Universal themes plug into any content and immediately get students thinking BIG. But, how can you apply universal themes to math? I love to use fractions as my test content to see if a technique really works. Fractions are, I think, one of the trickiest topics for students to understand and for teachers to make interesting (and interesting is my goal).
Step Away From The Pizza
So many fraction lessons try to entice students by dividing up pizzas. Friends. I have news for you. Dividing pizza is not interesting. Nor is it useful. No one does any kind of fraction arithmetic when eating pizza. Putting pizza into a fraction lesson is a perfect example of fake engagement. It’s cute, but it doesn’t move students toward higher-level thinking.
Universal Themes and Fractions
So, what would a Universal Theme look like with fractions? First, we’re trying to move beyond (far beyond) mere calculations). We’re planning for students who can successfully add fractions (or multiply or whatever). They need something more – and you know it shouldn’t be more practice problems 🤢.
Using Universal Themes, I can move students’ thinking toward ideas like:
- Which has more power: the numerator or the denominator? (I have a Byrdseed.TV lesson about this.)
- Explain the conflict in a fraction. How are the numerator and denominator opposed to each other? (Do check out an example built on this idea.)
- A fraction is a system. In what ways do the numerator and denominator work together?
- What happens when a fraction changes? How does a change in the numerator affect the fraction? What about the denominator?
Do you see how this is interesting thinking rather than just more challenging math?
Numerators and Denominators Are Interrelated
These questions all lead me to the same big idea: numerators and denominators can work together or be opposed to each other. I think that fractions become interesting when you look at them as two parts that can both compete and cooperate.
Finding this big idea allows students to connect fractions across disciplines. Numerators and denominators are locked in conflict/cooperation like:
- the branches of the US government
- the parts of an ecosystem
- Rome’s plebians and patricians
Once I realize that a fraction is similar to an ecosystem or a group of people, I’m off to the races! By starting with a Universal Theme, I now have the inspiration I need to go way beyond the default pizza fraction lesson and start exploring some truly interesting ideas.
There’s Room For Differentiation
All of this thinking raises the ceiling. It gives me room to take my most advanced students to interesting thinking – not just more challenging worksheets. Now, not everyone needs to go to the same level. That’s differentiation. Some students will still just work on remembering which one’s the numerator and which one’s the denominator.
But, now, some students will create a story that compares the interaction of numerators and denominators with the interactions between predators and prey.
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