Morning Math – Fraction Division (May 24th)

Dear Alexander Morning Math Families:


 Today we started with short group lesson on division of fractions. Today we used the Montessori “round”, “circle” or “pie” shaped fraction material.

A smaller group of students stayed after the lesson to work with materials and “diagram” the lesson. Others worked independently.

When we “diagram” a lesson, it means that we draw a picture and label it, to help reinforce the concept we studied.

The lesson started by taking out the materials to demonstrate simple story problems: sharing pieces of pizza with small groups of friends.

I emphasized again to the children to that when we write number sentences, it can describe a “situation”, or be a statement of some thing we OBSERVE.

For example, if I lay out the fraction pie piece of ½, then say, “I want to share it with three friends – what do I do?” the children respond, “cut it in three equal pieces.”

So we took out three little green “skittles” (shaped to resemble people, with little round heads) then found the three fraction pie pieces that together equal ½.

We shared them equally with the skittles, and found that each skittle (person) got 1/6 of a whole pie.

So I invited the students to LOOK at the materials as they worked with them, and consider how to write statements that are OBSERVATIONS of what they see, then to copy my diagram.

When a child learns to DRAW the picture of the materials, we see that some “process” the example more deeply than if they did not.

They actually traced the fraction pieces, OR simply drew the picture as a copy of my own, and labeled the diagram.

I also wrote the number sentence that was true:  1/2 ÷ 3 = 1/6.

Please see the following posts with the other two examples – we created three examples of fraction division in all.

They did a great job!

Please note that these pictures may not be perfectly proportioned or to scale…

These are the drawings I made on pieces of paper, which the children copied.

The plan here is to reinforce CONCEPT. Many adults and children understand basic fractions concepts, BUT as we explore advanced fractions work, such as fraction multiplication, many adults and children stop understanding the concepts and simply learn the rules of the algorithm, like (for division)  “invert and multiply across”…

…but then we have to remember when to apply which rule, when what is best is to learn the concept that resulted in the rule.

Please, never get frustrated with the child for not “getting” or “remembering” a concept… it takes TIME, PRACTICE, and mental, developmental GROWTH to fully understand concepts. I didn’t really “get” some of these concepts until I had completed my Montessori training and taught the material for a number of years!

I plan to continue to add this reminder at the end of the blog.

Please note:

The separate blog for general school information and updates is now:




www.alexandermontessorisunblog.blogspot



The morning math blog page is:

http://alexandermontessorimorningmathsunblog.blogspot.com/

I suggest you bookmark these addresses for ease of access.

We have placed restrictions on them so that for the moment they would not be searchable via Google, for example.


Please don't expect a "mandatory" daily posting at either site. I will try to post at least weekly, and to inform families by Alertnow e-mail when I make the "weekly" post.

Thanks!
James McGhee II, Headmaster