**Un Questions About Derivative Applications** – This example explains the concept of derivative and is intended for 11th grade (US curriculum) students. The template is primarily designed as an introduction, but it can also be used as a form of reinforcement in the middle or at the end of a title block that concludes your content.

There are some ideas on how to use the slides, but you can use the template whenever you want. Each room has objectives and other information that you may find useful as a teacher. The general idea of all questions is that students should work on a Think-Pair-Share (TPS) model. The use of TPS requires students to first answer the questions individually, then discuss in pairs (or groups of three), and then discuss in a class meeting, led by the teacher. As a final note, slide content is primarily designed to develop students’ understanding of mathematical concepts, not procedural “how tos.” Therefore, student discussion and questions are a key part of using the presentation, and your skills as a teacher play a leading role in clearing up misconceptions and leading classroom discussions.

## Un Questions About Derivative Applications

Instruments are an important part of computing and have many practical applications. However, studies have shown that students often do not fully understand this concept. Part of this is due to lack of prior knowledge. Asia, etc. (1997) examined students’ constructs. They emphasize the importance of students having a rich understanding of the f(x)-labeled function. Other important terms he mentioned were the slope of a line and the graphical representation of points in a coordinate system. Therefore, the concept of slope is strongly emphasized in the initial parts of the template to fill potential gaps in knowledge. Also Asia et al. (1997) it is important for students to see: “The relationship between the slope of a tangent line and the graph of a function at a given point.” This visual representation is also the main part of the presentation.

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Slide 1 – Introduction: Introduction to the topic of the lecture and introduction to learning objectives. For example, it can be shown that derivatives are an important part of calculus with many practical applications.

Slide 2 – Overview: Inform students about the TPS process, how their responses can be accessed anonymously, and in an interactive presentation.

Slide 3 – Success Criteria: Introduction to “Success Criteria” which will be discussed and reviewed at the end of the lesson. The idea here is to visualize learning so that students can see that they have learned something.

Slide 4 – According to the students, as a result… This will help clear up misconceptions.

## Part 1: Applications Of Differentiation

Slide 5 – Prerequisites for this lesson. [Content Slide]: Review the concept of slope. Research has shown that this is an important condition for understanding what is happening.

Slide 6 – Understanding Slopes: This slide gets you thinking about what slopes mean in a mathematical sense, and as a teacher you can see if your students are really comfortable with calculating slopes.

Slide 7 – Intervals of points in non-linear functions: show what the tangent line is. This is a key concept for visual understanding of derivatives.

Slide 8 – Slope at a Point of a Nonlinear Function: This slide reinforces the understanding of tangent lines and how the tangent line can be used to think about the slope at a point of a nonlinear function.

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Slide 9 – Secant line: Introduction to the concept of a dividing line. This is a key concept in understanding derivatives.

Slide 10 – Calculating the slope of a secant line using only x-values and functions: This is the key slide! Here, students should understand how to calculate secant lines using only x0 and x1 and functions (without direct information about y0 and y1). It is essential that all students understand the content of this slide in order to understand the definition of derivative limits.

Slide 11 – Reducing the distance between points on a dividing line: This is the key slide! The idea here is to get students to think about what happens when two points on a secant line are really small.

Slide 12 – Dividing line and variable line are the same [Content slide]: Imagine what happens when the distance between two points on a dividing line is really small.

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Slide 13 – Moving from a divided straight line to a diagonal line. [Content Slide]: Switch from the dividing line definition to the diagonal line expression. It is important to understand the origin as the intersection of the tangent line at a point on the graph.

Slide 14 – Show a Limited Definition of Dervish [Content Slide]: This is the main slide! Move two points (Q and P) through the given field. Talk about limited insight. Here, it might be a good idea to have students write down the manufacturer’s definition of limitations.

Slide 15 – Derivatives in Practice: Here, students must apply their understanding of graphs to what graph is the sum of tangent lines at different points. They also begin to think about the practical implications of their findings.

Slide 16 – Using Constraint Definitions: This is the key slide! Here you can get an idea of your current level of understanding as a teacher. Spend a lot of time figuring out what the derivative (2x) expression really means. This is important information for the next slide.

#### Questions On Differentiation

Slide 17 – Success Criteria Revised: Return to the topic presented at the beginning of the lecture so that students understand that they have learned something specific.

Slide 18 – Question and Answer: Ask students to write down what they do not yet understand about formation.

Slide 16-24 – Quiz competition! Teach students to write their real names. As a teacher, challenge students in a fun way while experiencing specific learning levels. This information can be used to support students who need extra guidance.

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