I kind of stopped posting about our Montessori math activities past 2016 because it felt like we were just winging the presentation on the spot. Presentations take all of 15 minutes and the kids often don’t do follow ups, what is there to say about it?
Fast forward 2 years, now that I’ve figured out you can use task cards, Evan Moore, and IXL for follow ups instead of having the kids wait for me to get my act together, we’re half back on track to Montessori math again.
One of the thing about Montessori math is that for the beginning stuff like fraction, decimal, geometry, squaring and cubing, it is happening all at the same because they all get the kid to practice their operations. Everything can be presented sensorially per kids interest from first grade, though you will quickly find that your child will let you know whether or not they’re ready for a concept by their confused look during your presentation.
Anyways, all this lead up to say, this week we re-started on fraction multiplication, since Astroboy has a very good command of his multiplication table already. Side note, when I did this with Thumper, she didn’t have her facts down and had a tougher time. So, in terms of scope and sequence, multiplication memorization of most number should come before fractions.
The Montessori sequence for fraction multiplication is a bit different from the curriculum I see in Evan Moore. The Evan Moore worksheets for 5th grade jumps straight into multiplication of two fractions. IXL 4th grade starts with multiplication of fraction by whole number.
The suggested sequence from some Montessori curriculum is:
- Multiplication of fraction by whole number
- Division of fraction by whole number
- Multiplication of fraction or whole number by fraction
- Multiply fraction on graph paper
In the AMI albums, the whole fraction curriculum starts from 1st to 3rd grade, in AMS NAMC curriculum, it goes from 1st to 5th. Of course these are all just suggestions; you have to follow the child. I used to find this advice totally useless because it doesn’t give me an estimate of when I may think about introducing them.
But having gone through it with 2 kids, I understand now that the child reveals his readiness to you. Just know you can start the basic concept of fraction and equivalence starting from kindergarten, and you introduce fraction operation when they’re close to mastering the specific operations. You know they’re ready because they aren’t frustrated and confused by your presentation. The hardest part about fraction is actually fraction equivalence. You have to have a very good command of multiplication and division facts. So spend a lot of time on that.
Moving on.
The presentation starts by taking 1/3 2 times （三分之一 三次）and asking the children what that is. Then you try it with other fractions. Depending on age of child, you either do all concrete material, or some writing of numbers on paper, or in our case, we wrote everything on our white board. You make sure to have an example that results in mixed numbers.
We then tried to get a mixed number by taking 1/2 5 times (二分之一 五次).
Here’s what happens when you don’t follow a worksheet. I asked Astroboy to make up a fraction to multiply. He was faced with indecision so we pulled out the dice and he generated his numbers. The first thing he really wanted to do was to multiply by 12, big big numbers.
I had to convince him to start with a smaller number and then let him do whatever he liked.
We are following up with some equation slips from NAMC. Next week I will probably have Astroboy try either the Evan Moore worksheets or IXL.
Lastly, Astroboy really love games. And I’m trying to not be lazy and follow more of his learning style. I found this really good looking fraction multiplication math game online from Teachers Pay Teachers. The old me would have waited to translate the game into Chinese, which meant we actually don’t play. The new me tries not to feel guilty about the lack of Chinese on the game board and we get some fraction work done. But! I was still lazy and used dice instead of cutting out the included number slips. (Yes, I try to celebrate my laziness when I can.)
Notes
1. The most important thing about these presentation is understanding the concept of multiplication, which is xx times of something. So the language for multiplying is to say “take 1/3 3 times” “三分之一 三次”. Be very consistent about saying it this way so they really learn the concept.
This bears repetition. The goal of these presentations is to understand the concept of multiplication, not just learning to be a calculator. Otherwise once you have the multiplication table memorized, a child can just do those calculations easily without understanding why it is.
I saw how important this was when I introduced squaring. Astroboy had a hard time remembering that exponents is when you have x x times, taken y times. He kept wanting to do straight multiplication.
2. Some of the things not really emphasized in my album are the special cases, like reducing to equivalent fractions, converting your answers into mixed fractions, and multiplying by 0. You may want to make sure you have follow up practice problems that address this.
3. To keep it more fun, you can have a child make up their own numbers, roll a dice to generate their numerator, denominator and whole number to multiply. Children really love big numbers. Plus, they may run into unexpected math issues when they use their own numbers instead of using a work sheet.
4. Don’t let the kids jump to abstract so quickly. Astroboy grasped the concept of multiplying fraction quickly. But he often misses the details and to actually really understand the concept, I kept having to refer back to the concrete material. For example, when we did the follow up worksheet, he said, 1/3 x 1 has the same answer as 1/3 x 0. I had to have him work through it with the material to see that it isn’t the same thing.
5. Another important concept here is equivalence and mixed fractions. They may get the multiplication and forget to find its smallest equivalence. You need to have a very solid understanding of multiples, multiplication and division facts down to really move to the abstraction level. But it’s okay. They can continue to learn fraction equivalence by using the concrete material. There’s no need to push this. You go as far as the kid is able to in this topic, and then come back again next year. That’s how one can spiral in the Montessori curriculum.
Here is the presentations on EdVid so you can get a better idea of the presentation. Notice how the presentation used number slips for their presentation, whereas I was too lazy and wrote it all on a whiteboard.
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