Can someone help me understand the following in terms that i can understand because i've read the book,definitions i've done research and i am new with this and i still don't understand.The teacher is hopeless at explaining that's why i am here for help.
1) What are the difficulties of understanding radical expressions? How 2) what are square roots? can somone explain it to me in easy words to understand.
3) What are cube roots?
4) what are i believe this is how you write it n^th root
5) what are radicals?
these concepts?
6)What are some limitations of square root?

thank you i figured it out

Let me answer questions 2 and 3 anyway...even if you did figure it out. This answer may help others and may help you have a better understanding of why we call it a 4^3 "four cubed" and why we call 4^2 "four squared."

In Montessori, we have something called the Bead Cabinet. You can see a picture of one here:

It is made up of beads (hence the name...) Sometimes, you will hear the work refered to as a "bead chain" because it consists of beads that are put together in a chain. The small three chain looks like this (each "o" would be a bead and each "-" is a link that links them together):


We have a set of plastic arrows to go with this. There are 3 of them. One says 3, the other says 6, and the last one says 9.

The child can count the beads and put the right number at each break. So it will look like this when they are done:

3 6 9

There are 3 sets of 3's...which is 9. 3x3 is 9. OR 3 squared is 9. Why call it 3 squared though? We can take the chain and fold it so it looks like this:


Then fold it again so it looks like this:


Well...close to it. It will actually make a square (rather than a rectangle). So it really IS a "3 square" They just counted it up and know that there are 9 beads. So now they know that 3 squared is 9.

With cubes, we link three of the three chains together (those are what you see hanging in the picture). So they look like this:


The child learns how to count it out (arrows are provided for 3, 6, 9, 12...up to 27) then fold it properly so it looks like this:


Notice how it's 3 of the three squares? Now, go back to the picture of the bead frame again. You can see what the 10 squares and the 9 squares look like fairly decently. (Hard to see 3 just because of the angle of the picture). But if you take the 3 "three squares" we have and stack them on top of each other, we have the same thing as the three cube (see the cubes along the top of the bead frame?) So you usually just have to ask the child, after they did this, "how much is 3 cubed?" They'll look and say "27."

They might not have it memorized or be able to put it in exponential form (3^3), but they understand the concept of it. And, if I explained it well (hard to do without the materials actually in front of you to show you), I hope you do too :)


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