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Montessori Math Equivalence & Crisis of Nine Tray


What do you get when you cross a Montessori math equivalence sensibility with an impending crisis of nine tray? Quite the conundrum, if we do say so ourselves!

What we mean to say is that while many teachers may be inclined to use traditional counting methods during times of duress, Dr. Maria Montessori’s approach to mathematics offers another solution: using materials that allow for exploration and classification. Come see how we put this theory into practice in our latest blog post!

What is the Equivalence Tray?

This activity introduces place value to kids. Specifcially, the activity teaches the child that 10 units (or beads) are the same as 1 ten (1 ten bar), that 10 tens (10 ten bars) are the same as 1 hundred (one hundred square), and that 10 hundreds (ten hundred squares) are the same as 1 thousand (a thousand cube).

Equivalence Tray

How to Give the Equivalence Tray Lesson – Presentation I

Invite the child to see some new work with the golden beads.

Spread a mat: “This is the equivalence tray. Some people call it the Crisis of Nine Tray. Let’s look at these beads and count them. We’ll start with the units.”

  • Count the units from their tray into the mat below in a vertical line, touching each other.
  • “Ten units is the same as a ten bar. When we have a ten bar, we must move to a new place. We can’t stay in the unit’s place anymore.”
  • Use the same approach and language with tens/hundreds and hundreds/thousand: “Ten bars is the same as a hundred square. When we have a hundred square, we must move to a new place….”
crisis of nine

How to Introducing Exchanging – Presentation II

  • Return to the row of units: “Now, let’s count these again.”  Make a big deal of moving to the ten’s place and picking up a ten bar “because ten units are the same as one ten.” Continue to the thousand cube by counting the hundred squares.
  • Summarize and quiz the child: “ten units make what? Ten bars make what?” etc.

Equivalence & Crisis of Nine Tray Variations

  • Use separate mats for each quantity so the child must move his body considerably to count the beads.
  • Ask the child to give you or to bring you various quantities. Occasionally ask for ten of something to check if the child understands the exchange.
Montessori Equivalence Tray

Equivalence & Crisis of Nine Tray Extensions

  • Make a Take Home Booklet showing equivalence. So, ten units on one page and a ten bar on the opposite-facing page. etc
  • Draw or color the bead material

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