Reflection: Diverse Entry Points Writing the Rules - Section 1: Warm Up

The first time I gave this assignment I don't think I explained the directions very well. It was obviously unclear that students were supposed to use exactly 4 fours, no more, no less, and no other numbers. This lead to several incorrect solutions. At first I thought I would have to clarify the directions better the next time I gave this assignment. But I realized that even though students had not written expressions that matched the directions exactly they had still been working with the same standard at a level that was comprehensible to them. If the directions had been clearer students may have shied away from the problem and assumed it was too hard for them. Their misunderstanding made the problem more accessible to them which allowed them to enter the problem and start to make sense of the math involved. I concluded that the initial confusion over the directions was actually helpful and provided another entry point for students.

When they came into class many of them were really excited to have found so many different ways. And when I noticed that they had not followed directions I knew I had to address their error without crushing their enthusiasm and making them feel like they had wasted their time. Instead of going over the directions again I asked them to share the work they did and used their expressions to help us find patterns and generalizations and illustrate the important mathematical properties, review exponents, grouping symbols, etc. Their work still gave them insight into the relationships between numbers and operations even if they used all fours but not necessarily exactly 4 fours. Even if they used any numbers students still had the opportunity to refresh their thinking about order of operations writing expressions. Inevitably, another student points out the error and clarifies the directions. But by this time the students who have erred have done enough math to make sense of the problem. Students realize the problem is trickier than they initially thought, but they feel equipped to handle it.

Diverse Entry Points: Making mistakes

Writing the Rules

Unit 1: Order of operations & Number properties
Lesson 1 of 9

Big Idea: Students explore their prior knowledge of order of operations to create expressions.

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53 minutes

Erica Burnison

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