Exploring conflict in a math lesson brings drama to unexpected places, like identifying the attributes of quadrilaterals.
Lower The Barrier
If you open a lesson by defining “congruent sides” and “bisected diagonals,” students will shut down. So let’s lower the barrier of entry and open with a discussion of conflict, framed with the big idea: “details cause conflict.”
I’d begin with a funny story about a conflict between my wife and I over some small detail. Then we could discuss details that cause conflict between characters, conflict on the playground, or famous historical conflicts.
After ten minutes or so, we’ll move on and ask students to identify details that cause conflict between quadrilaterals.
Conflict Between Shapes
You: Class, what details would cause these shapes to have conflict?
With the right images, kids jump on this idea quickly.
Student: Shape 1 starts to go up to a point, but 2 has only straight sides.
We can gradually increase our expectations, sneaking academic vocabulary in since it’s actually useful to students now.
You: Yes! Those straight sides are called parallel lines! This means…
Write down the student’s idea along with the academic language.
Keep going, using new shapes. Deliberately plan these combinations to draw out certain details. A rectangle next to a parallelogram highlights different details than a parallelogram and a rhombus.
Here’s a PowerPoint file with some shape combos.
Kids might name details that don’t match your expectations, like “one is bigger than the other.” Don’t dismiss those ideas or students will shift back into “math lesson mode.” Keep them engaged and excited. But, as you move through the lesson, prune those options away until you’re down to the desired set.
You: We came up with tons of details that cause conflict, some I hadn’t even thought of! Let’s focus on these three details as we move towards the quadrilateral battle!
Q: I carefully and deliberately planned my shape images to highlight the conflicts, but no one thought of congruent sides!
A: Then just tell them. “Hey, there’s one more I noticed. Look at this shape’s sides. They’re exactly the same size! I bet there’d be conflict because the other shape has no sides that are the same. When sides are the same size we call them congruent.”
We’ve got the required details. Now let’s check students’ understanding. Ask them to draw “quadrilateral recruits” based on your requirements.
You: A quadrilateral army is recruiting shapes with two sets of parallel lines. Nothing else matters, but they want a wide variety. Create three recruits on your whiteboards.
Check their drawings. Adjust your lesson as necessary. Kids might draw faces on their quadrilaterals. That’s awesome.
What an interesting group of shapes! Yet they all fit the requirements. These recruits are called parallelograms!
Encourage students to explore a wide variety of shapes that fit the requirements. Check if anyone drew a rectangle. Confirm that, yes indeed, a rectangle is a type of parallelogram.
Another army wants shapes with two pairs of parallel lines and four right angles. Create three different recruits.
Check their drawings.
Great! I see lots of different versions of this shape: the rectangle.
Did anyone draw a square? Point out that this is a type of rectangle as well.
Here is a PowerPoint file with some of these requirements.
Keep going and be aware of struggling students.
Now your class will more formally identify conflicts between quadrilateral. Put students in groups. Grab those students who you noticed struggling and work directly with them.
Students work together to fill out a conflict table:
Here’s a blank version to print various versions of the table.
Notice that we hit the high-level thinking skill of “judgment” by asking kids to rank shapes by conflict. This leads to debate, and when students debate about quadrilaterals, it’s a great day.
The academic vocabulary is fully integrated now, but we got here slowly by setting the stage with “conflict.”
The Final Challenge
This 3rd-grade common core standard wants students to “draw examples of quadrilaterals that do not belong to any of these subcategories.” What a great final challenge!
Students! There is a mutant quadrilateral on the loose. It fits into no known categories but still has four sides. What could it look like?
And finally, this lesson sets up a great math narrative. Feel free to integrate a skit, comic book, or short story about The Great Quadrilateral Conflict!
Please, please send me feedback if you try this lesson! Your ideas really help me: firstname.lastname@example.org or @ianabyrd
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