I am convinced that my students have another idea of what they want the 5th grade curriculum to be:) No matter how much I plan, they will always send me in a different direction, which I love. It started yesterday with these two grids and responses…
That led to these journal entries and our conversation today….
I led with thinking about the fraction (or decimal) in a decimal. We did some more grids and the students were seeing the thousandths like taking a fraction and breaking it into smaller pieces to still have equivalents, like 1.5/4 = 3/8. Then a group of students who were done with the grid work, asked me if there can be a fraction or decimal in a denominator…..here we go…
I asked them what they thought it meant and this is their starting point. They jotted some examples and started playing around with 1 / 2/8. He drew it with 2/8 size pieces, came out with 4 but said that looks the same as 1/4.
I asked him if it could be, and his intuition was saying no, but he couldn’t figure out why. I asked him what happens when a denominator number gets smaller, he says piece gets bigger. So he started with 1/4, 1/3, 1/2, 1/1, said 2/8 / 2/8 = 1. From there he realized that 1/ 2/8 was improper. Here is where he ended because class ended.
I had another working with 100 grids trying to figure percentage-wise is 1/4.5 fell between 1/4 and 1/5 and here are a few others…
So much to chat about, but after a long day, my brain needs a break:)
I just love how a thousandths grid lesson can lead to this, I want my students to publish a “Kids Curriculum” as a supplement to mine, because they obviously have so many amazing curiosities! (Or maybe, Christopher, we can name it Kids Kurriculum)
This decimals series has been fascinating! You are working with 5th graders, and I work with 11th graders, who are no further along in their thinking about fractions. They, however, want to turn them all into decimals. We are working with rational expressions right now – a polynomial fraction! I am taking a day or two to work with them and your idea with these grids – I need them to be more fluent in their fraction – decimal relationships! And I hope we’ll get to see how you resolved this fraction within a decimal!
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