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**Planning Step 1: Lesson Curriculum: What are the Learning Goals for this lesson?**

**Lesson Standards**

Always include a writing standard.

NC.M2.F-BF.3

Build new functions from existing functions

CCSS.MATH.PRACTICE.MP3

Construct viable arguments and critique the reasoning of others.

CCSS.ELA-LITERACY.W.9-10.1

Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

**Students Will Be Able To… (Do)**

- Skills from standards including thinking (cognitive verbs).
- This is not activities.
- One or more goals should be Higher Order Thinking (Levels of Learning 3 or 4), and/or Reading Comprehension.
- Sequence these goals in the order in which they should be learned.

Describe of the effects of a , h , and k on a quadratic function

Represent a quadratic transformation by writing the function that corresponds to it

Justify why a certain quadratic function matches a certain quadratic graph

**Students Will Know**

Knowledge from standards such as vocabulary, facts, formulas.

Parent function of a quadratic

Transformations of a quadratic

Reflection

Horizontal Shift

Vertical Shift

Vertical Stretch

Vertical Compress

**Lesson Essential Question**

- A question that communicates the Learning Goals.
- Reflect the Higher Order Thinking and/or Reading Comprehension Learning Goal(s).

How is any quadratic function related to another quadratic function and the parent function f(x) = x2 ?

**Planning Step 3: Lesson Instruction: How will students learn?**

**Activating Strategy**

- Plan this after you plan your Learning Activities. How will you introduce the Lesson Essential Question?
- How will you draw attention to important vocabulary in the Lesson Essential Question?
- How will you build/link background knowledge?
- What prerequisite content might students need to know before the lesson?
- >Which key vocabulary from the Learning Goals needs to be explicitly taught?
- Are there other vocabulary words that you think need to be taught?
- Which vocabulary strategy will you use?
- Previewing:
- Advance Organizer
- Prerequisite Content
- Vocabulary

Students have learned how to write quadratic functions into vertex form y = a(x – h)2 + k.

Students will be given a list of quadratic functions written in vertex form. They will work in pairs. There will be a quadratic function in vertex form on the board. Students will work on this independently first. They will identify what the a , h , and k is in a quadratic function. I will then put two quadratic functions on the board. Both of them will be the same, except one will be plus h and the other will be minus h. Ask the class if the general vertex form equation has x minus h. What does it mean when it says plus h? Students will make a prediction about what they think that means independently. They will write it down and share with their partners. Let them know that they will find out as we go along.

Key Vocabulary (for explicit instruction):

reflection , horizontal shift , vertical shift , vertical stretch , and vertical compression.

Vocabulary Strategy:

4 Box Word Analysis Matrix

Previewing (what, who, when):

Students will be given a partially filled in organizer. They will have the word already filled in. We will work together on filling this out.

**Graphic Organizer**

- How will students store and organize information as they learn during this lesson?
- Base the organizer on the Higher Order Thinking or Reading Comprehension in the
*Will Be Able To… (Do)*Learning Goals. - Determine how the organizer will be previewed for struggling students.
- Determine how the organizer will be scaffolded for struggling students.

Transformation organizer

**Learning Activity 1**

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

- Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
- Content students need to learn
- Chunk activity:
- Several opportunities for thinking, talking, writing to learn
- Distributed summarizing and/or practice
- Questions to ask
- Higher Order Thinking and/or Reading Comprehension Questions to ask

- Active engagement:
- Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
- Variety
- Movement

- Previewing prerequisite knowledge/skills
- Scaffolding content and process

Students will be working on a pre-made desmo activity. I will explain to students that they will be working in pairs to explore the desmo activity as well as complete their graphic organizer. Explain to students that they will be looking for the patterns of the effects of a , h , and k on the quadratic function, more importantly the parent function. Explain that on the screen is the parent function, which they will not touch. They can manipulate a , h , and k. Students will work with their partners exploring the patterns of each transformation. The graphic organizer gives them a guide of how to manipulate a , h , k to lead them to what they are looking for. They will discuss their thoughts, justify their conclusion, and write it down in their graphic organizer. At some point, remind students of the prediction they were asked to make in the activating strategy. Students should have a discussion about what they notice about what the h value is and how it looks in the equation.

Previewing (what, who, when):

Whole class. Students will play around with desmos. They will get use to using the functions on the website. They will use the same premade activity as they will in the actual learning activity. Students will practice scrolling the bars that manipulate a , h , and k.

Scaffolding (what, who, when):

There may be some questions to ask to help guide students to what they are looking for and writing in their graphic organizer.

“What is happening as the ‘a’ is getting larger?”

“How does that compare to x2?”

**Assessment Prompt for ****Learning Activity 1**

- Formative assessment of the Learning Goal(s).
- Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
- Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

Write a note to an absent student explaining how a , h , and k affects the quadratic graph.

