Tuesday, September 6, 2016

Montessori Math -- Long Division with Bows .......or Ninjas

Oh, boys!! I am borrowing this ninja-division idea from MBT because I thought it would appeal to my boys. I presented the regular lesson, long division with bows, to my daughter a couple of years ago. D runs away screeching when anyone comes near him with a hair tie. Ninja-math it is then.

Long Division with Bows is a primary lesson, usually presented at the end of the golden bead sequence. This work explores division with divisors larger than 10.

...this is because I can never remember with thinking about it a second time!

By now, the child is familiar with:
Prerequisite Skills
  • counting out golden bead quantities in all categories (units, tens, hundreds and thousands)
  • finding and composing category cards (in this case we are using a 100 card, a 40 card and a 4 card)
  • color categories (green is units, blue is tens, and red is hundreds)
  • matching golden bead quantities with category number cards
  • exchanging 10 of one category for 1 of another (10 unit beads can be exchanged for 1 ten bar and visa versa)
  • dividing a quantity of golden beads up into equal portions (much like we do with snack crackers, hot wheels cars, and a lot of other things we need to share)
  • and dynamic addition, subtraction, and multiplication using the golden beads 
It is time to present long division with ninjas.


  • Golden beads
  • Large number cards
  • Small number cards
  • Wooden tray for fetching
  • (12) Green felt rectangles (or you can use green colored trays)
  • (1) Blue felt rectangles (later on you'll need a total of 12 blue felt rectangles and several red felt rectangles too)
  • 12 green bows--or ninjas
  • 1 blue bow--or ninja (later on you'll need a total of 12 blue bows, or ninjas, and 5 or so red bows, or ninjas)

Here we start with "144 ÷ 12 =" both in number cards and in golden beads. (I think that there are four unit beads in that cup, you just can't see them all.) We will call this 144 quantity our dividend, and this will be our quantity we will divide up among our 12 ninjas. Large number cards represent our largest dividend quantity, and small number cards will represent our quotient.

Our golden beads, number cards and tray are from Montessori Outlet. I purchased our alien ninjas from the dollar store.

We set out "12" ninjas. The blue ninja is the boss-man of 10 green-foot-soldier ninjas and he is going to pay out a wage to each of them. The green ninjas aren't bosses of anyone else and represent themselves. They will each receive their own single wage. The "ten" ninja goes to the left, as we would put the tens place holder to the left of the units place holder.

We give a blue ninja 10 times what we give to a green ninja. When a green ninja gets a unit bead, the blue ninja gets a ten bar. When a green ninja gets a ten bar, the blue ninja gets a 100 square.
D found the small number cards that represent the quotient or the wage of one foot soldier. In this case our quotient was "12."

Then we tackled "1,572 ÷ 12 =." You can barely see in this shot that a single foot soldier receives "131" golden beads.
Then we asked the question, does the blue ninja really have enough to give 10 green ninjas their "131" wage?
We  laid out ten green felt rectangles. (There should be felt rectangles under each ninja, oops.) And then laid down ten green unit ninjas on each rectangle.  Then we divided up the golden beads the blue tens-ninja received (1,310) among the green ninjas. After exchanging the thousand cube for ten hundred squares, and a hundred square for ten ten-bars, we found each green ninja did receive "131" golden beads.

Long division can be a total-body-workout.

Direct Aim:
Preparation for long division; demonstrating that the quotient is the portion of the dividend that a single unit receives.

And there you have the first moment of the Long Division with Bows, er...ninjas, presentation.

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