Montessori Elementary Homeschool Blog - with documentation of our infant Montessori, toddler Montessori, and primary Montessori experiences; as well as preparation for the upcoming adolescent Montessori homeschool years.

Saturday, February 7, 2015

Montessori Decimal Checkerboard: Multiplication of Decimal Fractions by Decimal Fractions

My son loves the decimal fraction checkerboard so pulled it out again and... I got pictures this time!

(one day break from the "Week in the Life of Legoboy - Montessori Homeschooling" series to present this work he did LAST week. And give me some time to catch up on including photos in the blog posts of his week!)

5,429 taken 0.38 times. 

Set up the numbers so the units in the multiplier and the multiplicand land in a unit square on the board. 

First row of multiplication.

Second row of multiplication. 

Just before exchanging the final answer.
We have slid the answer diagonally across equivalent squares,
not changing the value. 

He took this one for a close-up for you all. 
Final Solution
We can read the whole numbers down the side, then decimals across the bottom
(unit in the corner).

How NOT to do the Decimal Fraction Checkerboard Multiplication: 

The multiplicand is OK.
The multiplier does not have belong ON the squares
and the unit of the multiplier should be placed such that when multiplied by the unit of the multiplicand,
the answer will land in a unit square.
(the multiplier is 0.38 and should be moved two squares down - and off the board)

The only rule for where to place the multiplicand is such that the answer doesn't go off the board (in this case, if we had moved the multiplicand one column to the left, taking the 5 3 times would have resulted in a "1" being off the board. The children can problem solve what to do in this situation - re-do the entire problem, shift the answers already created, or figure out how to calculate the solution anyway. (hint: The answers would still be in the correct VALUE of squares...).

Past Work on Decimal Fractions: 

When to Start the Decimal Fraction Board (the work that comes before the decimal checkerboard)

CAVEAT: See that white line across the top of our decimal checkerboard? IF you have that strip on your board, the numbers should match the numbers along the *bottom*. When I first made this board, a LONG time ago, I didn't fully understand the depth of this material and thought I would "do it right" (meaning in a way that made sense to me). Well, turns out, I was wrong and that top row makes no sense. Rather than fix it, we just simply ignore it. Nowadays, I make these boards for other people and I make them correctly ;)

This is why it is *so* important to understand the depth of each material before making changes. Modifications can certainly be made, but not to the core concepts!


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