School level

# 11th May

## 11th May: Number - Indices and Logarithms

Learning Outcomes

Students working at LCFL should be able to:

• solve contextual problems involving numbers represented in the following ways:

Students working at LCOL should be able to:

• solve problems using the rules for indices

Students working at LCHL should be able to:

• solve problems using the rules of logarithms

Teaching & Learning Plan
Indices
Logarithms
Calculator instructions
SEC Past Exam Questions

### Introducing e - Plan

The aim of this Teaching & Learning plan is to introduce the number e as the base rate of growth for all continually growing processes. Students will be able to
• Link continuously compounded interest and the number e
• Understand the relationship between e and the natural logarithm (loge)

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 2. Calculus

Suggestions for use: To introduce the number e as the base rate of growth for all continually growing processes

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

### Introducing e - Plan

The aim of this Teaching & Learning plan is to introduce the number e as the base rate of growth for all continually growing processes. Students will be able to
• Link continuously compounded interest and the number e
• Understand the relationship between e and the natural logarithm (loge)

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Suggestions for use: To introduce the number e as the base rate of growth for all continually growing processes

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

### Indices

https://www.scoilnet.ieuploads/resources/29900/29636.pptx Added: 24 Jun 2019 Contributor: PDST Resource type: Presentation / Other

A series of tasks on indices to check student understanding. Students write their answers and
justifications to show their understanding of indices. Any misconceptions can be identified and sorted.

SC Mathematics
JC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: A series of tasks on indices to check student understanding.

JC
Mathematics

Strand: 2. Numbers

Strand unit: 1.Representing Numbers & Arithmetic Operation

Suggestions for use: A series of tasks on indices to check student understanding.

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

### Indices Diagnostic Test

This is an assessment of student understanding of indices.

JC Mathematics
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 2. Numbers

Strand unit: 1.Representing Numbers & Arithmetic Operation

Suggestions for use: Use with the teacher instructions for Indices Diagnostic Test

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: Use with the teacher instructions for Indices Diagnostic Test

Asset type: Document
Language: English
Special Needs:

### Instructions for Indices Diagnostic Test

This guide is for use with Indices Diagnostic Test.

JC Mathematics
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 2. Numbers

Strand unit: 1.Representing Numbers & Arithmetic Operation

Suggestions for use: Instructions for using Indices Diagnostic Test

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: Instructions for using Indices Diagnostic Test

Asset type: Document
Language: English
Special Needs:

### Exploring Exponential Functions

https://www.scoilnet.ieuploads/resources/26428/26164.pdf Added: 24 Apr 2018 Contributor: PDST Resource type: Worksheet / Activity

A booklet for students to study the properties of exponential functions and explore the features of their graphs. They compare the graph of f(x) = a^x where a> 1 with the graphs f(x) = a^x where a<1 .

JC Mathematics
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 4. Algebra and Functions

Strand unit: 7. Functions

Suggestions for use: Introduction to exponential functions ( 2^x, 3^x)
Introducing graphs of exponential functions
Using exponential functions to solve real life problems

Key Skills: Communicating Managing Information and Thinking Working with Others Literacy Numeracy

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Suggestions for use: Review of exponential functions ( 2^x, 3^x)
Reviewing graphs of exponential functions
Using exponential functions to solve real life problems

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

### Introducing Logarithms

Further Exploration of Exponential Functions. Switching between Exponential and logarithmic forms of Equations. Students discover that the concept of logs is everywhere. Examples include the ph scale, sound levels, comparing earthquake sizes, google ranking of pages and compound interest.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: To introduce the concept of logs to students

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

### Introducing Logarithms

Students explore Exponential Functions through a series of activities that include compound interest, doubling and trebling. Students switch between exponential and logarithmic forms of equations. Graphs are used to move from discrete to continuous functions.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: To test students understanding of the concept of logs.

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

### Logarithms

https://www.scoilnet.ie/pdst/maths/student/lc/lc-numbers/logarithms/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive file to learn how to change a logarithm with any base to a specified base.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Asset type: Online Resource
Special Needs:

### Logarithmic Functions

https://www.scoilnet.ie/pdst/maths/...tudent/lc/lc-functions/logarithmic/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive Geogebra file to learn about logarithmic functions and their graphs.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Online Resource
Language: English
Special Needs:

### Relationship between e^x and ln(x)

https://www.scoilnet.ie/pdst/maths/...udent/lc/lc-functions/relationship/ Added: 09 Nov 2019 Contributor: PDST Resource type:

Interactive Geogebra file to understand the relationship between an exponential function and a logarithmic function with the same base.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 5. Functions

Strand unit: 1. Functions

Asset type: Online Resource
Language: English
Special Needs:

### SHARP Calculator Zipped File

Calculators are an invaluable tool when doing maths. Students need to become proficient at using their calculator. An important part of this process is learning how a calculator carries out certain calculations. While calculators are an important tool for doing maths, students still need to understand how to do calculations without a calculator and to understand if the results of a calculation are reasonable or not.
Here you will find instructional videos, PowerPoints, and activities to help students to learn how to use their SHARP calculator.

JC Mathematics
LCA Mathematical Applications
SC Mathematics
TY TY Core Subjects

#### How it maps to the curriculum

JC
Mathematics

Strand: 2. Numbers

Strand unit: 1.Representing Numbers & Arithmetic Operation

Suggestions for use: Download the zipped file to access the wide range of resources.

LCA
Mathematical Applications

Strand: Module 1 - Mathematics for Living

Strand unit: 1. Estimation & Calculator

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

TY
TY Core Subjects

Strand: Mathematics

Asset type: Presentation
Language: English
Special Needs:

### Casio Calculator Presentations

Calculators are an invaluable tool when doing maths. Students need to become proficient at using their calculator. An important part of this process is learning how a calculator carries out certain calculations. While calculators are an important tool for doing maths, students still need to understand how to do calculations without a calculator and to understand if the results of a calculation are reasonable or not.
Here you will find instructional videos, PowerPoints, and activities to help students to learn how to use their CASIO calculator.

JC Mathematics
LCA Mathematical Applications
TY TY Core Subjects
SC Mathematics

#### How it maps to the curriculum

JC
Mathematics

Strand: 2. Numbers

Strand unit: 1.Representing Numbers & Arithmetic Operation

Suggestions for use: Download the zipped file to access the wide range of resources.

LCA
Mathematical Applications

Strand: Module 1 - Mathematics for Living

Strand unit: 1. Estimation & Calculator

TY
TY Core Subjects

Strand: Mathematics

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Asset type: Presentation
Language: English
Special Needs:

### LCFL past exam questions - Indices

SEC past exam questions to assess student understanding of indices

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: Past exam questions

Asset type: Document
Language: English
Special Needs:

### LCOL past exam questions - Indices

SEC past exam questions to assess understanding of indices.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: Past exam questions

Asset type: Document
Language: English
Special Needs:

### LCHL past exam questions - Indices & Logarithms

SEC past exam questions to assess understanding of indices and logarithms.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 3. Number

Strand unit: 2. Indices & Logarithms

Suggestions for use: Past exam questions

Asset type: Document
Language: English
Special Needs:

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