My mother was a public school teacher for 30 years. She was certified for K thru 12 but settled into teaching second grade. At the time one of the major hurdles she had was teaching them place value. The curriculum that they had took a few weeks to get the concept across.
I went in there and had in done in two days literally. 100% competency every kid in her class understood the numbers have two parts "the how many part" and "the what kind part" and the numbers tell you how many the places tell you what kind combined with base ten blocks even the SPED kids had NO PROBLEM.
I remember my mother asking wryly, "now what are we going to do for math for the next too weeks?"
So I taught them algebra.
The principal of the school who had a minor in mathematics came to the classroom for something and he stopped at the door as I was casually teaching a group of 2nd graders to factor polynomials...by then they were giving me the factors of problems like x² + 9x + 20...
Anyhow, here are some vids covering a simple and expanded lesson on place value and the names of numbers.
When you start out you can just do the numbers from one to 1 million, three at a time, and then the next day do the numbers smaller than 1. Use a three period lesson. Treat place value like vocabulary...you are just learning the names of numbers and the pattern is easy to discover.
I did it all at once for this student because this student was older. He had some questions about the decimal point and where the one-ths place went the way MOST kids do.
Now you can get this handled and understood in a few days...give them a little home work and I would bet on 2 days. [b]THEN YOU CAN DO SOMETHING ELSE.[/b]
I bet if you as an adult were forced to do the same thing over and over again and the subject matter was presented in a way you really didn't understand they be telling to you had ADHD or ADD and would try and pump you full of drugs too.
Place value should be easy. By the time you spend some time on this page you should be quite comfortable presenting these concepts to your students. Remember to break it up and add more meaning as you go. Very little kids only need to learn up to 1,000 to start. Then you can play games and ask questions: what does the 2 in 1,257 mean? Which is more in that number the 2 or the 5? Etc.
Manipulatives make division easy and even fun. Here is the page at the House of Math on Division. Here are a couple of videos covering division mostly for parents and teachers. The first is much longer and the second is much shorter.
You don't have to teach division last you can teach it first if you want AND you can use it to teach subtraction and multiplication. Conventional wisdom is you have to know how to multiply and subtract to learn the algorithm for division.
Face it. Kids hate long division. They hate it for a lot of reasons. They haven't mastered multiplication; they don't like subtraction because counting backwards can pose challenges they aren't sure where to start counting. Manipulatives and the concept based base ten block methodology erase all of that. Mortensen Math rocks.
As you can see this is edited a little, the whole thing is available HERE. Only about 5 or 6 minutes is missing, the part covering negative polynomial division.
Here is a follow up video:
Between these to videos, the division page at the hous of math and this blogpost
you should be very comfortable presenting division concepts to your young students.
Practice with easy problems that have no remainders FIRST. Get comfortable. SPEND THE TIME, and do a lot of problems. THEN start doing problems with remainders and bigger problems and problems that are hard to model with manipulatives. All the while DO NOT leave out the part where they draw pictures. When we get to the problems that are hard to use blocks to model we can draw pictures and finally we can move to the the symbols ONLY. And the student knows what they are doing and why and although division may never be their favorite thing, it won't be confusing or hard either.
Now we are serious when we say that you can start with smiley face division books if you like because the baby step approach allows you to teach counting as you go. Here a couple of shots from the beginning of the smiley face series.
Keep in mind these books are made for PRE-SCHOOLERS. It should be obvious that older students can benefit from these books too. I suggest that they start at the beginning and "breeze through" until it begin to hit their level rather than skip the first books altogether. Here is book one:
Here is the end of book one. When you are 4 this is a lot of counting! I have seen people fool around with little 2 and three year olds where the child sits in their lap and just points to the right answer. Also because the price has gone up so far using a sheet protector and wet erase marker to get more milage out them is advised. They are no longer priced as consumables although they were originally intended to be.
He is a scan showing book 5. Expanded notation helps with understanding and is used as an intermediate step. I have a personal problem with the placement of the quotients and this was supposed to get fixed but we never got around to it. When Crewton Ramone comes out with a similar series it will be available in pdf form and some of these oversights and compromises will be fixed. It also had to do with the tech of the day 20 years ago but this is no longer an issue.
Remember bigger is funner. Also remember to let them make up a bunch of their own problems that are NOT in the books. As the parent or teacher you should make up some problems too. Practice.
Each booklet is 20 pages long and designed to be non-threatening. So you can see I am showing you page one and then the end of the books. This is the end of book 10. I have seen 5 years olds complete these books. Kindergarten math at a public school is pretty much a snap after that. Tee hee. If you can not afford the books just do lots of problems using the blocks and have them keep track of the problems they did in a journal. YOU may have to do a lot of the drawing and symbols for them because the whole point of these books is that they can learn math without the fine motor skills required to work a pencil.
Hat tip to Elizabeth Stevens for doing all the scans.
Divinely Dandy Non Difficult Division
Get Divinely Dandy Non Difficult Division for just $19.99. This book will show you everything you learned here and MORE laid out step by step with links to videos and pages that give simple concise explanations for how to use the rectangle to organize thought, how to introduce division concepts at a very young age, and how to make fun while you are doing it. I guarantee that video alone will expand your thinking when it comes to division and math.
Watch the video on the Preview and Purchase page that gives you a page by page over view of the PDF so you can "try before you buy", see exactly what you are getting and be confident it will be money well spent.
