School level

# 24th March

## 24th March - Learning Outcomes

Calculus:

• Find first and second derivatives of linear, quadratic and cubic functions by rule.
• Associate derivatives with slopes and tangent lines
• Apply differentiation to rates of change, maxima and minima, curve sketching.
Student Activities
GeoGebra Files
Workshop Material
Explanatory Videos

### Varying Rates of Change - Tasks

Introduce students to calculus through rates of change using these three recommended tasks. These tasks were developed by the PDST Maths team. Supplementary GeoGebra files provided within.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Asset type: Presentation
Language: English
Special Needs:

### Introducing Calculus - Questions

The following document contains effective questions for introducing calculus. Each question has a sample answer provided. Students should use these questions alongside the other resources highlighted within the document.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Asset type: Document
Language: English
Special Needs:

### Rates of Change - Student Worksheet

The learner
(i) will sketch a graph to show the rate at which the height of the water level changes with time for two cylindrical containers of different radii and an inverted cone of given radius.
(ii) investigate constant speed

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 4. Algebra

Strand unit: 2. Solving Equations

Suggestions for use: As an introduction to differential calculus

Strand: 4. Algebra

Strand unit: 1. Expressions

Suggestions for use: As an introduction to differential calculus

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### GeoGebra - Filling Vase

https://www.scoilnet.ie/pdst/projec...-vase-investigating-rate-of-change/ Added: 19 Apr 2018 Contributor: PDST Resource type: Simulation / App/software

How does changing the shape of a vase affect the rate at which it fills and how does this manifest on its graph?

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: App
Language: English
Special Needs:

### Filling Cylinders

https://www.scoilnet.ie/pdst/projec...ders-Investigating-Rates-of-Change/ Added: 18 Apr 2018 Contributor: PDST Resource type: Simulation

How does the shape of a cylinder affect how quickly it fills with water and how does this manifest itself on a graph?

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Use in class with students to get them thinking about rates of change and graphs. Use suitable questioning to encourage students to consider key concepts.

Asset type: App
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Introduction to Calculus - Plan

A Teaching & Learning plan to help students
• understand what is meant by, and the difference between, average and instantaneous rates of change
• recognise the need for differential calculus in terms of real-world problems
• understand the concept of the derivative of a function
• understand that differentiation (differential calculus) is used to calculate instantaneous rates of change
• understand how to apply differentiation to calculate instantaneous rates of change

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Suggestions for use: As an introduction to differential calculus

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Newton, Leibniz, and Usain Bolt

https://www.khanacademy.org/math/ap...2-1/v/newton-leibniz-and-usain-bolt Added: 24 Mar 2020 Contributor: PDST Resource type: Audio / Video

Why we study differential calculus? What does Newton, Leibniz and Usain Bolt has in common? Watch the Khan Academy recommended video to find the answers to the above two questions.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Suggestions for use: Stimulus.

Asset type: Video
Language: English
Special Needs:

### Derivative as a Concept

https://www.khanacademy.org/math/ap...ew/ab-2-1/v/derivative-as-a-concept Added: 24 Mar 2020 Contributor: PDST Resource type: Audio / Video

Introduction to the idea of a derivative as instantaneous rate of change or the slope of the tangent line using this Khan Academy video. Video is seven minutes in length.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Suggestions for use: Explanatory video for students to independently watch.

Asset type: Video
Special Needs:

### Average Rate of Change

https://www.khanacademy.org/math/al...roduction-to-average-rate-of-change Added: 24 Mar 2020 Contributor: PDST Resource type: Audio / Video

Introduce students to the average rate of change with this Khan Academy video. By watching the video, your students will be able to answer the following question:
What's the average rate of change of a function over an interval?

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Asset type: Video
Language: English
Special Needs:

# Registering for a Scoilnet Account – your first step to contributing and sharing

## What you need...

To register for a Scoilnet Account you will need to have a Teaching Council number and a roll number for your school in Ireland.