Indices & scientific notation

This is the teacher notes page identifying the outcomes addressed in these lessons. Copy each lesson link and send it to your students. For printable versions of these materials log into the teacher information section of the Department of Education.

Introduction

Students will:

• interpret the meaning of a number with a negative index

• know how to use and understand their calculators for both input and output of numbers with negative indices 

• convert between decimal notation and negative indices 

• perform operations with negative indices 

• understand the need for scientific notation and investigate very large and small things 

• use terminology, numbers, and expressions for large and small numbers 

• convert between decimal notation and scientific notation 

• know how to use and understand their calculators for input, output, and calculation of numbers in scientific notation 

• order numbers in scientific notation and relate them to a number line 

• use index laws to calculate numbers in scientific notation 

• understand the limitations of the calculator in performing calculations with very large numbers 

• apply knowledge and skills in using scientific notation to interpret information and perform calculations.

Outcomes:

• MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts 

• MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context

• MA5.1‑5NA operates with algebraic expressions involving positive-integer and zero indices and establishes the meaning of negative indices for numerical bases  

• MA5.1-9MG interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-7NA applies index laws to operate with algebraic expressions involving integer indices 

1. Negative indices

Students will:

• interpret the meaning of a number with a negative index 

• know how to use and understand their calculators for both input and output of numbers with negative indices 

• convert between decimal notation and negative indices 

• perform operations with negative indices.

Outcomes:

• MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts 

• MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context

• MA5.1‑5NA operates with algebraic expressions involving positive-integer and zero indices and establishes the meaning of negative indices for numerical bases  

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-7NA applies index laws to operate with algebraic expressions involving integer indices