##
* *Reflection: Developing a Conceptual Understanding
Graphing Functions: Lines, Quadratics, Square and Cube Roots (and Absolute Values) - Section 2: Graphing Quadratics

After completing the Entry Ticket, students work in groups to practice the skill of graphing quadratic functions. I typically provide students with examples to graph from Kuta Software.

In terms of how students graph the functions, I try to give students options to choose tools and technology strategically, in line with Math Practice 4. For example, students can use the TI NSpire applications on the classroom iPads and screen shot a picture of the function and table that they create. Alternatively, some students learn about structures and relationships between graphs and equations by graphing by hand.

*Developing a Conceptual Understanding: Technology for Deeper Understanding*

# Graphing Functions: Lines, Quadratics, Square and Cube Roots (and Absolute Values)

Lesson 5 of 13

## Objective: SWBAT graph linear and quadratic functions and show intercept and critical points (maximum and minimum). SWBAT graph square root, cube root, step functions and absolute values and compare different types of functions.

## Big Idea: Students learn to graph different types of functions AND compare and contrast key features of families of functions!

*90 minutes*

This **Entry Ticket: Graphing Functions: Lines, Quadratics, Square and Cube Roots** ties in directly to the standard **IF-7a **as I ask students to graph a linear and a quadratic function. The ticket also gets at the math practice of Modeling (see **MP4 **video for more info) because it gives students two tables of values and asks them to se the data and model it to a graph.

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#### Graphing Quadratics

*20 min*

After completing the Entry Ticket, students work in groups to practice the skill of graphing quadratic functions. I typically provide students with examples to graph from Kuta Software.

In terms of how students graph the functions, I try to give students options to choose tools and technology strategically, in line with Math Practice 4. For example, students can use the TI NSpire applications on the classroom iPads and screen shot a picture of the function and table that they create. Alternatively, some students learn about structures and relationships between graphs and equations by graphing by hand.

*expand content*

In this section, students actively take notes in **2-column format** (see strategy folder) based on a Khan Academy video going through an examples of graphing square and cube root functions.

While students are watching the Khan Academy video, I pause the video and have them complete one of the example problems from each (square root and cube root) type of function as practice in pairs.

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In this subsection I write the following on the Smart Board:

Graph the following function.

x |
f(x) |

-3 |
3 |

-2 |
2 |

-1 |
1 |

0 |
0 |

1 |
1 |

2 |
2 |

3 |
3 |

After students finish graphing the function, I have a class wide discussion on what students notice about the graph and the table. I ask if anyone can think of a function, expression or equation that we have worked with that fits this pattern. I give the hint, remember about the work we did on the operation that means we want to find the distance from zero if students need a prompt. We identify the function as an absolute value and students take notes identifying the term, and include the graph as an example in their notes. This subsection ties into the common core standard **HSF-IF-7b **on graphing square and cube root functions.

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#### Exit Ticket and Homework

*15 min*

To close this lesson, I have each group complete the **Exit Ticket: Graphing Different Types of Functions, **which is a graphic organizer to organize and elaborate on the different types of functions we graphed in class today.

I ask students to focus on the area of providing examples/evidence to support their ideas, as I am trying to focus on explicitly teaching, and providing practice opportunities, for one of the five main skills of academic conversations for each unit. During this time, students each have a copy of the graphic organizer and work on completing the template using their group notes. One way to differentiate this section is to allow each group to generate one Idea Organizer to take the fine motor demands off of some students. Students could then take a picture of the group’s Idea Organizer so they had access to it at home and still be able to complete the homework for the lesson.

The prompt for the exit ticket is: Look at your examples from class notes today. Identify at least three different types of functions we graphed. Compare and contrast key features (what the different graphs look like) of the three functions you choose. Explain at least one strategy on how we can graph functions.

With 5 minutes before the end of the lesson, I assess where the class as a whole is on the Idea Organizer and assign homework as completing the graphic organizer if they are not close to finishing it. If students have, for the most part, completed the task, then for homework I ask students to write a 1-2 paragraph written response based on their work. That way I am giving students a chance to practice their writing skills and also review the concepts from class with a high level of support. This exit ticket ties directly into the Math Practice standards of **MP3 **because I am asking students to develop arguments and also understand and integrate the perspective of their classmates to come to a deeper understanding of the concepts covered in class today.

*expand content*

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Introduction to Quadratic Functions
- LESSON 2: Interpreting and Graphing Quadratic Functions
- LESSON 3: Rate of Change & Comparing Representations of Quadratic Functions
- LESSON 4: Rearranging and Graphing Quadratics
- LESSON 5: Graphing Functions: Lines, Quadratics, Square and Cube Roots (and Absolute Values)
- LESSON 6: Building Quadratic Functions: f(x), kf(x) and f(kx)
- LESSON 7: Factoring and Completing the Square to Find Zeros
- LESSON 8: Forming Quadratics: Math Assessment Project Classroom Challenge
- LESSON 9: The Three Musketeers: Simplifying the Quadratic Formula
- LESSON 10: Quadratic Quandaries: Modeling with Quadratic Functions
- LESSON 11: Performance Task: Pulling It Together with Quadratics
- LESSON 12: Study Session for Unit Test on Quadratics
- LESSON 13: Unit Assessment: Quadratic Functions and Equations