According to Montessori curriculum, kids start in earnest with fractions in first grade. Last semester, I tried to get Thumper to learn her fractions. While it was obvious whenever we did it that she understands quickly and can advance to the next stage, she did not want to do it AT ALL. Case in point, after introduction to fractions, we did nomenclature matching (Chinese to English to pictures to numbers), I had to kind of make her do it. By that I mean putting it on her work plan and she dragged and dragged her feet till I pointed out to her it’s on her work plan. Then it was fraction equivalence, I don’t even know when we started that work. November? October? She just finished that this week, mid January. So that took 2+ months.
One thing I got out of homeschooling last semester is that maybe I need to really just accept the way my child learns and think of ways to appeal to her. I know I know, such a Montessori concept. But this means that I cannot just use the Montessori materials and presentations as I was taught. Thumper is a creative one. Show her how to do something, and more often than not she wants to play with it, see it used a different way.
This week, I remembered that I saw a fractions game at a Montessori school I observed. After asking around and looking at albums, I learned that it’s not in the albums. It’s just an extension the teacher made up. We played this game this week. Thumper had much fun. In fact, I had much fun. This week, school in general felt great because most of our time spent together was happy times.
The game is simple. Fractions cards from 1, 1/2, 2/2, 1/3, 2/3,….10/10 are shuffled. Each player takes one card, takes the fraction circles to make up that number, and compare the fractions. The person with the bigger fraction takes all the cards and the person with the most number of cards by the end wins. The direct aim of the game is to see visually how a fraction is represented and become familiar with it.
Extensions: Take out the large fractions if you really want to illustrate the fraction equivalent concepts in a concrete way. Ask children to name fractions in English.
Here’s a game that Thumper made up. In this version, 1 is the same as Draw 4.
- Deal each player 7 cards
- Draw one card from the Draw Pile. For example, 5/7.
- Going in round, each player places his/her card which has a matching number. For example, 3/5 or 7/8.
- A player with no matching number can either:
- Draws one card from the Draw Pile. They can either play that card if it matches or pass.
- Play the 1 card, which is the equivalent to Uno’s Draw 4.
- When the player plays the next to last card, say “Uno!” Draw two cards if you fail to do so.
As an extension, we are doing equivalence matching as well.
How We Played It
Though Astroboy is only 4 and maybe a bit too early for fractions, he wants to play too. I have read of bloggers whose kids do some fractions as young as 4 and 5 for awhile and then drop it for a year or two before coming back to it. I guess this is how sensitive periods run.
First Astroboy is giving a lesson on labeling the fraction metal insets. He already had an intro to the fraction skittles last semester. He got confused between the top number and bottom number, often looking at the top number for the fraction circles. But eventually he got very good at reading the fractions. Note that knowing how to read isn’t the same as understanding. And I’m not too stressed he doesn’t understand as it is quite an advanced concept. I know he is in his sensitive period for reading numbers right now only and that is why I knew he would enjoy labeling the fractions.
We played the game pretty straight the first 2-3 times. From that, it was evident Thumper got the concept of which fraction is bigger or smaller. For the next turn before we found the fraction circles, I asked her to guess which fraction was bigger. We then confirmed it with the fraction circles. I pointed out to her once that 5/7 is bigger than 3/8 because half of 7 is 3+ and so 5 is so much closer to 7. Whereas half of 8 is 4 and 3/8 is less than 4/8, and therefore less than half of 8/8. This made much more sense when I explained it to her. Anyways that was enough of a hint for her to get all the other really hard fraction comparisons. (I know I know, you’re supposed to let them figure it out. I can’t help myself.) I had to stop her at the end from shouting out the answer because Astroboy needs to see the fraction circles laid out still. He naturally thinks that a bigger denominator means bigger number.
After the game, we played Uno Fraction. I have to say, the kids love this game so much more. Probably because Astroboy loves Uno. We’ve been playing this every day this week. We started on the straight version listed above and moved on to equivalence yesterday. She’s done the fraction equivalent “research” but I told her since I helped her so much with those worksheets (she kept whining she couldn’t do it), she has to figure this one out herself as we play and write it down. I said this because she has often taken the initiatives to do this for math concepts she’s working on just randomly while playing. Though I knew that the answers will come from me anyway while we play, I also know that she has shown understanding (without me teaching) of equivalence. She knows the multiplication table of 2s and 3s very well and quickly gets why 1/2 is same as 4/8. The hard ones are things like 2/6 = 3/9. But that’s where playing the Fraction War Game helps.
Thumper cried and cried because it is so easy to see the full fractions (2/2, 3/3) come up but you have to know the equivalent fractions and it doesn’t appear to come up often. “It’s UNFAIR!” she said, because Astroboy gets to play his special cards while she doesn’t. I got so mad because she often doesn’t play nice in games. But I kept my cool and said “Let’s play 1-2 times to see how this works out.” The funny thing is, I managed to win Astroboy 2 out of 3 games because of fraction equivalence. Each time I always happened to, with one card remaining, draw a card from the deck and have it be an equivalent card.
But honestly, having her feel bad about the unfairness of it all could mean she doesn’t want to play in the future. Who knows, we’ll see how it goes today. It’s been such great work periods the last few days because we play and have fun sometimes. I’m happy and she’s happy. She seems to do more work in general without me nagging, which in turn makes meeven happier because I already feel like I’m not being a good teacher when I nag her.
To keep the game interesting, I added English to the mix after it was clear Thumper got it in Chinese. As I’ve stated before, it’s a hard concept to learn. Astroboy said, “No, it’s three FIVE, not three fifths.” Thumper started confusing the numbers in Chinese the minute English was introduced. My goal is to not have them be fluent in both yet. I just want her to at least be introduced to the terms “fourths, fifths, sixths, etc.”
I love the fraction cards! I love the fact that it’s skinny enough so Astroboy can hold it easily like a deck of cards. I love the versatility of these cards. I can foresee myself using it for many fraction related work. I don’t love the numbers though. It’s easy to confuse 6 and 9. Good thing the numbers are slightly lower on the deck so you can see which side is up.