Tag Archive | Mathematics

DIY: Golden Beads

One of my favorite Montessori materials are the Golden Beads.  These are math materials that really allow the child a concrete experience to develop an understanding of place value as well as addition, multiplication, subtraction, and division.

The first presentation with the beads allows the child to experience sensorially the differences between the categories, not only in bulk but also in shape and weight.  The unit bead, ten bar, hundred square, and thousand cube clearly show the geometric progression of the decimal system; each category is ten times the previous one.  That initial presentation is so important for understanding those differences, that I went ahead and bought the real set.  It’s not cheap, but it’s one of the materials worth the money.  (At Montessori Outlet, it’s around $35, and at Nienuis, it’s anywhere from $65-$160.)

Golden Bead Tray

However, once I was ready to move on to Formation of Large Numbers with Beads and Cards and the Collective Exercises, I really didn’t want to pay the money required to buy the full set of Golden Beads.  (One thousand cube is $30 and up.)  Wooden hundred squares and thousand cubes are much more reasonable (you can get 9 wooden cubes for basically the price of one bead cube), but honestly, I was doing this last minute and didn’t want to wait for a slow Montessori Outlet order to arrive.

wooden cubes

So I starting searching the internet for homemade alternatives.  I saw a lot of instructions on how to construct your own with real beads – whether with wire, pipe cleaners, or whatever else, but I wasn’t looking for something that crafty.  Plus, I didn’t want to have to run out and buy materials.  I kept looking.

I finally stumbled across a page which had a print-out of a cube pattern, complete with the dots.  Perfect!

IMG_9020

I printed out enough to use for both thousand cubes and hundred squares.  Now, just as cardstock paper, I was going to lose most of the sensorial benefits of the Golden Beads, so I had to do a little work.

I already had foam board on hand, so I glued the hundred squares onto foam board squares so they would be at least somewhat 3-D.  That barely added any weight however, so I grabbed some coins.  I taped two pennies onto each square, between the paper and the foam.

IMG_9122

For the cube, I taped a penny onto each square and then glued the whole thing together.  I had thought about trying to use foam board inside these as well, but decided not to.  Six months later, I’m kind of wishing I did – several of them are a bit dented in.

IMG_9105  IMG_9112IMG_9121

The final result turned out to be…definitely usable.  They are in no way up to the quality of the bead or wooden materials you can buy, but with a low budget, they do the job.  They cost literally pennies to make!  😉

You can see here how they compare with the bead materials in terms of size.

IMG_9124     IMG_9126

IMG_9120  IMG_9117

DIY: Spindle Boxes

Here’s a great DIY for anyone whose child is learning numbers, whether you typically use the Montessori method or not.  Probably all parents have smiled as their very young child sang the alphabet song, long before the child could use those letters in writing or even identify the symbol for each letter.  The same thing occurs with numbers – children learn how to verbalize a string of numbers in order long before they understand the concept of what those numbers actually mean.  That’s where the Montessori Spindle Box comes in.

The Spindle Box has 10 equal compartments, numbered 0 through 9.  The child puts the appropriate number of spindles in each box.  Doing this work helps the child understand that each number, a quantity in itself, can be made up of separate objects.  It also demonstrates in a concrete manner that zero represents no quantity.  In addition, it is an indirect preparation for the fact that there are no other symbols but 0 to 9.

For some reason, I absolutely love this lesson, and I absolutely love the Nienhuis material for it.  It’s a pretty easy DIY material, but I still had to convince myself not to spend the $30 to buy it!

Convince myself I did, though, and I must say that I love the result!  Dr. Montessori emphasized that materials for young children should be beautiful, and I think this one really is!

My first step was to decide what to use for my 45 spindles.  Popsicle sticks would work perfectly, but I didn’t have any of those on hand.  Unsharpened pencils could work if I had enough.  Q-tips were a possibility.  Sticks would be awesome when doing this as an outside activity.  I finally decided on toothpicks.

Next, I needed a container to divide into the ten sections.  We have a ridiculous number of Amazon boxes of all shapes and sizes tossed into our garage at this point, but I wanted something prettier.  I looked through the kitchen and found a beautiful tray that seemed like it could work quite well.

To make the dividers, I simply cut small strips of cardstock and held each in place with a piece of tape on each side.  I did my best to make them centered and equally sized.  I was a little off, as you can see, but I figure it’s close enough.

Next, I needed to add my numbers.  I have tons of alphabet/number stickers, so I just picked a sheet of those, stuck the stickers on cardstock, cut them, and taped them onto my tray.

   

The only other material I needed was something with which to tie together each group of toothpicks.  My manual says to tie ribbons around each group, but Drama Queen isn’t that good with tying bows yet.  Rubber bands would work, but I couldn’t find that many small rubber bands.  I was just about to decide to skip that step (I’ll explain all the steps below), when it occurred to me that I have a little girl.  Which means I have hair loops.  Lots and lots of colorful hair loops.  I raided her hair accessory container and chose 8 loops, each of a different color (she doesn’t have 8 of any one color).

To add a little festiveness, I used Christmas items to hold the toothpicks and hair loops.

   

The next morning, both kids were immediately drawn to the beautiful new materials.  These are the steps of the lesson, as Drama Queen did them.

1.  Bring spindle box, toothpicks, and container of loops one at a time to the table.

2.  Point to “1”.  Ask child to read it.

3.  Point at other numbers through 9, asking child to read them.

4.  Tell child and demonstrate how to place the toothpicks gently one by one, counting out loud, into the compartments.

5.  Demonstrate the first two or three compartments and allow the child to continue.  (Drama Queen was very eager to do it herself!)

