TOPIC: 4SURDS & INDICES

OUTCOMES:Stage 5: NS 5.3.1 Performs operations with surds and indices ( p68 )

SUGGESTED TIME:

CONTENT KNOWLEDGE AND SKILLS RESOURCES TERMINOLOGYKey Ideas for Stage 5 Students learn about

defining a rational number:

A rational number is the ratio of two integers where

b ≠ 0. distinguishing between rational and irrational numbers using a pair of compasses and a straight edge to

construct simple rationals and surds on the number line defining real numbers:

Real numbers are represented by points on the number line.Irrational numbers are real numbers that are not rational.

demonstrating that is undefined for x < 0,

for x = 0, and is the positive square root of x when

using the following results for x, y > 0:

using the four operations of addition, subtraction, multiplication and division to simplify expressions involving surds

expanding expressions involving surds such as

or

rationalising the denominators of surds of the form

New Coarse Maths Yr9 Int Ch 4

New Century Maths Int 9Ch 1 p42 – 45

New Century Maths Yr 9 Adv Ch 5

New Century Maths Yr 10 Adv Ch 1

Maths Works 10 Int Ch 13

Mathscape Yr 9Stage 5·3Ch 8

surdrationalirrationalrationalisebinomialconjugateradical

1. Define the system of real numbers distinguishing between rational and irrational numbers

2. Perform operations with surds

3. Use integers and fractions for index notation

4. Convert between surd and index form.

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using the index laws to demonstrate the reasonableness of the definitions for fractional indices

translating expressions in surd form to expressions in index form and vice versa

evaluating numerical expressions involving fractional

indices eg

using the key on a calculator

evaluating a fraction raised to the power of –1, leading

to

WORKING MATHEMATICALLY

explain why all integers and recurring decimals are rational numbers (Communicating, Reasoning)

demonstrate that not all real numbers are rational (Communicating, Applying Strategies, Reasoning)

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