appc lesson 1.2 homework math medic answer key

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Helping math teachers bring calculus to life

A Library of Parent Functions (Lesson 3.1)

Unit 3 day 1 ced topic(s): 1.12, unit 3 day 1 day 2 day 3 day 4 day 5 day 6 day 7 day 8 day 9 day 10 all units, ​learning targets​.

Understand that the parent function represents the most basic function in a family of functions.

Describe the key features of six parent functions: identity, absolute value, square root, quadratic, cubic, and reciprocal.

Analyze and compare the key features of parent functions.

Quick Lesson Plan

Activity: building a library.

Lesson Handout

Experience first:.

This lesson helps students to review six of the parent functions that they have studied in previous years. We expect that students already know the basic features of these graphs, so we encourage them to complete the activity without the use of a calculator. Students may choose to fill out more or less ordered pairs on their table depending on their familiarity with the shape of the function. As you are monitoring students, you can ask students to compare the different parent functions, making note of similarities and differences. Students that are comfortable with the shapes of the graph and/or finish early could be challenged to come up with scenarios that could be modeled by each of these function families.

Monit oring Questions:

How is the absolute value function like a piecewise function?

What can you say about the rate of change of this [identity] function?

Why isn’t y=mx+b included in this list?

What can you say about the rate of change of y=x^2?

What can you say about the rate of change of y=x^3?

What can you say about the rate of change of y=sqrt(x)?

Which of these six functions are concave up? Which are concave down?

Formalize Later:

While this lesson is not formally included in the AP Precalculus course framework, we thought it was valuable to include before students explore transformations (Lesson 3.2) and determine an appropriate function model (Lesson 3.4). Understanding families of functions and how they behave is critical in this course and the six parent functions students look at today are a good starting toolkit. Exponential and trigonometric parent functions will be introduced throughout the course.

Although students have seen all of these functions before, some students may struggle to remember some of these key features, specifically for the reciprocal function. Note that the reciprocal function and the square root function are the only parent functions in this set with restricted domains, and the reciprocal function is the only one with a vertical asymptote. It is important that students understand the key features of the parent function before investigating the effect of transformations in subsequent lessons. Students also review intervals of increasing and decreasing from Lesson 1.2. The vocabulary of “identity function” may be new to students. Ask them to consider why it is called this. Make sure students understand that the identity function is the parent function of all linear functions.

The Check Your Understanding questions increase in rigor. The last question provides a good challenge for students as they consider how the outputs of the six parent functions differ over the interval from x=0 to x=1. The answer may go against students’ intuition about which functions grow faster. This is a good opportunity to review some elementary concepts of fractions and decimals, and later concepts of exponent properties.

Helping math teachers bring statistics to life

Displaying Categorical Data

Chapter 1 - day 4 - lesson 1.2, all chapters, learning targets.

Make and interpret bar charts of categorical data.

Interpret bar charts.

Identify what makes some graphs of categorical data deceptive.

We decided that we are going to give less homework problems with the hopes that students recognize the value of homework and work on it authentically.  The magic number we settled on is 5.  Only 5 homework problems.  Typically the first 2 or 3 will directly address the learning targets, the next 2 will be problems where they need to put it all together, and then 1 review problem (read  Make It Stick  if you want to know why – interleaving learning).  This means that at the start of each day, we often will only go over 1 homework problem.

Activity: What is Your Social Media of Choice?

Answer Key:

We are going to try to have some sort of activity to start each new lesson.  We use the word “Activity” loosely, but as a general rule means that students are doing something within a real context.  Today, we asked “What is the most used social media app by students?”  Students collected the data for the class and displayed it in a frequency table and a relative frequency table (so we can connect new learning to previous learning).  Then we used iPads to make bar charts and pie graphs. We are going to use the applets found here for several activities in Chapter 1.

So we are going to try to run this whole class with no calculators….just iPads.  Today I have students working with one iPad for each pair of students.  This allows students to help each other if they are not familiar with the use of an iPad.  I demonstrated the use of the iPad by beaming my iPad to the projector using an Apple TV.  This process is not yet seamless but will hopefully getting better.

Going Through the Text and then Applications

Again I modeled going through the text with highlighting and annotating.  Students worked again in groups of 4 to pick out the major ideas of the lesson.   Then we worked on a few example problems to make sure that they could apply their new learning.