**Max is organizing a trip to the airport for a party of 75 people. He can use two types of taxi.**

**A small taxi costs $40 for the trip and holds up to 4 people.****A large taxi costs $63 for the trip and holds up to 7 people.**

**(a) If Max orders 6 large taxis, how many small taxis will he need?****(b) How much will the total cost be?****Max can organize the journey more cheaply than this! How many taxis of each type should Max order, to keep the total cost as low as possible?**

Performance Based Tasks have been a great way to push my students to think critically and to break them out of the multiple choice comfort zone.

I try to use performance tasks and lessons from the Mathematics Assessment Project because they provide great student rubrics and exemplars with each task. Getting a clear picture of what I want my students to produce is sometimes half the battle.

Last week we did our third performance task to wrap up a decimal operations unit. Our first two tasks were sample CC items and weren’t graded too critically (to build students’ confidence).

This time the PBT was used/graded as an assessment. Students were given 30 minutes to individually brainstorm potential solutions and then worked with a partner for 50 minutes. I provided a rubric and a non-example to give them some direction.

The biggest challenge students faced was keeping track of all of their numbers and calculations. This resulted in careless mistakes and some overwhelmed students. My more meticulous students created tables and drew pictures; they were able to successfully accomplish the task.

When reflecting on how the task went, we analyzed anonymous peer samples. Students were asked to identify where things had going wrong (i.e. “He wrote 6 instead of 7 people in a large taxi”). Seeing several student samples with the same type of mistakes helped them internalize the importance of systematically attacking an open-ended problem.

I would love to hear what you all have tried in your classrooms. Let me know if you have PBT resources to share or need help finding some grade /objective appropriate tasks!

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