Count with Base 10 Blocks!

Here we see a 3 x 12 matrix. The youngest started by counting out three. Then we skip counted as we added macaroni. The oldest did most of the work and the youngest just listened to the patterns without any understanding of the meaning...3 twelves, 12 threes...we counted to 10 several times as we built up...

Counting with base 10 blocks, makes learning to count easy, which will make math easy...Because all we do with numbers is count; basic concept number one.  We can get creative with our counting and do some complex counting without getting complicated. 

Build stuff. Count it. Count them different ways.  Count the sixes using threes, count the threes three at a time, counting by 5 is easy, counting by sevens could be (for 6 of them), 6(5 + 2). Which is easier? 7 x 6 or 30 + 12? 

Give them free time to build whatever they want, it is up to you to add the math. Count creatively. Play with a purpose in mind, learning to count or identify numbers can involve lots of games and activities that are fun and engaging AND teach counting or adding (which is just counting) or other basic operations. Perhaps the object is multiplication by 7, make that he focus of several games and activities. 

Any base ten blocks will do. 

You don't have to use Mortensen math blocks to count with base ten blocks. In fact, you don't even need to use  base ten blocks to start...don't have money for expensive manipulatives? Bet you have some macaroni.  Bet you have a deck of playing cards, you can teach counting with playing cards by playing fun games

Build Stuff And Count It. 

Concept #1: Mathematics is the study of numbers and all we can do with numbers is COUNT.

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting. ~Ernst Mach

All math is. is counting. Every math problem counts something. Believe me, i've had this argument in seminars with professors and teachers across the USA. If you aren't counting something you aren't doing arithmetic. Period. So one of the most basic concepts i teach ANY student is to ask "what are we counting?" when confronted with a math problem.  If you learn to count with base 10 blocks, you will have a much easier time teaching all the math later.

There are many games and activities that make counting with base ten blocks fun and easy.  We're just playing but playing IS learning when you use base ten blocks.

This page gives specific, time tested yet cutting edge techniques on how to teach counting with base ten blocks to your preschoolers or to your toddlers.

HOW TO TEACH COUNTING. 

Here is another page that shows you even more "how to's:" 

This is where it all starts: Learning to count.

Sesame Street can help.

Learning to count is the beginning of a long journey, it's the first of the five basic concepts.

First hurdle: counting to 5. All the fingers on one hand. 

Use a three period lesson to develop the vocabulary and names of the first five blocks. The names of the base 10 blocks are just vocabulary. The same way, for example, this is a "pen", this is a "one"...simple.

Start with one two and three...

...and then add four and five. 

THEN count to 9 by adding the other four blocks.

Start with just three base 10 blocks, then five when they know those names, add three more and at last all nine. Small steps keep it easy and FUN.

Then you can play what's under the cup where you place 9 blocks on the learning surface and put a cup over one of them. 

You can put all nine blocks under a cloth take out one with the cloth so they can't see which one you took and ask which one is missing. Then use two blocks each. 

This process will take several lessons over several days. Unless the student is older these lessons should be short and will take a couple of weeks depending on many factors but mostly on the age of the child. Younger is better and will take more time.

Then count to 20...first you count the nine blocks make a big deal out of it when you get to ten. Then show ten and one is 11, ten and two is 12 and count to 20...the student will see the pattern. 

We counted to 10 three times.  Then we counted by threes adding 3 ten times...notice the egg carton in the background. A perfect toy to teach counting...

Once you can count to nine you can begin playing games...like what's under the cup or what's in the box. 

PDF Shows How to Use Base 10 blocks.

The Completely Cool Curious Counters Compendium will help immensely.
Get this book and read it as a bedtime story.

i have several PDFs/Books now that help you use base 10 blocks for learning math. They are colorful and bright, chock full of graphics and math concepts. Children love them and so do parents. Check out all the testimonials. 

You will need passwords to go here for even more fun pre-school math activities. Go here for more on cross teaching multiple concepts, with counting that includes addition, multiplication and fractions, you will need the site wide (MODIII) password to get into those pages. 

Before we can learn to count, the child must develop a one to one correspondence with numbers. That is, if there are three things on the table...like three pieces of macaroni...they need to see it's three and stop at three. Young students will count after the pattern they have heard. 1, 2, 3, 4, 5, and may keep going even though there are only three things there. This is common and "NORMAL."  This PDF will make learning to count and developing that correspondence EZ; using base ten blocks makes it easy and fun. Don't want to spend any of your homeschool math budget just yet?  Take advantage of all the free stuff first. Several Charter Schools may allow you to "expense" a password.  

128

i could go on and on about all the ways to count that simple tower. 16 is eight 2s, four 4s, two 8s.  Eight 16s are 128. 4x4 = 16 = 4² 

4 x 4 x 4 = 64 = 4³ 

We literally made a cube out of fours. Which involved destroying this tower. so before we did that we counted.  

2 x 2 x 2 x 2  is one level.  2⁴ = 16 So what is 2⁴ x 2? Well that's the same as two levels, 16 + 16 = 32 = (2 x 2 x 2 x 2)2 = 2⁵

128 = 2ˣ Solve for x: count blocks. (2 x 2 x 2 x 2)(8) One level of 2s eight times. (2 x 2 x 2 x 2)(2 x 2 x 2) = 2⁷ White board or paper and pencil to keep track. We are just counting 2s in a special way. 

128 = 4ˣ Solve for x: count blocks. 

We're just playing with twos and fours and counting twos and fours and learning all manner of math concepts like distribution and exponents as a matter of course.  But all we did was count. Younger students get less of a lesson, older students get more of a lesson. Same tower; how much you do depends on the child's ability, interest and engagement.  Always leave them wanting more. There is so much more you can do. Count creatively. 