6.  When all the compartments have been filled, show that the toothpick dish is empty.

7.  Show empty “zero” compartment.

8.  Say, “There are no toothpicks because this number is zero.  Zero means nothing, no quantity.’

9.  Get out loops and tell child, “We will tie together each group of toothpicks.”  Do not tie “1” since it is not a group.  This gives the sensorial impression to the child that the separate objects represent one number.  Double wrapping the loops was quite a challenge for Drama Queen at first, but she was determined to learn how to do it, so she kept working at it until she got it.

    

10.  Remove all loops and place back in box.  Return toothpicks to dish.

11.  Invite child to repeat exercise.

There’s also a fun Zero Game you can play with the child after she’s done some work with the spindle box.  You can do this with multiple children or just one.  Ask each child to carry out quick actions a certain number of times.  After asking a child to do something zero times, plead with her, “Why are you not doing anything?”  Allow her to explain that she was told to do it zero times.

DIY Sandpaper Numerals

Sandpaper is quite important in a Montessori Primary class.  The Touch Boards are a Sensorial material that refine the child’s tactile sense and control muscular action by the necessary lightness of touch.  They also serve as preparation for writing.

The Touch Tablets, another Sensorial material, train the child’s tactile sense so that he can discern fine distinctions between varying degrees of roughness.

Once a child has worked with those, he is ready to start working with the Sandpaper Letters.  These are just as they sound, sandpaper cut into the shapes of letters and glued onto a wooden board.  They’re one of the key materials in the Primary classroom.  Their purpose is to make the child aware of the symbols which represent sounds in words.  The child learns the letters by means of visual, muscular, and auditory memory.  They are also a preparation for writing.

The Sandpaper Numerals have pretty much the same purpose as Sandpaper Letters, but obviously for numbers.

So, all of these are great materials, and no Montessori Primary classroom would be without them.  However…I do not run a Montessori Primary classroom.  I run a home.  That is based around Montessori ideas.  With a family budget.  Not a private school budget.  I really have to pick and choose which materials I buy (because they’re ridiculously expensive*), which materials I make (that can take a fair amount of time – and apparently I’d rather spend my time blogging), and which I just do without.

The Touch Boards and Tablets have not made it into our preschool yet. (Although I may make them for Mr. BANG.  It actually has been a detriment to Drama Queen to not work with those prior to the Sandpaper Letters.)  I did actually purchase the Sandpaper Letters.  And after much consideration, I decided to make the Sandpaper Numerals.  With no sandpaper.

That, my friends, is what led me to sit in Starbucks with a couple of friends the other night, sipping hot chocolate, exchanging girl talk (the you-won’t-believe-this-private-parts-of-the-body-conversation-I-had-with-my-kid type), and cutting up felt and foam.  This was the result:

It was actually very easy.  Due to the size of the foam pieces, I just cut them in half to achieve the perfect size for my boards.  Then I drew the numbers on felt.  I did it freehand, and you can certainly tell, but it’s good enough.  Then just a little snip snip with the scissors, a touch of glue, and behold…my own Tactile Numbers.  (Drama Queen prefers to call them Touch-a-Truck Numbers.  As she laughs profusely.)

They made quite a hit with that little girl.  She was super excited as soon as she saw them, and has spent a good bit of time practicing with them.  She has known her numbers, but never tried to write them before.  After her introductory lesson with the Tactile Numbers, she sat down with her sketch pad and wrote “911” all down the page.  She said she wanted to write it down so she knows what to dial when there’s an emergency.

Now, what do you actually do with these, you ask?

Here’s the official presentation, using the three-period lesson**:

  1. Bring the tray with the Tactile Numbers to a table.
  2. Take out number 1.
  3. Trace it and say, “This is one.”
  4. Ask child to trace and name it.
  5. Do same for 2 and 3.
  6. Do second period, guiding child to trace at every step.
  7. Do third period, having child trace, then asking, “What is it?”  First do it in sequence, then out of sequence.
  8. If the child appears to be very familiar with the numerals, you may continue on in the same lesson.  Put away the first three so they do not distract, then get out the next three for the new lesson.  Some children may be able to breeze through all the numbers through nine.  Otherwise, continue the lesson in the following day or days.  Always review the numbers starting with one.  Do not introduce the zero yet.

*I’ll compare for you the cost for each item from Nienhuis (what all other Montessori companies try to be like; this is the company that Dr. Montessori hired to make the first materials for her Montessori communities) and Montessori Outlet (my favorite discount Montessori store).

  • Touch Boards $35.40/$11.95
  • Touch Tablets $64.80/$19.95
  • Sandpaper Letters $94.50/$31.95
  • Sandpaper Numbers $29/$6.95

**Many, many Montessori lessons are given using the three-period lesson. 

  • Period one:  Introduce the item/concept and its name.  Give the child a sensorial experience with it.  (In this case, they trace it.  When working with Sound Boxes, they would shake the little cylinder to hear the sound of that particular one.) 
  • Period two:  Give the child many opportunities to handle and name the object/concept.  In the case of Tactile Numbers, it would be things like, “Trace the two and put it in my hand.”  “Trace the seven and turn it over.”  You make this a fun game and do it repeatedly, in a variety of ways.
  • Period three:  Allow the child to have a sensorial experience with it again, then ask what the name of it is.