All of these topics are connected. It's important to understand factors and multiples in order to find common denominators and to simplify fractions, and it's important to understand the idea of sharing out fairly, because the "cut line" in a fraction is another way of writing the division sign.
(If you know the saga of the Math Gnomes and the King of Numberland, you know that Mr. Divide is the one who finally solves the king's problem.)
If you are looking for a hands-on and joyful introduction to fractions, I highly recommend The Beauty of Play. We will be using some of her ideas (incorporating the Cuisenaire rods) as well as the Montessori materials.
Here are my notes from Week 1 of Introduction to Fractions:
Mon - K/W/L Chart
- a lot of the students in my group were nervous about fractions, so I thought I'd start out with a simple K-W-L chart (FREE on TpT)
after they filled in the K and W, that was the end of today's lesson!
Tue - 1/2, 1/4, 1/8
- decorate front cover of MLB
- This MLB is working in a slightly different way than the others. The goal is to emphasize the learning journey, to have them write about operations with fractions in their own words, and to keep a record of their new questions as we go along. I am not doing an edit of what they write. I'm just letting them use it as an exploration journal. "Best guess" spelling is allowed!
add what you wrote in the W column of the K-W-L chart as the first two page spread with room for more questions as the block goes on
what is half?
when you each have a half, are the pieces the same size?
recall Math Gnomes... how are fractions related to Mr. Divide?
divide a circle in half (red), then cut half of a half (magenta), and then half of a half of a half (brown)
- I have these Folding Sheets from Heutink (16 cm) and the colors are a perfect fit with the colors of the Cuisenaire rods!
label each paper piece with its name written in the fraction-y way (how many, cut line, what kind)
- Fractions are special numbers because they have bonus information in them!
There are three parts of a fraction. The top number ("how many"), the "cut line" (which tells you that it's a fraction), and the bottom number (the "name" of the fraction).
Unlike regular numbers, which always just tell you "how many," fractions also tell you what kind of piece they are talking about. Each fraction piece has a name. Instead of naming fractions "Joe" or "Tom" or "Sally," which would be really complicated, we name them by saying how many of the pieces are needed to have the whole circle again.
paste one of each (1/2, 1/4/ 1/8) into the MLB and write what we did along with your observations
Wed - Making Thirds & Halving Thirds
- we started out by reviewing their observations from yesterday
they all pointed out that the bottom number of all of yesterday's fractions were even, and one child asked, "how would you get a fraction that's an odd number?"
read The Little Mouse, the Red Ripe Strawberry, and the Big Hungry Bear by Don and Audrey Wood and consider, what if you had to divide the strawberry into three equal parts? is that possible?
yes! okay, so how would you divide a circle into three equal parts?
they rightly pointed out that you would need to know the center and then "there would be a lot of measuring"
divide a circle into thirds (light green) using a pin to prick the center (I just folded one circle into fourths to get the exact center point and then pricked the center of each of theirs) and tracing a 1/3 piece from the Metal Fraction Circles to get the angle exact
next divide those thirds into halves (dark green) but predict first, what size pieces will we get? was your prediction correct?
review how to write a fraction in the correct way
explain that the "cut line" is another way of writing the division sign (1/3 is one whole divided into three equal parts)
do Fractions Worksheet
- A lot of confusion in fractions comes from children making incorrect assumptions very early on and then sticking to them. So I wanted to show them right away that fractions aren't always circles, and the top number isn't always 1!
paste one of each (1/3, 1/6) into the MLB and write what we did along with your observations
Thu - Fractions of a Group, Equivalent Fractions (Houses on a Street)
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we started out by reviewing their observations from yesterday
one little girl brought me her SSR book Druids, Gods & Heroes from Celtic Mythology (World Mythology Series) by Ann Ross (p.56) because she found a reference to fractions in it, and I read it to the class because it was a perfect transition into Fractions of a Group!
- from The Story of Fionn
"Before long, however, he crept out by himself once more. This time he made his way to a place called the Plain of Life where there was a fortress and where he could see the boys of the household playing a game of shinty on the green. He went up to them and challenged them to individual contests in running and shinty, winning each one easily. He returned the next day to find a quarter of their number ranged against him and still he beat them all. Next day a third of them played against him and then, since he was still an easy winner, they made him take on the whole group altogether. He defeated them utterly."
is it possible to have a fraction of a group of things?
use Mandala Sets from Grapat to demonstrate a fraction of a group ("one-fifth of my pieces do not match the others")
can anyone think of a fraction sentence they can make with our group of people? ("5/6 of the people in our group are wearing socks")
our last activity for fractions of a group also introduced the idea of equivalent fractions ("half of the houses on my street are green")
have people draw a street with first 2, then 4, then 6 houses keeping half of the houses on the street green each time
then let them decide on a larger number of their choice and draw the houses, still keeping half of them green! 1/2 = 2/4 = 3/6 = ?
like the idea of fractions of a group, I think it's important to introduce the idea of equivalent fractions very early on
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Immersive Experience
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