Thanks to that user for pointing this out. Mistakes do happen when I’m converting these worksheets into .pdf format, so if anyone notices anything awry please shoot me a note so I can get it fixed.

On another note, since launching this experiment numbersheets worksheets have been downloaded over forty two thousand times, and the site has been accessed from nearly one hundred different countries – including Sudan, Macao, and the Isle of Man.

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Word problems: you’ll be seeing more of these in all of the grade levels.

In third grade kids start cranking up the pre-algebra skills and need to start thinking in terms of algebraic expressions. Standard Skill 3.OA.D.8 reinforces this. There’s a new worksheet on the fourth grade page that helps kids practice:

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**Common Core State Standards:** I noted in an earlier post that since I currently live in Virginia and previously lived in Texas I had not been exposed to Common Core State Standards – either Virginia nor Texas have implemented CCSS. But as I’ve added topics to this website I’ve increasingly started using the CCSS standards to organize the worksheets. I find that even though the public school that my kids attends here in Virginia doesn’t subscribe to CCSS I can still make an almost one-to-one match between the topics they teach and the CCSS standards. I haven’t yet formed an opinion on whether or not Virginia should join, but since this website gets visitors from all over I figure it it worthwhile to organize based on a universal standard. I’d be interested in how topics are standardized in other countries…

**Four thousand downloads:** Numbersheets.com hit this milestone this week. My kids find this interesting – that I’m inflicting our family math worksheets on kids around the world who we’ll never even meet. In a future graphing worksheet I’ll have to integrate a plot showing the website’s increasing traffic over time.

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Prime numbers, essentially, are the components from which integers are constructed. A **prime number** is a number, greater than 1, that can only be evenly divided by 1 or by itself. A **composite number** is a number greater than 1 that can be evenly divided by a number other than 1 or itself. So if a number greater than 1 is not a prime number, it is a composite number.

**12** =** 2 x 6** = **2 x 2 x 3**. So 12 is a composite number. In the future there will be times that your kid will need to think of 12 as **2 x 2 x 3** or as **2 ^{2} x 3**.

13, on the other hand, does not cooperate. **13 = 1 x 13**. It can’t be broken down any further. So 13 is a prime number.

Figuring out whether or not a number is prime will be something of a trial and error process for grade schoolers. We know that **all even numbers greater than 2** are composite numbers, since they’re all divisible by 2. We also know that **any number with a 5 in the ones place** is also a composite number and will be divisible by 5. So as candidates for prime numbers we’re left with numbers ending in **1, 3, 7** and **9**.

The foolproof trial-and-error method for determining whether a number is prime is to try dividing it by every number from 2 through the square root of the number. If none divide evenly then the number is prime. That, however, gets tricky for big numbers. The method I’m trying with my kids is simply to have them study and remember this chart. There’s only 25 primes between 1 and 100 – and the ones below 20 (8 in all) are the most important.

Here’s a study sheet showing the Grid of Prime Numbers from 1 to 100. And you can find study worksheets on the fourth grade math worksheet page.

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One passage resonated with me as I reflect on the discipline (and eventually, I hope, the passion) that I’m trying to instill in my kids as they develop first and third-grade math skills…

“*…the initial stages of learning a skill invariably involve tedium. Yet rather than avoiding this inevitable tedium, you must accept and embrace it. The pain and boredom we experience in the initial stage of learning a skill toughens our minds, much like physical exercise. Too many people believe that everything must be pleasurable in life, which makes them constantly search for distractions and short-circuits the learning process. The pain is a kind of challenge your mind presents – will you learn how to focus and move past the boredom, or like a child will you succumb to the need for immediate pleasure and distraction? Much as with physical exercise, you can even get a kind of perverse pleasure out of this pain, knowing the benefits it will bring you. In any event, you must meet any boredom head-on and not try to avoid or repress it. Throughout your life you will encounter tedious situations, and you must cultivate the ability to handle them with discipline.*“

It’s easy to dislike the testing-heavy curriculum that is proliferating in our educational system. But early repetition builds mastery of the basic skills that will allow kids to lean into the higher mathematical concepts that’ll be exposed to later on. An eight-year-old can wrestle pretty successfully with this repetition if she’s been doing it as long as she can remember. And the every now and then we both get an enjoyable payoff when she grasps a new concept building on the foundational skills that have become second nature. Kids are more resilient that we realize – setting expectations high pays off.

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**Place value models** are an intuitive way of helping kids conceptualize numbers. And as an added bonus they reinforce geometrical concepts that will be useful later one. Two-for-one learning…can’t be beat.

There are four types of groupings you’ll find in these worksheets:

*Units*: single bocks (1’s)*Rods*: rows of ten units (10’s)*Flats*: groups of ten rows (100’s)*Cubes*: Groups of ten flats (1,000’s)

Count up the number of cubes, that’s the number of thousands. Count up the number of flats, that’s the number of hundreds…and so on. You get it. And so will your kid.

This worksheet is a fun way to reinforce some important concepts.

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Check out the fact triangles worksheets on the first grade worksheet page.

Fact triangles do a couple of important things. First, they reinforce a critical first grade objective: memorizing addition facts with sums up to 18. But in addition they also start to reinforce in your first grader the inverse relationship between addition and subtraction.

Example:

4 + 5 = 9

5 + 4 = 9

9 – 4 = 5

9 – 5 = 4

You’ll find two types of fact triangles. The first (pictured here) includes all three digits. In the second type the student is provided with two numbers and has to use reasoning to figure out the third.

Have fun!

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I mentioned in a recent post that the worksheets on this website are based largely on the standards published by the State of Virginia, augmented by materials from Texas and the National Council of Teachers of Mathematics. This, in large part, is because those are the two states in which I most recently lived.

Another approach is the approach endorsed by the Common Core State Standards Initiative (CCSS), which has been adopted by 45 states in the United States. As I glance at the map on the CCSS website one thing jumps out (to me, at least) – both Texas and Virginia are among the two states yet to adopt the initiative. Which, I suppose, is why I’m not particularly familiar with it in practice. In the future I’ll be the math worksheet exercises on this website to the CCSS standards.

In the meantime I think that the **eight CCSS mathematical practices** – common from kindergarten to eighth grade – are a useful set of principles to consider and reinforce when teaching math concepts:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Like all learned skills – from math to music to sports – it is not enough simply to practice. To move ahead student have to practice with a purpose. These are rules that I strive to reinforce with my kids.

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You may note that some of the entries aren’t consistent with the ideal that the simplest solution is the most elegant. The entry for 9, for example, could have simply been “9”.

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