1

WORK PROGRAM  MQ 9 NSW 5.2 Pathway

Chapter 15 Surds

Strands: Number, Patterns and algebra

Substrands and outcomes:

Operations with whole numbersNS4.1 Recognises the properties of special groups of whole numbers and applies a range of strategies to aid computation

Fractions, decimals and percentagesNS4.3 Operates with fractions, decimals, percentages, ratios and rates

Rational numbersNS5.2.1 Rounds decimals to a specified number of significant figures, expresses recurring decimals in fraction form and converts rates from one set of units to another

Real numbersNS5.3.1 Performs operations with surds and indices

Algebraic techniquesPAS4.3 Uses the algebraic symbol system to simplify, expand and factorise simple algebraic expressions

Algebraic techniquesPAS5.2.1 Simplifies, expands and factorises algebraic expressions involving fractions and negative fractional indices

Section / GC tips, Investigations,
History of mathematics, Maths Quest challenge, 10 Quick Questions, Code puzzles / SkillSHEETS, WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD–ROM) / Technology applications
(CD–ROM) /

Learning outcomes

Are you ready? (page 532) / SkillSHEETS (page 532)
15.1: Simplifying fractions
15.5: Converting a fraction into a decimal
15.6: Writing a recurring decimal in short form
15.7: Converting a terminating decimal into a fraction
15.8: Finding square roots, cube roots and other roots
15.9: Rounding to a given number of decimal places
15.13: Expanding to remove grouping symbols II
15.14: Expanding to remove a double set of grouping symbols / NS4.1
  • finding square roots and cube roots of numbers
  • applying a range of mental strategies to aid computation
NS4.3
  • reducing a fraction to its lowest equivalent form
  • rounding decimals to a given number of places
  • using the notation for recurring (repeating) decimals
  • converting fractions to decimals (terminating and recurring)
  • converting terminating decimals to fractions
PAS4.3
  • expanding algebraic expressions by removing grouping symbols (the distributive property)
PAS5.2.1
  • expanding algebraic expressions by removing grouping symbols and collecting like terms where possible

Rational and irrational numbers (page 533)
Rational numbers (page533)
WE 1a-b, 2a-b
Ex 15A Rational numbers (page 535) / SkillSHEET 15.1: Simplifying fractions (page 533)
SkillSHEET 15.2: Converting a mixed numeral into an improper fraction and vice versa (page 533)
SkillSHEET 15.3: Adding and subtracting fractions (page 533)
SkillSHEET 15.4: Multiplying and dividing fractions (page533)
SkillSHEET 15.5: Converting a fraction into a decimal (pages533, 535)
SkillSHEET 15.7: Converting a terminating decimal into a fraction (pages533, 536)
SkillSHEET 15.6: Writing a recurring decimal in short form (page535) / GC program – Casio: Converting fractions to decimals (page 535)
GC program – TI: Converting fractions to decimals (page 535)
Mathcad: Finite and recurring decimals (page535)
Excel: Converting decimals to fractions (page 536)
Excel: Converting recurring decimals to fractions (page 536) / NS4.3
  • using the notation for recurring (repeating) decimals
  • converting fractions to decimals (terminating and recurring)
NS5.2.1
  • writing recurring decimals in fraction form using calculator and non-calculator methods
NS5.3.1
  • defining a rational number
  • explaining why all integers and recurring decimals are rational numbers (Communicating, Reasoning)
  • explaining why rational numbers can be expressed in decimal form (Communicating, Reasoning)

Irrational numbers (page536)
WE 3a-d, 4
Ex 15B Irrational numbers (page 539) / GC tip – Casio: Calculating roots of numbers (page536)
History of mathematics: Richard Dedekind (page538)
Maths Quest challenge: Q1-2 (page 540)
Investigation: Irrational numbers on a number line (page 541)
Investigation: Plotting a graph of (page541)
10 Quick Questions 1 (page 542) / SkillSHEET 15.8: Finding square roots, cube roots and other roots (page539)
SkillSHEET 15.9: Rounding to a given number of decimal places (page 539)
SkillSHEET 15.10: Rounding to a given number of significant figures (page 539)
SkillSHEET 15.11: Using Pythagoras’ theorem (page 540)
WorkSHEET 15.1 (page540) / GC tip – TI: Calculating roots of numbers (page 536)
Mathcad: Irrational numbers (page 539)
Excel: Square roots (DIY) (page 539) / NS5.3.1
  • distinguishing between rational and irrational numbers
  • using a pair of compasses and a straight edge to construct simple rational numbers and surds on the number line
  • defining real numbers
  • demonstrating that is undefined for x < 0, = 0 for x = 0, and is the positive square root of x when x> 0
  • demonstrating that not all real numbers are rational (Communicating, Applying strategies, Reasoning)
  • solving numerical problems involving surds (Applying strategies)

Simplifying surds (page542)
WE 5a-b, 6, 7, 8a-c
Ex 15C Simplifying surds (page 545) / Investigation: Braking distances (page 547) / SkillSHEET 15.12: Simplifying surds (page545)
Game time 001 (page 546) / Mathcad: Simplifying surds (page 545)
Excel: Simplifying surds (page 545)
GC program – Casio: Surds (page 546)
GC program – TI: Surds (page 546) / NS5.3.1
  • using the following results for x, y > 0:
  • distinguishing between rational and irrational numbers

Addition and subtraction of surds (page 548)
WE 9a-b, 10
Ex 15D Addition and subtraction of surds (page 549) / Code puzzle (page 551) / WorkSHEET 15.2 (page550) / Mathcad: Addition and subtraction of surds (page 549) / NS5.3.1
  • using the operations of addition and subtraction to simplify expressions involving surds

Multiplication and division of surds (page 552)
WE 11a-c, 12a-c, 13, 14ab, 15
Ex 15E Multiplication and division of surds (page555) / Career profile: Peter Richardson (page558)
10 Quick Questions 2 (page 558) / SkillSHEET 15.13: Expanding to remove grouping symbols II (page556)
SkillSHEET 15.14: Expanding to remove a double set of grouping symbols (page 557)
Game time 002 (page557) / Mathcad: Multiplication and division of surds (page 555) / NS5.3.1
  • using the operations of multiplication and division to simplify expressions involving surds
  • expanding expressions involving surds
  • explaining why a particular sentence is incorrect (Communicating, Reasoning)

Writing surd fractions with a rational denominator (page 559)
WE 16a-b, 17
Ex 15F Writing surd fractions with a rational denominator (page 560) / Maths Quest challenge: Q1-2 (page 561) / SkillSHEET 15.15: Conjugate pairs (page561)
SkillSHEET 15.16: Applying the difference of two squares rule to expressions with surds (page 561)
WorkSHEET 15.3 (page561) / Mathcad: Rationalising denominators (page 560) / NS5.3.1
  • rationalising the denominators of surds of the form

Summary (page 562)
Chapter review (page 563) / ‘Test yourself’ multiple choice questions
(page 564)
Topic tests (2)