WORK PROGRAM
Chapter 4 Indices
Strands: Number, Patterns and algebra
Substrands and outcomes:
Operations with whole numbers NS4.1 Recognises the properties of special groups of whole numbers and applies a range of strategies to aid computation
Rational numbers NS5.1.1 Applies index laws to simplify and evaluate arithmetic expressions and uses scientific notation to write large and small numbers
Algebraic techniques PAS5.1.1 Applies the index laws to simplify algebraic expressions
Algebraic techniques PAS5.2.1 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 102) / SkillSHEETs (page102)4.1: Index form
4.2: Using a calculator to evaluate numbers in index form
4.4: Linking between squares and square roots
4.5: Calculating square roots
4.6: Linking between cubes and cube roots
4.7: Calculating cube roots
4.8: Estimating square roots and cube roots
4.9: Using a calculator to evaluate square roots and cube roots / NS5.1.1
· describing numbers written in index form using terms such as base, power, index
· evaluating numbers expressed as powers of positive whole numbers
NS4.1
· recognising the link between squares and square roots
· using the notation for square root and cube root
· finding square roots of numbers
· recognising the link between cubes and cube roots
· finding cube roots of numbers
· applying a range of mental strategies to aid computation
· finding square roots and cube roots using a calculator, after first estimating
What are indices? (page103)
WE 1a-b
Ex 4A What are indices? (page 103) / Investigation: The chessboard problem (page 104) / NS4.1
· using index notation to express powers of numbers (positive indices only)
NS5.1.1
· describing numbers written in index form using terms such as base, power, index, exponent
· solving numerical problems involving indices (Applying strategies)
Powers and bases (page105)
WE 2, 3, 4, 5
Ex 4B Powers and bases (page 106) / SkillSHEET 4.1: Index form (page 106)
SkillSHEET 4.2: Using a calculator to evaluate numbers in index form (page 106) / Mathcad: Index form (page 106) / NS4.1
· using index notation to express powers of numbers (positive indices only)
NS5.1.1
· describing numbers written in index form using terms such as base, power, index, exponent
· translating numbers to index form (integral indices) and vice versa
Multiplication using indices (page 107)
WE 6, 7, 8, 9, 10
Ex 4C Multiplication using indices (page 109) /
Maths Quest challenge Q1-3 (page 109)
Code puzzle (page 110) / Excel: Multiplying with indices (page 109)Mathcad: Multiplying with indices (page 109) / NS5.1.1
· developing index laws arithmetically by expressing each term in expanded form
· using index laws to simplify expressions
PAS5.1.1
· using the index laws previously established for numbers to develop the index laws in algebraic form
· simplifying algebraic expressions that include index notation
· linking use of indices in Number with use of indices in Algebra (Reflecting)
PAS5.2.1
· applying the index laws to simplify expressions involving pronumerals
· applying the index laws to simply algebraic expressions
Division using indices (page 111)
WE 11, 12, 13, 14, 15
Ex 4D Division using indices (page 113) / 10 Quick Questions 1 (page 114) / SkillSHEET 4.3: Simplifying fractions (page 113)
Game time 001 (page 113)
WorkSHEET 4.1 (page113) / Excel: Dividing with indices (page 113)
Mathcad: Dividing with indices (page 113) / NS5.1.1
· developing index laws arithmetically by expressing each term in expanded form
· using index laws to simplify expressions
PAS5.1.1
· using the index laws previously established for numbers to develop the index laws in algebraic form
· simplifying algebraic expressions that include index notation
· linking use of indices in Number with use of indices in Algebra (Reflecting)
PAS5.2.1
· applying the index laws to simplify expressions involving pronumerals
· applying the index laws to simply algebraic expressions
Zero index (page 114)
WE 16, 17, 18, 19
Ex 4E Zero index (page115) / Excel: Zero index (page115)
Mathcad: Zero index (page 115) / NS5.1.1
· establishing the meaning of the zero index
· using index laws to simplify expressions
PAS5.1.1
· establishing that a0=1 using the index laws
· simplifying algebraic expressions that include index notation
· explaining why x0 = 1 (Applying strategies, Reasoning, Communicating)
· linking use of indices in Number with use of indices in Algebra (Reflecting)
PAS5.2.1
· applying the index laws to simplify expressions involving pronumerals
· applying the index laws to simply algebraic expressions
Raising a power to another power (page 117)
WE 20a-b, 21, 22
Ex 4F Raising a power to another power (page118) / Maths Quest challenge Q1-2 (page 119) /
Game time 002 (page 119)
WorkSHEET 4.2 (page119) / Excel: Raising a power to another power (page 118)Mathcad: Raising a power to a power (page 119) / NS5.1.1
· developing index laws arithmetically by expressing each term in expanded form
· using index laws to simplify expressions
PAS5.1.1
· using the index laws previously established for numbers to develop the index laws in algebraic form
· simplifying algebraic expressions that include index notation
· linking use of indices in Number with use of indices in Algebra (Reflecting)
PAS5.2.1
· applying the index laws to simplify expressions involving pronumerals
· applying the index laws to simply algebraic expressions
Negative indices (page120)
WE 23a-b, 24a-b
Ex 4G Negative indices (page 121) / 10 Quick Questions 2 (page 121) / Mathcad: Negative indices (page 121)
Excel: Negative indices (page 121) / NS5.1.1
· establishing the meaning of negative indices
· writing reciprocals of powers using negative indices
PAS5.1.1
· simplifying algebraic expressions that include index notation
· linking use of indices in Number with use of indices in Algebra (Reflecting)
PAS5.2.1
· applying the index laws to simplify expressions involving pronumerals
· using index notation and the index laws to establish that
· applying the index laws to simply algebraic expressions
Square roots and cube roots (page 122)
WE 25, 26
Ex 4H Square roots and cube roots (page 123) / SkillSHEET 4.4: Linking between squares and square roots (page 123)
SkillSHEET 4.5: Calculating square roots (page 123)
SkillSHEET 4.6: Linking between cubes and cube roots (page 123)
SkillSHEET 4.7: Calculating cube roots (page 123)
SkillSHEET 4.8: Estimating square roots and cube roots (page123)
SkillSHEET 4.9: Using a calculator to evaluate square roots and cube roots (page 123)
WorkSHEET 4.3 (page123) / Mathcad: Square roots and cube roots (page 123)
Excel: Square roots (DIY) (page 123) / NS4.1
· using the notation for square root and cube root
· recognising the link between squares and square roots and cubes and cube roots
· finding square and cube roots of numbers using a calculator, after first estimating
· questioning whether it is more appropriate to use mental strategies or a calculator to find the square root of a given number (Questioning)
NS5.1.1
· using index laws to define fractional indices for square and cube roots
· writing square roots and cube roots in index form
PAS5.1.1
· simplifying algebraic expressions that include index notation
PAS5.2.1
· applying the index laws to simplify expressions involving pronumerals
· establishing that
()2 = ´ =
· using index laws to assist with the definition of the fractional index for square root
given
and
then
· using index laws to assist with the definition of the fractional index for cube root
· applying the index laws to simply algebraic expressions
· explaining why finding the square root of an expression is the same as raising the expression to the power of a half (Communicating, Reasoning)
Summary (page 124)
Chapter review (page 125) / ‘Test yourself’ multiple choice questions
Topic tests (2)
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