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## Week 2 - Friday (Day 10)

##### All Weeks
###### Focus Areas
• Rate-in/Rate-out FRQs

• Vocabulary

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# Materials: 2018 AB1 or 2019 AB1

###### Teaching Tips

Students will work individually today for the entire 15-minute session. As before, we reviewed our procedures and policies for completing a timed FRQ and confirmed that students had at least one functioning calculator.  Because these FRQs are similar, half of our students completed 2018 AB1 and half of them completed 2019 AB1. This generated excellent conversations when responses were returned to students as they compared and contrasted the given information and questions. These are challenging --- but valuable! --- FRQs. The average score for 2018 AB1 was only 2.82 and the average for 2019 AB1 was 3.70.

Each FRQ is an excellent representation of the classic Rate-in/Rate-out calculus applications: each problem presents complex functions (calculator required!) for one or more opposing rates. Students then use analytic processes to demonstrate their understanding of multiple concepts.  Common skills include:

• Storing complex functions and important values in their calculator and accessing the  information when needed

• Recognizing a rate by its units; knowing that a rate is a derivative; remembering that rates produce accumulated values by integration.

• Using the FTC to find the change in amount by integrating a rate.

• Using units on given rates and related functions to interpret solutions in context

• Finding maximum and minimum values of rates by performing the First or Second Derivative tests

• Determining when a rate is increasing or decreasing by examining second derivatives

• Reading through unknown terms. Students must be able to navigate problems about gravel or escalators whether they recognize the objects or not.

• ENCOURAGE careful and patient reading, both of the stem (particularly the units assigned to each rate or function) and the individual questions. For example, in 2018, students confused the number of people entering the line with the number of people in line. Encourage students to multiply the units of the integrand with the units of the differential to determine the units on the integral expression.

• DISCOURAGE ambiguity! Functions without names or integral expressions without differentials may not earn full credit

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# Materials

###### Teaching Tips

Teams take turns describing as many Calculus words and phrases to their teammates as they can in a 60-second time interval.

Instructions:

• The 32 cards below are cut up and placed in a bowl. Students are split into two teams.

• A representative from each team is chosen and takes one word at a time from the bowl and describes it to his/her group members until they arrive at the correct phrase. The representative keeps picking words from the bowl until the 60 second time limit has been reached. No part of the word or phrase can be used when describing. No “rhymes with…”

• Teams go back and forth, choosing a new representative each time.

• Once the bowl is empty and all the words have been described, have each team count up their cards and record the sum. Return all the cards to the bowl to begin Round 2. In this round, only one word can be used to describe the word/phrase. Students will have heard all the words before so it’s a bit easier.

Modification: Distribute small pieces of paper and have each student write 1-2 Calculus words or phrases and place them in the bowl instead of using the list below.

Decide ahead of time if you will let students skip words they are stuck on. (We usually don’t!)

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