Principles of Calculus · SHS2 Additional…

Lesson notes

Learning Objectives

Indicator: 2.3.1.LI.1 - Distinguish between partitioning an interval for a given step size and the number of subintervals.

By the end of the lesson, learners can:

State the relationship between the step size, the length of an interval, and the number of subintervals using the formula h = (b - a)/n.
Partition a given interval [a, b] into subintervals of equal length when the step size is given.
Partition a given interval [a, b] into subintervals of equal length when the number of subintervals is given.
Determine the number of subintervals for a given interval and step size, and justify the answer.
Explain in their own words the difference between choosing a step size and choosing a number of subintervals, and how one determines the other.

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Curriculum details

Strand: Calculus (Strand 3)
Sub-strand: Principles of Calculus (3.1)
Content standard: 2.3.1.CS.2 - Demonstrate a conceptual understanding of the connection between integration and limits and integration as a reverse process of differentiation. 2.3.1.LO.1 Determine the appropriate rule and use it to find the derivative of a function. 2.3.1.LO.2 Estimate the area under a curve using the trapezoid rule.
Indicator: 2.3.1.LI.1 - Distinguish between partitioning an interval for a given step size and the number of subintervals.
Suggested placement: Semester 2, Week 10 (Week 30 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

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Curriculum reference: NaCCA curriculum document, p. 390

Exemplars (from the NaCCA curriculum)

Talk for Learning, Think-pair-share, Experiential Learning, and Group Work/Collaborative Learning.
Activity 1: Partitioning of an area within an interval In mixed-ability groups, learners investigate the process of partitioning an area within a given interval into subintervals of equal size.
Example: Construct N subinterval on the interval [𝑎, 𝑏] '*& Step 1: Compute the step ℎ = B Step 2: Get the subintervals as follows [𝑎, 𝑎 + ℎ), [𝑎 + ℎ, 𝑎 + 2ℎ), ... ... ... , [𝑎 + (𝑛 − 1)ℎ, 𝑎 + 𝑛ℎ]
NB:
- The length of each subinterval is the step size.
- The relationship between the step size and the number of subintervals allows for partitioning once we know the step size or the number of subintervals.
Example: How many subintervals will be from [0,10] for a step size of 2?
Teaching and Learning Resources:
- Reading resource colour pens
- Notebook
- Graph sheets
- Mathematical sets
- Technological tools
Assessment (2.3.1.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.