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).
2,063.02

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: 

Introduction to Decimal Fractions - with LEGOS!

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!

:) 

Montessori Math - Word Problems - Option: Zaccaro's Challenge Math

Legoboy and I received our copy of Upper Elementary Challenge Math two days ago and all I can say as I go through it is YES! Yes, yes yes yes yes yes!

As I suggest in the comments on my first post on the Challenge Math series, I find that for typically developing Montessori children, we can add 1-2 years to Mr. Zaccaro's age suggestions. These books were designed for gifted children and they tie in wonderfully with our math and geometry experiences.

This book says grades 3-5 - and I say YES! Adding two years puts it at Montessori "grades" 5-7 (misnomer there but bear with me ;) ). My son is "5th grade" and I would say he is just about ready for this book, the first levels of each chapter. I have a few more reviews I would like him to do in the first book (Primary Grade Challenge Math) before we dive into this one; if we hadn't been waylaid by other life events, he would be entirely ready for this book.

Now the difference between Upper Elementary and Primary Grade? There are additional problem sets (3-8 pages of them!) before even getting to the "levels". Both books have the same levels - Level 1, Level 2, Level 3 and Einstein. Primary Grade did not have the additional problem sets though and at times I feel like there are not "enough" word problems... to the point I re-wrote a few (just a few in the end) with different numbers, just for more practice. This book fills it ALL in. If I had known what was coming, I would have let it go and just enjoyed the Primary Grade Challenge Math for what it is, holding out for Upper Elementary Challenge Math.

Well now I know. And I love it.

I could see this book carrying us through the rest of elementary and getting us started in adolescence. Then moving into the original Challenge Math book. At the time we started Primary Grade, the next step available was Challenge Math - so this Upper Elementary Challenge Math fits a nice little transition stage perfectly!


I LIKED math growing up - because I always knew there was something more there - I picked up pieces of it here and there, but mostly missed the boat.

This is ONE EXCITED Montessori Mama - I get to do all of this too!

Negative Snake Game - Signed Numbers - Upper Elementary

He wanted to build a snake that would definitely be negative - gray - and deep negative - lots of gray.

So he did. 

But see - he is actually just slightly beyond this work. He is 10, but started this work in lower elementary - he was just ready (LOVE that about Montessori ;) ). He needed (and requested) review before we move into operations with signed numbers (negative numbers) and it has been a while since he has worked with the negative snake game. (see disclaimer regarding the name of this material at the end of this post).

Thus, being this work is not a challenge for him, he MADE it a challenge. Instead of bringing down two bead bars at a time and doing this work based on math facts and number lines, he found various patterns:

• all positives/negatives that cancel each other out - eradicate and move on
• grouping together a series of negatives, getting one answer (such as negative 38), then grouping together some positives and balancing it out
• groups of beads (3-bar and 4-bar in positives, eradicate those with a negative 7-bar
• verified by finding all those matches again, grabbing them in matching groups rather than aligning one positive and one negative - definitely a sign he's beyond the work ;) 

Well, hey, he's using his math facts ;)

When he wrote the work on paper, before beginning to change the color of the snake, he grouped together each "set" of positive and negative bars, writing -16 for a -4, -7, -5; then writing +12 for +9, +3; etc. 

His idea:
use the underside of the boxes for the bead stairs.
Glue felt underneath the boxes, he says. 

Final answer. 

I started to sort the bars to actually match;
then realized, better to show what Legoboy actually does ;) 

So the final value of the snake is the positive (colored beads) matched against the negative beads;
what is leftover from either side should match what the snake turned into. 

He did this whole process with two snakes - which is a lot. One long snake is usually sufficient - providing a worksheet full of math facts, but he very clearly stated he wanted practice, he wanted good photo ops (to him, these are fantastic photos ;) ), and he wanted to prove his smarts. He said that. Goof.
(Again, I emphasize: ONE long snake is sufficient for one day. Really.)





***Disclaimer: My AMI albums have the following snake games:
1) Addition Snake Game - primary
2) Subtraction Snake Game - primary
(children can review these in lower elementary)
3) Negative Snake Game - later lower elementary or early upper elementary; other signed numbers work can come later

I have heard of other snake games, but these all seem to be one of the following:
1) an extension of one of the snake games listed above
2) a form of verification on one of the snake games listed above
3) unnecessary for most children
4) another NAME for one of the snake games listed above (I have seen the subtraction snake game for the primary level called the "negative snake game" - which makes no sense, because we are subtracting at that point, not "adding negative numbers")

Link to Montessori Nugget on Snake Game names. 

Montessori Guide Cards - Mathematics and Geometry

Legoboy has been busy-busy-busy.

He is an awesome reviewer (read: nitty-picky, tedious, tough audience to please) - as he has combed through the mathematics guide cards I have been developing while adding illustrations to, editing and clarifying points in the elementary Montessori mathematics album. One chapter at a time and it is getting done! Yay!

These guide cards are to be used for follow-up work. I moved away from calling them Montessori task cards or Montessori work cards as others have similar items listed... because these ones do NOT provide specific math problems to solve, instead focusing on "select several addition fraction problems to solve. Write them on your paper, use the materials to solve, and note your answers." Or "select several division problems with a zero in the middle of the 3-digit divisor". In this way, the child is still working on specific skills but is not limited by an outside authority.

There is so much flexibility with these cards - the adult can add a card with some sample problems (one of the fraction cards requires it, to keep the initial work within the scope of the material), add cards or notes to utilize specific pages in other resources; the child himself can add these ideas, or add questions to research, ideas for research, note favorite areas of study, etc. Legoboy has come up with some ideas - and my 3 adult reviewers have as well.

Geometry is done - as one complete file only (not divided by chapters).

Mathematics is half-done (through chapter 6) but those who purchase the entire set or the later chapters today, will receive them as I get my final reviews back from (darling!) Legoboy --- there is only so much he can do with some of it, because he is only just starting some of the later chapters, so this last part will go even quicker. By this time next week, all chapters will be done.

They print out with 2 cards on a page - cut in half - plenty of room for adding further ideas or illustrations as needed.

Legoboy really-really-really wants me to point out that an individual child could use these for recording SOME work (not bigger work and not items that need graph paper - but some work).
;)


Garden of Francis - Keys of the Universe Elementary Montessori Downloadable and Printables

Note: if you have paid for access to Keys of the Universe online support, you have a 75% discount code to use ;)


Other subjects are upcoming! Geography, Music, Biology, Language, History