Algebraic Expressions Unit Outline
Key Skills and Knowledge:
 Apply the four operations to simple algebraic fractions with numerical denominators
 Apply knowledge of index laws to algebraic terms, and simplifying algebraic expressions
 Understand the relationship between factorisation and expansion
 Factorise algebraic expressions by taking out a common algebraic factor
 Use the distributive law and the index laws to factorise algebraic expressions
 Apply the distributive law to the expansion of algebraic expressions,
 Expand binomial products and factorise monic quadratic expressions using a variety of strategies
 Express 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 in completed square form where a, b and c are integers by hand
 Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems
Key Vocabulary:
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





algebraic fractions
factorising
substitution
algebraic expression
commutative law
associative law
quadratic expressions




long division
factor theorem
remainder theorem
polynomials
Learning Intentions/Targets/Goals:












Simplify number sentences and algebraic expressions using index laws and highest common factors (F)
Add fractions using common denominators (F)
Recognise the highest common factor in a group of numbers or algebraic terms and expressions (F) (U)
Simplify expressions resulting from expansion of binomial products (U)
Factorise monic quadratic equations e.g. x2 + 7x + 12 using a variety of strategies (R) (PS)
Identify common factors including binomial terms in algebraic expressions (U)
Factorise algebraic expressions with four terms by using grouping in pairs (U) (R)
Recognise patterns for special binomial products e.g. (a+b)(a-b) and (a+b)2 to expand the products (F) (U)
Recognise patterns to factorise special cases of quadratic equations e.g. a 2 – b2 (F) (U)
Factorise quadratic expressions using the method of completing the square (U) (R)
Identify common factors including binomial terms in algebraic expressions (U)
Identify a polynomial expression and perform divisions of polynomials using factors and remainders (F) (U)
Set Class Work:
EX
2B
2C
PG
36
39
TOPIC
Algebraic Fractions #1
Algebraic Fractions #2
7A
225
Expanding Expressions
7B
229
Factorising #1
7C
234
Factorising #2
7D
19A
19C
19D
19E
19F
239
638
640
648
650
654
Completing the square
Polynomials
Long division
Polynomial values
Theorems
Factorising #3
SkillsSheet
SkillsSheet
SET QUESTIONS
2(acegik) 3(acegi) 4(acegi)
1(acegik) 2(acegi) 3(acegik) 4
1(adgj) 2(adgj) 3(adg) 4(adf) 5(aceg) 8(adgj)
9(adg) 10(adg) 11 12 16
1(adgjm) 2(ghikl) 7 8 9 10 12 14
1(adg) 2 3(cfi) 4(adg) 7(adg) 8(adg) 9(acegik)
11(ace) 12(ace) 15 16 17
2(ace) 3(egk) 4(acegi) 5
1 4 5 7
1(ace) 2(ace) 4(abef) 6(aceg)
1
1(aceg) 2(acegi) 3(aceg) 5 7
3
Fractions, Expanding, Factorising
Polynomials
Assessment Tasks:
1.
Linear Algebra Topic Test (SAC)
Year 10 Extended Core Mathematics
SIGN
DATE
Algebraic Expressions Unit Outline
Key Skills and Knowledge:
 Apply the four operations to simple algebraic fractions with numerical denominators
 Apply knowledge of index laws to algebraic terms, and simplifying algebraic expressions
 Understand the relationship between factorisation and expansion
 Factorise algebraic expressions by taking out a common algebraic factor
 Use the distributive law and the index laws to factorise algebraic expressions
 Apply the distributive law to the expansion of algebraic expressions,
 Expand binomial products and factorise monic quadratic expressions using a variety of strategies
 Express 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 in completed square form where a, b and c are integers by hand
 Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems
Key Vocabulary:







algebraic fractions
factorising
substitution
algebraic expression
commutative law
associative law
quadratic expressions




long division
factor theorem
remainder theorem
polynomials
Learning Intentions/Targets/Goals:












Simplify number sentences and algebraic expressions using index laws and highest common factors (F)
Add fractions using common denominators (F)
Recognise the highest common factor in a group of numbers or algebraic terms and expressions (F) (U)
Simplify expressions resulting from expansion of binomial products (U)
Factorise monic quadratic equations e.g. x2 + 7x + 12 using a variety of strategies (R) (PS)
Identify common factors including binomial terms in algebraic expressions (U)
Factorise algebraic expressions with four terms by using grouping in pairs (U) (R)
Recognise patterns for special binomial products e.g. (a+b)(a-b) and (a+b)2 to expand the products (F) (U)
Recognise patterns to factorise special cases of quadratic equations e.g. a 2 – b2 (F) (U)
Factorise quadratic expressions using the method of completing the square (U) (R)
Identify common factors including binomial terms in algebraic expressions (U)
Identify a polynomial expression and perform divisions of polynomials using factors and remainders (F) (U)
Set Class Work:
EX
2B
2C
PG
36
39
TOPIC
Algebraic Fractions #1
Algebraic Fractions #2
7A
225
Expanding Expressions
7B
229
Factorising #1
7C
234
Factorising #2
7D
19A
19C
19D
19E
19F
239
638
640
648
650
654
Completing the square
Polynomials
Long division
Polynomial values
Theorems
Factorising #3
SkillsSheet
SkillsSheet
SET QUESTIONS
2(acegik) 3(acegi) 4(acegi)
1(acegik) 2(acegi) 3(acegik) 4
1(adgj) 2(adgj) 3(adg) 4(adf) 5(aceg) 8(adgj)
9(adg) 10(adg) 11 12 16
1(adgjm) 2(ghikl) 7 8 9 10 12 14
1(adg) 2 3(cfi) 4(adg) 7(adg) 8(adg) 9(acegik)
11(ace) 12(ace) 15 16 17
2(ace) 3(egk) 4(acegi) 5
1 4 5 7
1(ace) 2(ace) 4(abef) 6(aceg)
1
1(aceg) 2(acegi) 3(aceg) 5 7
3
Fractions, Expanding, Factorising
Polynomials
Assessment Tasks:
2.
Linear Algebra Topic Test (SAC)
Year 10 Extended Core Mathematics
SIGN
DATE