﻿ PDST Post-Primary Maths | LC Functions
Working together to improve teaching, learning and assessment Leagan Gaeilge
Leaving Certificate ›› LC Functions
 This strand builds on the learners’ experience in junior cycle where they were formally introduced to the concept of a function as that which involves a set of inputs, a set of possible outputs and a rule that assigns one output to each input. The relationship between functions and algebra is further emphasised and learners continue to connect graphical and symbolic representations of functions. They are introduced to calculus as the study of how things change and use derivatives to solve various kinds of real-world problems. They learn how to go from the derivative of a function back to the function itself and use such methods to solve various geometric problems, such as computation of areas of specified regions. -Leaving Certificate Syllabus page 41
##### General Resources for Functions
 The following teaching and learning plans are available: Resources from the Junior Cycle page may be useful for teaching the Foundation Level Syllabus. Blended learning resources for introducing Calculus can be found on our dedicated ‘Teaching Calculus for Understanding‘ Page. Some useful resources for teaching Algebra can be found on the Workshop and Event Resources Page, in particular,  (2019 – 2020), NQT Workshop 5 (2018 – 2019), Project Maths Workshop 5 , Workshop 7,   (2008 – 2015) and Seminar (2014 – 2015). GeoGebra tutorials on using the may useful for the teaching of Functions. These mindmaps present a summary of the statistical concepts for Leaving Certificate Ordinary Level and Leaving Certificate Higher Level. There are a range of lesson plans developed by teachers available in our Lesson Study Library. There are a range of resources created by teachers available on Scoilnet to support teaching and learning of Functions.

#### Outcome 5.1

Functions

 This Presentation for teachers and activity for students explores shifting and scaling (transforming) graphs of functions. Student Poster giving an overview of shifting and scaling of quadratic functions. Student quiz on transforming (shifting and scaling) graphs of quadratic and other functions. Matching activity print out designed to assess understanding of transformations of quadratic functions and their graphs. Student activity on matching a wide variety of graphical representations to each graph’s context. Student activity on describing the graph of a function, focussing on understanding turning points and points of inflection. Teacher presentation on the concept of a function, types of functions (injective, surjective, bijective) and exponential functions. Teacher Presentation on introducing exponential functions and Student activity worksheets. Teacher Presentation explaining e, as a limit, using a problem solving approach. Student activity worksheet on using problem solving to introduce limits. GeoGebra file to visualise e as the limit of a function GeoGebra file showing the logarithmic function as the inverse of the corresponding exponential function Poster explaining the difference between injective, surjective and bijective functions Presentation explaining e as a limit and the concept of continuity of functions and student activities on limits and continuity A video showing exponential growth on a chess board and a video showing exponential growth in the world around us

#### Outcome 5.2

Calculus
 Activities on understanding linear rates of change Activities on instantaneous rate of change for linear and non linear functions Presentation on introducing calculus Presentation on relating the derivative to the slope function Activities on introducing differential calculus and relating the derivative to slope GeoGebra file of filling cylinders for investigating rates of change GeoGebra file of filling cones for investigating rates of change GeoGebra file of filling vase for investigating rates of change GeoGebra file using angry birds to explain calculus Activities on discovering the rules of differentiation GeoGebra file for discovering how to differentiate a polynomial by rule (use in conjunction with ‘Activities on discovering the rules of differentiation’) GeoGebra file relating the graph of a cubic function to its first and second derivative Student activity on describing the graph of a function Animated presentation on sketching derivatives Student activities on curve sketching derivatives GeoGebra file to support curve sketching derivatives of six basic functions (use in conjunction with ‘Student activities on curve sketching derivatives’) GeoGebra file to support curve sketching derivatives of any function Activity on graph matching functions and derivatives and Solutions A presentation developed by teachers on making sense of differentiation by rule An activity on understanding anti-differentiation as the reverse process of differentiation Student activity on finding a distinct anti-derivative using an initial condition Activity on calculating the area beneath a linear function Animated presentation,  GeoGebra file and activity on introducing integral calculus and how to calculate the average value of a function GeoGebra file on understanding the derivative of a vertically-shifted function