## Reflection: Developing a Conceptual Understanding Working at the Ice Cream Stand - Section 2: Investigation

When I taught this lesson this school year, students were struggling to write an equation for the length of the boy's shift once they knew the length of the girl's shift.  They were doing a great job coming up with possible shift lengths, so I knew they were doing the mental math necessary to find solutions to the equation.  I wanted to make this mental math visible to them and show them how they could use it to derive their equation.

I find a silent lesson to be a great tool to help students surface their thinking processes.  I did the first example myself, showing the steps to find the length of a boy's shift if I knew the length of a girl's shift was 3 hours.  Then, I wrote girl's shift is 1/2 hour with a question mark next to the length of a boy's shift and held up the marker for a student to come up and show his/her work. I did this two more times to show students the repeated calculations. Then I labeled those operations next to the steps.  The pattern for this particular problem is multiply the length of a girl's shift by 2, subtract this answer from 10, divide that answer by 3. From here, students were able to generalize using G to represent the length of a girl's shift and performing those three steps using the variable in order to find an expression for B.

In the IMP curriculum this problem is followed by a similar question about paying experienced and inexperienced workers different amounts and having a set amount that can be spent.  With different numbers, students basically follow a similar pattern and we practiced this the next day to give them a little more experience with generalizing repeated calculations.

Developing a Conceptual Understanding: Opportunity for Mini Silent Lesson

# Working at the Ice Cream Stand

Unit 2: Multiple Representations: Situations, Tables, Graphs, and Equations
Lesson 14 of 17

## Big Idea: How long should an employee's shift be? Students determine possible shift lengths to satisfy an equation.

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60 minutes

### Amanda Hathaway

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