**Learning Activity 2**

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

- Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
- Content students need to learn
- Chunk activity:
- Several opportunities for thinking, talking, writing to learn
- Distributed summarizing and/or practice
- Questions to ask
- Higher Order Thinking and/or Reading Comprehension Questions to ask

- Active engagement:
- Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
- Variety
- Movement

- Previewing prerequisite knowledge/skills
- Scaffolding content and process

Students will be given a whiteboard and a marker. Students will do Think-Pair-Share. I will display on the board some transformations. Students will write down a quadratic function that reflects those transformations independently. They will find one person to pair with and share their ideas to each other. They will hold their answers up. Students will justify their solutions. Have students share some ideas out to class.

After doing a few, I will add another component. I will put up a set of transformations and an equation in vertex form. Students will identify the errors made in the equation that was written and explain why they believe they are errors.

Previewing (what, who, when):

Scaffolding (what, who, when):

Model the thinking process of how to come up with the quadratic function that represents a set of transformations. The class will do a “I do , We do , You do” before the students actually get into the activity. I will put up a set of transformations. I will go through the process of first identifying the a , h , and the k. Then, show them how to put it in the vertex form equation.

Students should have done an error analysis before. Model the thinking process of recognizing an error and explaining why it is an error.

**Assessment Prompt for ****Learning Activity 2**

- Formative assessment of the Learning Goal(s).
- Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
- Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

Students will complete a One Question Quiz. There will be four different forms of the question so that all students do not receive the same question. Students must write down the quadratic function given a set of transformations. Students will be timed. When completed, students will trade with a partner. The partner must give feedback on whether they agree or disagree. If they disagree, they must explain why.

**Learning Activity 3**

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

- Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
- Content students need to learn
- Chunk activity:
- Several opportunities for thinking, talking, writing to learn
- Distributed summarizing and/or practice
- Questions to ask
- Higher Order Thinking and/or Reading Comprehension Questions to ask

- Active engagement:
- Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
- Variety
- Movement

- Previewing prerequisite knowledge/skills
- Scaffolding content and process

Students will first get into groups of four. Then they will choose a partner from that group. Each pair will be given five paper strips that have quadratic functions on them. They will also have a paper that has five quadratic graphs with no numbers. Students will match the quadratic function that matches each graph. Each pair should discuss why they chose to match a certain function with a certain graph. Students will be told to use their vocabulary words in their discussion so they should use their vocabulary organizer. They should also use their graphic organizer to support their decisions. After students finish matching their functions and graphs, the whole group of four will compare their papers and discuss any differences they may have had.

Previewing (what, who, when):

Scaffolding (what, who, when):

Model the thinking process with a different example from the activity.

**Assessment Prompt for ****Learning Activity 3**

- Formative assessment of the Learning Goal(s).
- Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
- Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

Students will be given a paper that has 2 coordinate grids with no numbers.. Each coordinate grid contains two parabolas. The parent function of a quadratic, f(x) = x2 and another parabola. For each one, the student will come up with their own quadratic function that best represents the graph. They will also have to explain why they chose certain numbers for a , h , and k. Students must use vocabulary in their explanation.

**Planning Step 2: Lesson Assessment: How will students demonstrate understanding of the Learning Goals for this lesson?**

**Assignment**

- Plan this before planning Lesson Instruction.
- How will students demonstrate their knowledge of the
*Will Know*Learning Goals and the skills in the*Will Be Able To… (Do)*Learning Goals (especially the Higher Order Thinking and/or Reading Comprehension)? - How will the Assignment be differentiated for support and challenge?
- Which students receive differentiation?
- For students who struggle with the Assignment, how will you remediate this lesson?

Student will receive a three question assignment on transformations of quadratic functions that was completed by a tenth grade student. The assignment is matching equations to the graph. Students will do an error analysis on each problem , write a note to the student explaining what their error was and how to find the correct answer. Some corrections could have multiple right solutions. Students should use their graphic organizer to support reasoning on how the mistake could be fixed. Students are explaining in their own words. In addition, students will write a brief summary for each graph explaining how it compares to the parent function and why. Students should use their 4 box word analysis matrix to ensure the use of the vocabulary words in their summaries.

Differentiated Assignment for Struggling Students:

Student will receive a three question assignment on transformations of quadratic functions that was completed by a tenth grade student. Students may choose two questions they would like to analyze. The assignment is matching equations to the graph. Students will do an error analysis on each problem , write a note to the student explaining what their error was and how to find the correct answer. Some corrections could have multiple right solutions. Students should use their graphic organizer to support reasoning on how the mistake could be fixed. Students are explaining in their own words. In addition, students will write a brief summary for each graph explaining how it compares to the parent function and why. Students should use their 4 box word analysis matrix to ensure the use of the vocabulary words in their summaries.

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