceptual knowledge of math focused on

1. numbers and operations,
2. algebra,
3. geometry and measurement, and ‚ÄĒ to a lesser degree ‚ÄĒ
4. data analysis and probability.

2) Higher entry standards into the program with teachers demonstrating mastery of geometry and algebra 2 at the high school level

3) Must demonstrate a deeper understanding of math than what they must teach to children

4) Elementary content courses must emphasize numbers and operations and student teaching must focus on delivery of math content

5) Math content delivered to teachers should be done within the purview of a MATH DEPARTMENT

The entire math report is 28 pages and contains some other interesting things should any of you wish to look over it.¬† I am eager for the report in August and can’t wait to see how <cough>BYU</cough> fares.¬† I’m not expecting it will be the lone passing school in the state.

Link to math report

The reading report is also great and tells us what we already knew, that phonics and explicit instruction work best.  Sorry whole language constructivism.  You lose again.

Link to reading report

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To my dear, lost, Alma Mater. Please find yourself.

This past week the citizens of my hometown made the press as their fight against Investigations math got big enough to attract attention. I just posted the below message to them on their fight site and encourage you to visit their petition site.

I am so sorry you have to go through this pain. As a graduate of the class of 1987, back when teachers required you to solidly understand and perform math, I remember with great fondness doing timed tests in 3rd grade at Park Forest Elementary school to master the 12×12 tables.
Those essential skills serve all other aspects of math (and life).
Foundational mastery and rapid recall is essential to be able to dissect algebraic equations where you must see connections invisibly and instantly to solve quadratics such as what two numbers add to 19 and multiply to 84. This must be low level programmed into the subconscious for further mastery.

I left State College thinking you an anchor being next to the great engineering college of Penn State. Moving to Utah and raising a family here, I was horrified to learn that my children weren’t being taught the times tables in my district. Parents were told not to teach them for fear it would “mess them up” because of the supposed critical thinking skills Investigations math would instill.¬† I thought, “if only I could be back in State College where the grass is greener.”
Then my sister told me a few years ago that you had adopted Investigations math and my world came crashing down. I have survived through the years by working to eradicate this program from Utah.

I have learned that there are NO studies that support Investigations math or constructivism as a curriculum. The International TIMSS exam proves that curriculum is the #1 determining factor for successful students. Singapore is #1 for a reason. Their math program teaches children the basics of algebraic problem solving starting in 3rd grade.¬† By the time they are in 4th grade, they have 7 times the number of students with an advanced understanding of math as we do in the United States. They’ve cracked the code.

I truly hope you will rise up and help the board members in State College understand that their job as elected officials is to represent YOU the taxpaying public and not be apologists and protectors of the school district administration who are being paid by YOU. It’s your tax dollars and the board’s responsibility is to ensure the wisest course of action (most bang for the buck).¬† This is the single biggest misconception of school board members who allow themselves to be bullied by district “experts” who tell them “all the studies say this is the best way to do it” and who are they to argue with experts?
It’s time they started arguing before this Enron of educational programs destroys our technical prowess in America.

The greatest thing you could do is adopt Singapore Math (Primary Series from When Benchmark elementary in Arizona did this, within a few years they were the top scoring school in the state for math, and 94% of students reported that math was their FAVORITE subject.  Imagine that.  Kids that master math love it.  When kids struggle with weak math, they hate it.  Which program do you think will better let your children move into a bright future?

Oak Norton¬† (be sure to click on America’s Dire Straits page, and Singapore and Utah math)