One of the most common reasons children struggle when learning fraction division is because they haven’t fully developed their understanding of division with whole numbers. Children need to understand different interpretations of division and have the opportunity to make connections between whole number division and fraction division. I created Theo’s younger sister Leah to help make those connections.
The relationship between Theo and Leah echoes my relationship with my big sister: typically competitive but with moments of warmth. I remember sitting in the back seat of our car, listening to my mother quiz my sister on her times tables.
At one point I chimed in the answer faster than her, much to her annoyance. That just fueled my enthusiasm. I had no idea what multiplication was, but every time I could answer faster was a victory.
You might find Leah precocious and annoying, which I have to admit reflects my first grade personality, but she plays a vital role in the story. Since she’s learning how to divide whole numbers, it gives the reader the opportunity to recall different models of division using simple whole numbers. When children can make direct connections between whole number division and fraction division, they are much more likely to successfully divide fraction.
The interaction between the siblings is also an opportunity to see Theo explain concepts to his little sister. Children reading the story might reflect about how they would explain thing to Leah. That’s one of the reasons why I’ve included note cards in the e-Supplements that feature her. Teachers can ask their students to write a note to Leah giving her different examples to help her learn fractions.
When children create new examples for Leah, they are not only inventing story problem, they are generating a collection of concrete examples that they can use to make meaning out of fractions and division. Teachers should encourage their students to see connections between whole numbers division and fractions in their stories but to also reinforce their conceptual understanding of division. In Newton’s Nemesis No. 1, Leah is learning about partitive or equal sharing division. In Newton’s Nemesis No. 2, she learns about the measurement model of division.
Leah struggles with some of Theo’s explanations, which provides another opportunity for children and teachers to discuss mathematical terms that can sometimes be confusing. Think about the number 1/5. We sometimes refer to it as “one-fifth” but occasionally as “a fifth”. Conceptually, 1/5 can be thought of a quantity, a ratio, the fifth item counted or the fifth item in an ordered list. This is true for any unit fraction (i.e., a fraction with a 1 in the numerator).
“Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning.”Common Core Standards for Mathematical Practice
Mathematical language can be nuanced and precision can be developed by having children write about math to explain their reasoning. Sometimes it’s challenging to explain things to others, and in Theo’s case it pays off in the end. In Newton’s Nemesis No. 3, Leah’s uses what she learned from Theo to help our heroes solve the final puzzle and unlock the mystery that might save Newton!