Working together to improve teaching & learning
Leagan Gaeilge

Welcome to our “Teaching Calculus for Understanding” page. Below you’ll find a unit of learning for introducing calculus to students. This page is designed to explore approaches for distance learning in mathematics. The content is not intended to be prescriptive – rather it is presented as a series of suggestions for teachers to take and adapt. To support you all in your distance-learning efforts we’re also including video tutorials which explore:

- key features of the lessons which make for effective distance learning
- how to use a learning management system effectively
- getting set up on your learning management system

The intention is that in highlighting these features, you might identify which ones you feel will work for your students and your context, take these ideas and apply them when you’re teaching other topics in maths. While we’ve chosen the introduction to calculus as our area of focus – the approaches used could be applied to any mathematical content.

The unit is designed to provide students with learning experiences which encourage development of deep conceptual understanding. While the unit takes time to complete, it is our experience that students who engage with the material are able to move through later parts of calculus more quickly and are better able to adapt their thinking to address new content and problems.

This unit of learning addresses the following learning outcomes from the Leaving Certificate Mathematics syllabus:

**All students should be able to:**

-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

**In addition, students working at HL should be able to:**

-differentiate linear and quadratic functions from first principles

-differentiate polynomial functions

-find the derivatives of sums and differences

This unit is made up of five lessons – each with its own learning intentions. An overview of the sequencing of the lessons within the unit is provided in the following graphic.

Learning Intentions
#### Resources for Teaching, Learning and Assessment

#### Support for Teachers using these Resources

**Organising the Lesson**

Students will be able to:

- calculate average speed
- recognise speed as a rate of change
- relate slope of a graph to rate of change
- recognise the characteristics of situations involving a constant rate of change
- understand that when dealing with situations with constant rate of change, rate of change at a point is the same as the average rate of change over an interval.

Brief overview of how the resources might be organised into a distance-learning less...

For support on using your Learning Management System in conjunction with the student resources please see our dedicated support section at the bottom of this page.

Learning Intentions
#### Resources for Teaching, Learning and Assessment

#### Support for Teachers using these Resources

**The Assignment**
For support on using your Learning Management System in conjunction with the student resources please see our dedicated support section at the bottom of this page.

Students will be able to:

- recognise situations involving non-constant rates of change
- understand that average rate of change and instantaneous rate of change are not equal when rate of change is not constant
- understand how to estimate instantaneous rate of change using average rate of change
- understand the difficulty of calculating instantaneous rate of change when rate of change is not constant

- Student Assignment Lesson 2
- Video of Usain Bolt’s World Record 100m Race
- Usain Bolt Data
- Help Video for using the Usain Bolt GeoGebra File
- Usain Bolt WR Run GeoGebra File

A look at some of the features of the assignment which support students in distance ...

Learning Intentions
#### Resources for Teaching, Learning and Assessment

#### Support for Teachers using these Resources

For support on using your Learning Management System in conjunction with the student resources please see our dedicated support section at the bottom of this page.

Students will be able to:

- estimate the instantaneous rate of change of a function at a point
- explain the difference between average rate of change and instantaneous rate of change

GeoGebra file for Lesson 3 – Student Assignment

Learning Intentions
#### Resources for Teaching, Learning and Assessment

#### Support for Teachers using these Resources

Students will be able to:

- choose appropriate notation to represent the coordinates of any point on a function
- calculate the instantaneous rate of change using first principles

Lesson 4 – Student Assignment 1

GeoGebra file for Lesson 4 Assignment 1

Help video for Lesson 4 Assignment 1

Lesson 4 – Student Assignment 2

GeoGebra file for Lesson 4 Assignment 2

Student Video for Lesson 4 Assignment 2

For support on using your Learning Management System in conjunction with the student resources please see our dedicated support section at the bottom of this page.

Learning Intentions
#### Support for Teachers using these Resources

**Lesson 5 Overview**
**Assignment & Feedback**
**Live Discussion**

Students will be able to:

- identify the slope of a tangent to a curve as the instantaneous rate of change
- write down the derivative of a polynomial of the form ax
^{n}

- Lesson 5 – Student Assignment 1
- GeoGebra file for Lesson 5 – Student Assignment 1
- Instruction video for using the Assignment 1 GeoGebra file
- Lesson 5 Student Assignment 2
- GeoGebra file for creating derivative functions
- Student feedback form
- Text of Student feedback form (for making your own form)

A brief overview of how the resources might be organised into a distance-learning le...

Presenting an assignment to students, providing formative feedback to extend the stu...

An overview of how to navigate a clasroom discussion remotely using effective questi...

For support on using your Learning Management System in conjunction with the student resources please see our dedicated support section at the bottom of this page.

How a student can join a classroom and an exploration of the classroom environment.

How a teacher can create a rich assignment & communicate with students about the ass...

How a student can submit an assignment using Docs, how to save a document on a PC an...

How a teacher can make a form, distribute the form via classroom and view student re...

How a student can join a classroom and an exploration of the classroom environment.

How a teacher can create a rich assignment & communicate with students about the ass...