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Montessori Math Equivalence & Crisis of Nine Tray

Equivalence Tray

Equivalence Crisis Tray – Montessori Math Lesson

Equivalence Tray – 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’sd 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 have to 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 have to move to a new place…”

crisis of nine

Presentation II – Exchanging

  • 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 on to the thousand cube by counting the hundred squares.
  • Summarize and quiz the child: “ten units make what? Ten bars make what?” etc.


  • 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 to you various quantities. Occasionally ask for ten of something to check if the child understands the exchange.


  • 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

Have fun!

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