Fractions lessons with one level, twelve is 3/4 of 16...eight is half (1/2) of 16...four is a quarter (1/4) of 16. They can SEE it.  Make them point to it. "Show me..."

Fractions lessons with two levels, now we have 32...16 is now half, 8 is now one quarter of 32. 4 is one eighth (1/8).  And we have fun lisping. Now how much is twelve? 4 = 1/8, 12 is 4 x 3, so one eighth three times is 12 and  (1/8) x 3 = 3/8 = (1/8) + (1/8) + (1/8) So how much is 24 then? What do you mean three fourths? 24/32 = (8 x 3) / (8 x 4)...that's no fun, get back to one...3/4. Two brown rectangles, three eights over four eights...

Counting and knowing 12 x 12 is 144 is faster and easier than adding the parts (1 x 4) [or 2x2] + (3 x 4 ) + (5 x 4) + (7 x 4) + (9 x 4) + (12 x 4) is a lot of counting and adding to get to 144.

How many sevens can you find in that robot? i count 16. What is 7, sixteen times? 

More FREE fun stuff for counting.

Here is a FREE base ten block app that will help them master the names of the blocks and build nines and tens.

Another fun way to learn to count is to find the base 10 blocks. This page is designed for toddlers with a simple preschool math activity that you can do with pre-schoolers without even leaving your keyboard. Maybe you like to play "find it" games. It's a "find the base 10 blocks" game. 

My PDFs help you with your homeschooling.

Eventually, they will learn that each number goes with the thing you are counting in a one to one correspondence and in a certain order. It happens one day...and once it happens they don't go backwards. They wake up and suddenly they count 5 fingers and stop at 5.

Once they master counting to nine we can really begin teaching math, including division and algebra right alongside more advanced counting (like 10 through 20) and addition, subtraction, and multiplication. You'll see if you watch videos on tis site and get M0AR Training. You can start with my free subtraction book right alongside learning to count...again all arithmetic is, is counting.  Arithmetic is how we DO math. 

i know this can be overwhelming to some because it's so completely different from the abject failure that is mathematics teaching in public schools currently. It is refreshing and wonderful to others. So here is a page that gives you an idea of how EZ PZ it can be. i give you a PDF and over view of what to do and how to do it.  Emphasis on fun, singing, and playing. 

If you have very young younglings get them to repeat after you and count to 20. Do this often. You don't have to do this during "math time", i mean often in the car out of the blue, or during dinner or bath time or bed time: any time is math time. Then count backwards sometimes from 20 to 1. Let them hear the pattern. Just like ABC's except you don't go backwards with ABC's, although you should.

Games & Activities 

Use games and activities to make learning to count simple and fun.  Use this website to keep it that way all the way through algebra, trig and precalculus. 

Basic lessons: you count and have them repeat after you one at a time. Then in strings of three, then five, then ten.

One, two, three...

One, two, three, four, five...

All the way to TEN. You can also just count the first three of each block in the top tray. Green ones: One, two, three; Orange ones: two, four, six; pink ones: three, six, nine...etc..

As you can see, there are many resources t help you get going. The old editions of the  Series A manuals are available online on this website. Along with my books, teaching counting should no longer be a problem. 

We don't need symbols or deeper understanding we just want to start off with hearing the numbers in order from one to twenty and back again. This will make things easier when they are introduced to base 10 blocks and the symbols. The next step is matching the symbol to the the block and the word. Example "six", "6" and the purple block. Check out Absolutely Amazing Addends and my wondrous workbooks for more. 

Even before we learn to count we can still learn the names of the blocks and symbols (my addends app will help) and then add more meaning from there.

It's basically boils down to learning vocabulary when the child is in the pre-counting stage. This will very quickly go from naming things to naming things in a certain order, which is what we grown-ups like to call counting. Here are some Pre-School Math Activites. Once we can count to nine, we can start doing "math." 

There are plenty of activities that can help you start the ball rolling.

There are several Products from Motensen Math to help start the process. Ebay is a great place to find stuff.  The go to kit is the combo kit. It is nice to have all the extra trays and sets but you don't need them  

A great book is "Ten Apples Up On Top" By Dr. Suess.  i have a video that shows you how to maximize this simple book for learning to count and add and do problem solving. Just reading it is good but you can use it to greater effect if you count apples, compare apples, add apples and have the child do it with you and for you. Great just before bedtime. Eat. Sleep. Math.

Math is everywhere all the time. Make it a fun part of their lives not drudgery and trauma. Remembe: put them in a math rich environment and they will learn math. Put them in a the Situation where they cannot fail and they will succeed.

Some of the best stuff for counting is often free or low cost...like raisins, Macaroni or simple playing cards.

Incorporate counting around the house: doing dishes, cooking, hanging clothes, folding laundry (count socks two by two) etc.

Learning to count should be painless and "natural", based on the child's curiosity and imagination. 

Go from this counting page back home. 

EZ PZ Overview
Place value with base ten blocks
Place value and more. 
FREE Fun Software App
FREE Preschool Math game
Sesame Street Counting Videos

Blog Posts On Counting
Blog Posts On Teaching Counting Using Algebra
Blog Posts on Teaching

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The essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~S. Gudder

"Although I am almost illiterate mathematically, I grasped very early in life that any one who can count to ten can count upward indefinitely if he is fool enough to do so. ~Robertson Davies, "Of the Conservation of Youth," The Table Talk of Samuel Marchbanks

" ‘Obvious’ is the most dangerous word in mathematics".~Eric Temple Bell, Scottish mathematician

"Mathematics allows for no hypocrisy and no vagueness".~Stendhal (pen name of Marie-Henri Beyle), French writer

Bonus Screencast:

Upcoming PDF.  More always being added. While it's in the works you can use this as an example for you homeschool.