Number Composition and the Place Value Dice

As Montessori educators we have some of the most phenomenal teaching materials available to us to introduce abstract concepts in a concrete way.  These materials, designed over one hundred years ago by Dr. Montessori, have stood the test of time and are as powerful today as they were back in their conception.  These manipulatives incorporate the principles of isolation of difficulty, self correction/control of error, building upon previous knowledge and precision.  One such material that embodies all of these are the Golden Beads or Bank Material.

Once children have a mastery of quantity from 0-9 they can be introduced to the Golden Beads and decimal work.  Initially this work starts out as a nomenclature exercise with the Introductory Tray.  The children are introduced to the material along with the language that represents the hierarchy of numbers:  this is a unit, this is a ten bar, this is a 100 square and this is a 1000 cube.  Along with this, the children would be introduced to the numeral cards representing numbers from 0-9,999.  (see the post on the 45 layout )  Once the language is successfully paired with the concrete representation the child can then move to gathering quantities to create large numbers.  A child could be asked to get 9 ten bars and 4 units.  Get 3 thousand cubes, 4 hundred squares, 5 ten bars and 6 units.  This goes on for some time until the child gains a real comfort level with the nomenclature and place value.

Each value in our work with the hierarchy of numbers has a designated color.  While the golden beads are always golden the numerals representing the different values follow this pattern:  numbers for units are green, numbers for tens are blue, numbers for hundreds are red and then the pattern repeats itself.  Numbers for thousands are green since they represent the units or starting point for the next hierarchy.   Ten thousands are blue, hundred thousands are red and when we move to millions we start with green again.  This color coding is the standard used from level to level in Montessori schools around the world.

To help reinforce the color-coding aspect of this work the Number Composition Mat was designed. Children use this mat as an underlay for the building of quantities.  So in sticking with the example above, they would bring 6 units to the mat and place them on the narrow green strip on the right, 5 ten bars and place them on the blue strip, 4 hundred squares and place them on the red strip and then 3 thousand cubes would be placed on the wider green strip to the left.  Numeral cards could then be placed below the mat showing the symbolic representation of the quantity:  3456

The Number Composition Mat

The Number Composition Mat

Now to introduce an element of independence to this activity and to encourage the needed repetition for mastery, a set of Place Value Dice can be added.  These 10-sided dice numbered 0-9, are color coded to correspond to the colors of place value.  (They come in several different varieties and sizes, all described on the website.)  So a child would roll the set of 4 dice and then place them below the corresponding sections of the number composition mat:  the green die below the units section, the blue die below the tens and so on.  Next the child would fetch the indicated quantities from the bank and build the number indicated by the dice.  By using these dice all numbers between 0-9,999 could potentially be rolled.

The Number Composition Mat being used with Place Value Dice

The Number Composition Mat being used with Place Value Dice

Children love rolling the dice to see what quantity they will get and teachers love not having to come with numbers on the spot (and remember them) for the children to compose.  What is even more interesting is watching children explore the patterns of numbers with the dice.  So when they think you aren’t looking they manually manipulate the dice so that they all “land” on the same number, for instance 5555.  Or they really like to explore what happens when zeros show up. This free exploration and engagement in the activity is where the real aha moments occur and connections are made!

I’ll save the discussion on the many other ways in which the Place Value dice can be used for the next post!

The Alphabet Dice

When people think of dice they naturally think of numbers and math.  What is often exciting to discover is that certain dice can be used in other curriculum areas such as language and cultural.

In this post I’m going to offer some suggestions as to how the ABC or Alphabet die can be used to enhance the learning of initial sounds and word building.  The mastery of initial sounds is dependent upon lots of repetition and practice and the ABC die offers the child a wide variety of ways to do just that.  Once a child has been introduced to the sand paper letters and has a pretty good understanding of symbol and sound the ABC die can be introduced to offer the needed practice and repetition in ways that are fun and engaging.

Finding objects in the environment that begin with the sound/letter indicated by the ABC die.

Finding objects in the environment that begin with the sound/letter indicated by the ABC die.

One of the early exercises this die is used for is finding objects, either in a basket or in the environment at large, that begin with the sound that was rolled.  For example, the child rolls the 30-sided ABC die and it lands with the “m” on the top.  The child then searches the basket  (or walks through the room) and picks the object  that begins with “m”.  An additional step to this would be to fetch an “m” from the moveable alphabet box or the sandpaper letters and place it at the top of the table or rug.  Then the object can be placed under that letter.  The activity goes on for as long as the child wishes, until 10 objects are found or until at least one object for each letter sound is found.

Rolling the ABC die together with a numeral die:  find 3 things that begin with the "l" sound.

Rolling the ABC die together with a numeral die: find 3 things that begin with the “l” sound.

