CHECKED _____________
____________________
Short-term plan for Mathematics in Grade 10
| Unit | Derivative |
| Teacher’s name | ____________________ |
| Date | _____________ |
| Class | Grade 10 Attendance: _____ Absent: _____ |
| Lesson topic | Definition of a derivative. The concept of differential function. Rules for finding derivatives |
| Learning objectives covered in this lesson (curriculum reference) | To understand the definition of the derivative at a point and grasp its physical (instantaneous rate of change) and geometric (slope of the tangent line) significance. To define the differential of a function and learn how to apply it for approximating function increments. To master the basic rules of differentiation (sum, product, and quotient rules) and apply them fluently to find the derivatives of various functions. |
| Lesson goal |
|
Lesson flow
| Lesson stage / Time | Teacher actions (complete prompts and instructions) | Student actions | Assessment (criteria • descriptors • points) | Resources |
|---|---|---|---|---|
| Lesson opening (5 min) Engagement (voting + discussion) |
Teacher: "Imagine you are in a car that moves according to s(t) = t² (metres). At exactly t=3 s, your friend says the speed is 6 m/s. How can we be sure? Who thinks 6 is correct? – raise hand. Who thinks it could be different?" (quick show of hands). "Let’s check: average speed between 3 and 3.1 s? (6.1 m/s). Between 3 and 3.001? (6.001). The closer we get, the closer to 6. That's the instantaneous rate of change – the derivative." Brief debrief: "We’ll now learn the formal limit definition and the rules to find derivatives quickly." AI tool suggestion (for teacher prep): Use ChatGPT to generate 3 more relatable rate-of-change examples. |
|
Descriptors (no points): • Participates in voting. • Offers at least one verbal guess. • Shows readiness to learn. |
Whiteboard / projector, slide with s(t)=t² graph (geogebra.org or Desmos), 🤖 AI: ChatGPT for generating extra scenarios; quick polling via Plickers (optional). |
| Откроется после регистрации: Lesson middle (20-25 min) · Lesson end (5-10 min) · Reflection (5 min) | ||||