Students will understand the basic concepts of calculus, including indefinite integrals and definite integrals.

Materials

Graph paper

Pencils

Calculator (optional)

Warm-up

Ask students what they know about calculus. Write their responses on the board.

Explain that calculus is a branch of mathematics that deals with continuously changing values, such as rates of change, tangents, and slopes.

Ask students to give an example of a problem that could be solved with calculus. Write their responses on the board.

Direct Instruction

Review the definition of calculus given earlier.

Explain that the basic concepts of calculus include differentiation, integration, and limits.

Differentiation is the process of finding the rate of change of a function. It involves finding the derivative, which is the function's derivative, or rate of change.

Integration is the process of finding the area under a function. It involves finding the integral, which is the function's area.

Limits are the boundaries that a function approaches as x approaches a specific number. They can also be described as the maximum or minimum value of a function as x approaches a specific number.

Use the handouts to provide more detailed explanations of these concepts.

Use examples to demonstrate each concept.

Guided Practice

Have the students work in pairs or small groups to complete a series of calculus problems, such as finding derivatives or integrals.

Provide assistance and guidance as needed.

Independent Practice

Have the students work on a project-based activity, such as creating a graph that shows the relationship between two variables (such as -have the students work on a project-based activity, such as creating a graph that shows the relationship between two variables (such as distance and time ) or finding the instantaneous rate of change of a variable (such as speed).

Closure

Review the main ideas of the lesson, including -Review the main ideas of the lesson, including differentiation and integration .

Ask the students to share their projects and discuss the results.

Assessment:

Observe the students during the independent practice and provide support as needed.

Ask the students to answer questions about the differentiation and integration concepts.

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