My daughter has laid down a marker when it comes to reasoning with fractions. Well, at least in my small world. She’s 10.

She won’t read this post for a long time because her mom and I know what she reads on the internet…at least we hope we do. Maybe she’ll never read it but I know she has great things in store and that makes us proud.  There might be a day or time when she feels defeated or maybe doesn’t feel like she has anything to contribute.  If that’s the case, I’m keeping this nugget in my back pocket.

In my 14 years of playing math with students AND teachers, she did something that teachers don’t teach, textbooks don’t show, and test prep academies might never understand. We were working on a task which led us to a parallel question.  I want to share the sequence of events that took place.

We started here…

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Solve the problem BEFORE pressing play and think about how you solved it.

What the hell just happened?!?  I get it… but what the hell just happened?

When she said “I don’t like multiplying fractions” I immediately thought she was going to jump to some trick or algorithm she’d been taught in 4th grade. I wanted to know more so I asked her to explain.

Partial products for multiplying fractions! I’ve never seen a student or teacher use this strategy and to be completely honest, I’ve never thought of it myself. But it’s beautiful and makes perfect sense.

Lesson 1: Don’t let anyone tell you that you have to multiply straight across when multiplying with fractions. Partial products work just as well.

With this being a student invented algorithm I wanted to try and break it. It’s what we do.  So I changed the 6 to a 7 because it isn’t so tidy when divided in half.

Another little gem of understanding was uncovered. Any predictions?

Silly me. It’s a student-invented algorithm so she owns the understanding.  Everything she’s doing here has me vigorously nodding my head in agreeance.

Lesson #2: Don’t let anyone tell you that you need a common denominator to add fractions. Partial sums work just as well.

Let’s change the other factor and see how you tackle it.

She didn’t do 60 questions in a minute. In fact, she never has because that’s not our jam. I don’t think anyone would argue that our daughter isn’t fluent.

Lesson #3: Don’t let anyone tell you fluency = speed.

If the definition of fluency asks students be efficient, flexible, and accurate she nailed it. So why is the definition of fluency different when we talk about addition and subtraction or multiplication and division of single digits? The same way our daughter decomposed numbers and used distributive property with fractions is the exact same way she learned her basic facts. Her understanding of number is scalable.

We started slow and took our time when she was in kindergarten because the turtle always wins the race. As our good friend Tracy Zager says, “The ROOTS of the work are in K. The FRUITS of the work are in 5th”.

Lesson #4: Memorization of facts and algorithms is a learning objective stopgap. It will never prevail in the long run.

Our work is paying off and I’m a #prouddad.

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