Download Chapter 4 Algebraic expressions and relationships

1
WORK PROGRAM  MQ 9 NSW 5.2 Pathway
Chapter 4 Algebraic expressions and relationships
Strand: Patterns and algebra
Substrands and outcomes:
Algebraic techniques
PAS4.1 Uses letters to represent numbers and translates between words and algebraic symbols
Algebraic techniques
PAS4.3 Uses the algebraic symbol system to simplify, expand and factorise simple algebraic expressions
Algebraic techniques
PAS5.2.1 Simplifies, expands and factorises algebraic expressions involving fractions and negative and
fractional indices
Section
Are you ready? (page 118)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles
SkillSHEETS,
WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD–ROM)
SkillSHEETS (page 118)
4.1: Alternative
expressions used to
describe the four
operations
4.2: Algebraic expressions
4.3: Like terms
4.4: Simplifying like terms
4.5: Multiplying algebraic
terms
4.6: Dividing algebraic
terms
4.7: Expanding to remove
grouping symbols I
4.12: Substitution into
algebraic expressions
Technology applications
(CD–ROM)
Learning outcomes
PAS4.1
 using letters to
represent numbers and
developing the notion
that a letter is used to
represent a variable
 translating between
words and algebraic
symbols and between
algebraic symbols and
words
PAS4.3
 recognising like terms
and adding and
subtracting like terms
to simplify algebraic
expressions
 simplifying algebraic
2
Using pronumerals
(page 119)
WE 1a-d, 2a-d, 3a-d
Ex 4A Using pronumerals
(page 121)
SkillSHEET 4.1:
Alternative expressions
used to describe the
four operations
(page 122)
SkillSHEET 4.2: Algebraic
expressions (page 122)
Generalised arithmetic
(page 122)
WE 4a-c, 5a-c
Ex 4B Generalised
arithmetic (page 125)
Maths Quest challenge:
Q1-3 (page 127)
WorkSHEET 4.1
(page 127)
Like terms (page 128)
WE 6a-d, 7a-d, 8a-c
Ex 4C Like terms
(page 130)
Investigation: Algebra
rectangles (page 131)
Code puzzle (page 132)
10 Quick Questions 1
SkillSHEET 4.3: Like
terms (page 130)
SkillSHEET 4.4:
Simplifying like terms
Mathcad: Displaying the
coefficients (DIY)
(page 121)
Mathcad: Collecting like
terms (page 130)
expressions that
involve multiplication
and division
 simplifying algebraic
expressions by
removing grouping
symbols (the
distributive property)
 substituting into
algebraic expressions
PAS4.1
 using letters to
represent numbers and
developing the notion
that a letter is used to
represent a variable
 translating between
words and algebraic
symbols
PAS4.3
 translating from
everyday language into
algebraic language and
from algebraic
language to everyday
language
 substituting into
algebraic expressions
PAS4.3
 recognising like terms
and adding and
subtracting like terms
3
(page 133)
Multiplication and division Maths Quest challenge:
(page 133)
Q1-2 (page 136)
WE 9a-d, 10a-d
Ex 4D Multiplication and
division (page 136)
Using grouping symbols
(page 137)
WE 11a-d, 12a-c, 13a-d
Ex 4E Using grouping
symbols (page 139)
Investigation: Oops! Any
errors? (page 140)
Investigation: The Bagels
game (page 140)
(page 130)
SkillSHEET 4.5:
Multiplying algebraic
terms (page 136)
SkillSHEET 4.6: Dividing
algebraic terms
(page 136)
WorkSHEET 4.2
(page 138)
SkillSHEET 4.7:
Expanding to remove
grouping symbols I
(page 139)
Mathcad: Multiplication
and division (page 136)
Excel: Expanding
grouping symbols
(page 139)
Mathcad: Expanding
grouping symbols
(page 139)
GC program – Casio:
Expanding (page 140)
GC program – TI:
Expanding (page 140)
to simplify algebraic
expressions
PAS4.3
 simplifying algebraic
expressions that
involve multiplication
and division
PAS4.3
 expanding algebraic
expressions by
removing grouping
symbols (the
distributive property)
 recognising like terms
and adding and
subtracting like terms
to simplify algebraic
expressions
PAS5.2.1
 explaining why an
algebraic expansion is
incorrect (Reasoning,
Communicating)
 determining and
justifying whether a
simplified expression
is correct by
substituting numbers
for pronumerals
4
Simplifying expressions
with grouping symbols
(page 141)
WE 14a-d
Ex 4F Simplifying
expressions with
grouping symbols
(page 142)
Algebraic fractions
(page 143)
WE 15a-c, 16a-c, 17a-b,
18a-b
Ex 4G Algebraic fractions
(page 146)
Maths Quest challenge:
Q1-2 (page 142)
Common factors
(page 147)
WE 19a-c, 20a-c, 21a-d
Ex 4H Common factors
(page 151)
Maths Quest challenge:
Q1-2 (page 152)
10 Quick Questions 2
(page 147)
SkillSHEET 4.8: Finding
and converting to the
lowest common
denominator (page 146)
SkillSHEET 4.9: Adding
and subtracting
fractions (page 146)
SkillSHEET 4.10:
Multiplying fractions
(page 146)
SkillSHEET 4.11: Dividing
fractions (page 147)
Game time 001 (page 147)
Mathcad: Expanding
expressions with
grouping symbols
(page 142)
GC program – Casio:
Expanding (page 142)
GC program – TI:
Expanding (page 142)
Mathcad: Algebraic
fractions (page 146)
Mathcad: HCF (page 151)
Excel: HCF (page 151)
GC program – Casio:
HCF (page 151)
GC program – TI: HCF
(page 151)
Mathcad: Factorising
using the HCF
(page 151)
(Applying strategies,
Reasoning)
PAS5.2.1
 expanding algebraic
expressions by
removing grouping
symbols and collecting
like terms where
possible
PAS5.2.1
 simplifying algebraic
expressions involving
fractions
PAS4.3
 factorising a single
term
PAS5.2.1
 factorising algebraic
expressions by
determining common
factors
5
Substitution and formulas
(page 153)
WE 22a-c, 23a-c, 24
Ex 4I Substitution and
formulas (page 155)
Summary (page 158)
Chapter review (page 159)
Investigation: Good health
(page 156)
History of mathematics:
Heron (c. 100 AD) and
Brahmagupta (598-668
AD) (page 157)
SkillSHEET 4.12:
Substitution into
algebraic expressions
(page 155)
Game time 002 (page 156)
WorkSHEET 4.3
(page 156)
‘Test yourself’ multiple
choice questions
(page 160)
Topic tests (2)
Excel: Factorising as2 + bx
(page 152)
Excel: Substitution
(page 155)
Mathcad: Substitution
(page 155)
Excel: Substitution game
(page 155)
PAS4.3
 substituting into
algebraic expressions