For
the past three weeks, I’ve been away from my Montessori learning environment (and
my students) due to the COVID-19 pandemic. Since I am feeling nostalgic for the hands-on didactic manipulatives that help children learn
without abstract formulas, I want to describe why these materials are so
wonderful. (I last wrote about Montessori math materials on this blog over seven years ago, in case
you want to search under the Math tab on the right hand side to learn more!) The following are Montessori math materials most relevant to the youngest learners
in a lower elementary classroom, the 6-year-old first graders.
100 board
This
material is often introduced in primary (age 3-6) Montessori learning
environments, and I also find it a helpful assessment of number sense for first
grade students and children new to the Montessori lower elementary classroom.
The hundred wooden tiles sit randomly in a two-column rectangular box and fit
neatly on a board with a hundred blue grid boxes. Children often enjoy doing
this work in partners, although it can also be done independently. One way of
giving this lesson is to ask the child to find all of the numerals that end in
zero, then all the numerals that end in five – and lay them out on the board
first, followed by other numbers per teen.
I
have observed some very linear children like to lay them out in order, some
children group them by teen, and some children who enjoy just taking their time
with it choose tiles at random and find where they go. There is no need for an
adult to intervene – by showing or asking the child where the tiles go. This is
an intuitive experience that is only disturbed by interruptions and
interventions. All Montessori materials are naturally self-correcting.
Golden Beads
numeral composition
Another
Montessori math material used frequently in primary classes that is also very
useful as an assessment for new lower elementary students is the set known as
the Golden Beads. One of each – a unit bead, a golden ten bar, a golden (or
wooden) hundred square, and a golden (or wooden) thousand cube – sit in a
rectangular presentation tray. Montessori guides (teachers) lay out a Golden
Mat (actually usually colored green with place value columns) and write, on a
board or piece of paper (or using wooden numeral tiles), a four-digit numeral.
Children take an empty tray to the shelf where the Golden Beads are stored and
retrieve the correct amount, sometimes all at once, and sometimes very slowly,
one place value at a time. There is even a little golden dish for the unit
beads to sit in.
The
child places the Golden Beads in the correct place value column and reads the
numeral aloud when they are ready. This lesson assesses number sense and place
value sequencing, as well as demonstrates the child’s spatial balance and
math-language abilities.
Infinity
Street
The
first official Math lesson I do with first graders and children new to the
Montessori lower elementary environment also reinforces place value
understanding. Infinity Street is not an original lesson created by Maria
Montessori in 1907, however it was introduced in my Montessori training. I
have used it with children for 15 years with great success. It takes awhile to
do, mainly because it has a few steps, a lot of coloring, and requires some
fine motor skills.
Infinity
Street is a basket containing twelve yellow houses that are in ascending order
of size, much like a two-dimensional set of nesting dolls. Each house comes
with a label (Simple, Thousand, Million, etc. up to Decillion, the largest
house in the basket – not the largest possible number family!) and a yellow “mailbox”
comma to put between each house. There are three “doors” on the front of each
house – green for units, blue for tens, and red for hundreds – as each house
contains these three place values. In the first lesson, the Montessori guide
tells the story of Infinity Street and invites children to help read or lay out
the labels and commas.
In
the first extension (maybe a day or two later), the children work in partners
to lay out the houses, labels, and commas in order. Size is the control of
error on the houses, and the labels and commas have number keys on the reverse
if children need to check their work. In the second extension, children lay out
their house and trace it onto a long swath of butcher paper. They write the
label name for the number family (such as the “surname” Trillion), and color
the house yellow and each of the doors green, blue, and red. They even draw the
comma “mailbox” between their house and the next child’s. At the end, we display
Infinity Street on a wall so all children can access it for reading large place
value numerals!
