Friday, March 6, 2009

Math, Math, Math

This has been a big math week in class, finally. The four year olds and the six year olds were working away. I recently made a material I found at Cultivating Dharma. It is a very challenging work even for my math wizards.

The student lays out the labels - "How many thousands," "How many hundreds," "How many tens" and "How many ones." Next, they place the quantity labels beneath the color coded labels. The most challenging are the thousands and ones in terms of placement because they are both colored green. As I have explained to my students many times, the reason for this is that hundreds, tens and ones are in the simple family and are found to the right of a comma for a sum greater that three figures. The thousand family is found to the left of the comma. One thousand, two thousands, are the ones of the thousands.

After laying out all of the quantity labels the child then tries to answer the question posed: Ex. How many tens? If the quantity is 3,456 the answer is 5. A card with the single digit 5 is placed to the right of the quantity card. I was very surprised to see some of my oldest and math capable students struggle with placement. They had to remind themselves to count over three figures for hundreds and four for thousands. I really recommend this work as it reinforces and allows children to practice placement and labeling of value.

Ria worked with the short chains for an entire morning. Logan had his first lesson working with the teens board.

The first year four year old students leaped from the teens and tens boards to addition with the small number rods and with the addition strip board. They really did a wonderful job proving that it was the right moment to present them with the work.

One of my second year students was very focused while she squared the five long chain she was working on and then cubed it.

Two of my older students are calculating the jeweled tower. The tower is constructed with all of the cubes from the bead cabinet. They counted each long chain, squared them and then cubed them. They wrote down each sum for each cube and next week they will cut construction paper squares to represent the different colored cubes and create a paper jeweled tower. They will write the sum for each cube next to its matching image and then write its total. They worked on it for almost a week. Next week they will finish and I will post pictures of their work.

Looking at the photo below, imagine each of the colored cubes placed one on top of the other, going from right to left, from single unit cube to thousand cube. It is easy to see how it would stand up to make a tower, the jeweled tower. Each of the cubes fit into each other perfectly - if you have never done this before try it. As you feel the eight cube and the nine cube and the hundred cube fit snuggly into each other, one on top of the other, you will instantly realize that they were made to do so.


Hannah said...

I am very impressed actually seeing the pictures and reading your descriptions of what the children are doing in math. My kids are way behind in that category, I think! It is mostly because I don't have the materials right now, and I am hesitating to make them because I would rather buy...the math materials are so beautiful!

My question for you is regarding the order of math presentations. I got a hint from this post, but want to double check. Do you progress from the simple number work (number rods, spindle boxes, numbers and counters) to the teens and tens boards, and then on to the colored bead bars and addition work...I have seen different orders of math presentation, and I am confused. When do you introduce the Golden Bead material? Does it really matter the order of some of the lessons?

Susan Y. Dyer said...

I do the teen and ten boards, the colored bead bars and then onto the small number rods (+) but I pair addition and multiplication, subtraction and division. So my older four years olds may use the multiplication bead bars as it is easy for them as they recognize the quantity for each color. I think that if you go on-line and google Montessori albums you will come up with a few on-line albums. Also, Montessori by Hand (Sew Liberated's old site) you can join her yahoo group and she has her albums available. So you can download her AMI math album and see her index for the order of presentations.

Also, I always remember a trainer at a refresher coarse saying "Follow the child not the materials." If a child is interested and ready don't hesitate because he did not have this lesson or that lesson first. You can return to this "earlier" lesson later telling the child that you think that the work will help him/her do better at this other "later" work.

Again, google Montessori By Hands Montessori Albums.

Big questions - little answers...sorry. Hope I have pointed you in the right direction.

Susan Dyer
The Moveable Alphabet