Another way to practice initial sound work with the ABC die is to simply roll the die and say a word that begins with the letter that lands on top.  This is an appropriate activity for a small group of children that need practice with initial sound work.  In addition to hearing the words other players come up with they are also being introduced to turn taking and group dynamics.  Each child can roll and say a word or they can take turns rolling but with each roll, every child has to come up with a word.  To take this to an even higher level, the ABC die can be paired with a numeral die such as the 1-3 die or the 0-5 die.  Both dice are rolled simultaneously and then the child needs to say the given number of words that begin with the given sound…say 3 words that begin with “m”.

This versatile die can also be used in conjunction with word composition activities.  Very similar to the oral activities mentioned above but now composition is involved, either with the movable alphabet or a pencil.  So the die can be rolled 10 times and with each roll the given letter is pulled from the movable alphabet.  Once 10 letters are drawn from the box (with the rule that 1 has to be a vowel) the child sets out to compose as many words as they can with the given letters.

Roll the ABC die 10 times and pull the corresponding letters from the movable alphabet.

Roll the ABC die 10 times and pull the corresponding letters from the movable alphabet.

 

 

 

 

 

Once 10 letters have been determined, see how many words the child can build with them.

Once 10 letters have been determined, see how many words the child can build with them.

 

 

 

 

 

 

 

Another writing exercise would be to write a word that begins with the rolled sound, or paired with a number die, write 3 words that begin with the sound.

To take any of these exercises to a more challenging level themes can be introduced. For instance, if the theme is animals then any word named or written would have to be animal related…3 animals that begin with “b”.   This is a great exercise in classification and word retrieval.

As you can see, this particular die has so many applications.  I’ve even had children use it in their handwriting practice.  They roll the die and then practice the given letter.  The addition of the ABC die provides the child with a game like experience, independence and above all, the needed repetition that will lead to mastery.  Why not see how many different ways you can come up with to use the ABC die to enhance the language curriculum?

 

 

 

 

Those Beginning Lessons

In our planning for the beginning of a new school year our thoughts turn to which introductory lessons we will be presenting in each of the curriculum areas.  In the Sensorial and Math areas there are actually beginning lessons for each different strand of instruction.  For example,  in Sensorial, there are the Cylinder blocks for gradation, Color Box 1 for color work, and the Touch Boards and Tablets for the sense of touch. Within  the math curriculum there are also several strands that the children can be working on simultaneously.  Once a child has a good understanding of 1-10 they can be introduced to the golden beads, continue work on linear counting with the teen work and hundreds boards and depending upon the child, may even begin work with the short bead chains.  As guides, we need to keep in mind that there are many starting points for the children and as such we have to be prepared for the various directions they may head in!

The 45 Layout or Bird’s Eye View, as it is sometimes called, is an important lesson in the sequence of the golden bead work.  This presentation allows the child to concretely see the growth of numbers and the progression through the hierarchy from one level to the next. Children are ready for this work when they can identify numbers 1-9 and after they have been introduced to the golden beads and the language of place value: units, tens, hundreds and thousands.  While this work has a great deal of repetitiveness built into it, I discovered long ago that the layout was often overwhelming for children and that they tended to avoid the work.  The 45 Layout Mat  was designed to provide a greater sense of organization for the child, to reinforce the importance of the color coding used in the place value work and to ultimately entice the children back to this important lesson.  With its strong built in control of error and beautiful appearance, I am happy to report that this mat has definitely served it’s intent…teachers report that children return to the 45 layout over and over again once they introduce the 45 Layout Mat into their classrooms!

The 45 Layout Mat

                    The 45 Layout Mat

Back to School

For those of us living in the south or mid west, the summer break from school is quickly drawing to an end. Despite the hot August temperatures, many of us will be returning to school within the next few weeks!

As I begin to prepare for the upcoming school year and my new group of students I am always looking for new ways to build a strong sense of classroom community and for activities  that will help make the children feel comfortable..  One such activity is to have each child create an “All About Me” page and then the pages from all the children are compiled into a classroom book.  It is by far the most popular and most frequently read book on our library shelf!  Another activity we do to help the children get to know each other utilizes the Interrogative Dice. 

Interrogative Dice

Interrogative Dice

Have the children work in pairs or small groups.  One child rolls the die and then asks a who, what, where, when, why or how question of the child sitting next to them.  For example, the child rolls the die and it lands on what.  They then formulate a what question for the child next to them…What is your favorite flavor of ice cream?  The activity can continue for as long as there is interest.  To extend the activity you can then have children introduce each other based on the information they have gained by asking questions…This is John and he lives in Tulsa (where),  his favorite ice cream flavor is chocolate  (what) and he goes to bed at 8:00pm (when).

Learning to ask questions is a challenging skill for young children.  By using the Interrogative Dice you are giving the children an opportunity to practice this skill in a fun and engaging way!

Best wishes for the upcoming school year!

Lori