WORK PROGRAM

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

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

and fractional indices

Section / GC tips, Investigations,
History of mathematics, Maths Quest challenge, 10 Quick Questions,
Code puzzles,
Career profiles / SkillSHEETs, WorkSHEETs, Interactive games, Testyourself, Topic tests
(CD-ROM) / Technology applications
(CD-ROM) / Learning outcomes

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Are you ready? (page 572) / SkillSHEETs (page572)
15.1: Finding the square root of a number
15.2: Finding the cube root of a number
15.3: Finding square roots, cube roots and other roots
15.5: Expanding to remove grouping symbols II
15.6: 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
PAS4.3
  • expanding algebraic expressions by removing grouping symbols (the distributive law)
PAS5.2.1
  • expanding algebraic expressions by removing grouping symbols and collecting like terms where possible

Introduction to surds (page573)
Simplifying surds (page573)
WE 1a-b, 2, 3, 4a-c
Ex 15A Simplifying surds (page 576) / Investigation:Braking distances (page 578) / SkillSHEET 15.1: Finding the square root of a number (page 573)
SkillSHEET 15.2: Finding the cube root of a number (page 573)
SkillSHEET 15.3: Finding square roots, cube roots and other roots (page573)
SkillSHEET 15.4: Simplifying surds (page576)
Game time 001(page 577) / Mathcad:Simplifying surds (page 576)
Excel:Simplifying surds (page 576)
GC programCasio: Surds (page577)
GC program TI: Surds (page577) / NS5.3.1
  • using the following results for x, y > 0:
    , ,
  • distinguishing between rational and irrational numbers
  • solving numerical problems involving surds (Applying strategies)

Addition and subtraction of surds (page 579)
WE 5a-b, 6
Ex 15B Addition and subtraction of surds (page 580) / Code puzzle (page 582)
10 Quick Questions 1 (page 583) / WorkSHEET 15.1 (page581) / Mathcad: Addition and subtraction of surds (page 580) / NS5.3.1
  • using the operations of addition and subtraction to simplify expressions involving surds
  • solving numerical problems involving surds (Applying strategies)
  • explaining why a particular sentence is incorrect (Communicating,
Reasoning)
Multiplication and division of surds (page 583)
WE 7a-c, 8a-c, 9, 10a-b, 11
Ex 15C Multiplication and division of surds (page587) / Maths Quest challenge: Q1-2 (page 589)
10 Quick Questions 2 (page 590) / SkillSHEET 15.5: Expanding to remove grouping symbols II (page 588)
SkillSHEET 15.6: Expanding to remove a double set of grouping symbols (page 588)
Game time 002 (page 589)
WorkSHEET 15.2 (page589) / Mathcad:Multiplication and division of surds (page 587) / NS5.3.1
  • using the four operations of addition, subtraction, multiplication and division to simplify expressions involving surds
  • expanding expressions involving surds
  • solving numerical problems involving surds (Applying strategies)
  • explaining why a particular sentence is incorrect e.g.
(Communicating,
Reasoning)
Writing surd fractions with a rational denominator (page 590)
WE 12a-b, 13
Ex 15D Writing surd fractions with a rational denominator (page 592) / SkillSHEET 15.7: Conjugate pairs (page592)
SkillSHEET 15.8: Applying the difference of two squares rule to expressions with surds (page 592)
WorkSHEET 15.3 (page592) / Mathcad:Rationalising denominators (page 592) / NS5.3.1
  • rationalising the denominator of surds of the form

Summary (page 593)
Chapter review (page 594) / ‘Test yourself’ multiple choice questions
Topic tests (2)

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