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Writing Terms and Expressions
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Foundational Skills
Recognise letters as unknowns
\[ n = \text{?} \]
Understand that letters represent unknown numbers.
Identify the unknown
\[ y = \text{Sam’s age} \]
Identify what a letter represents in a context.
Constants and variables
\[ 3n + 7 \]
Distinguish between constants and variables.
Reading Algebraic Notation
Multiplication notation
\[ 4y = 4 \times y \]
Letters together means multiply.
Substitution
\[ 3n \text{ when } n = 5 \]
Calculate value for a given variable.
Implicit coefficient of 1
\[ n = 1 \times n \]
Variable alone means coefficient is 1.
Division as fractions
\[ \frac{n}{4} = n \div 4 \]
Fraction notation represents division.
Division with numbers
\[ \frac{n}{3} \text{ when } n = 12 \]
Calculate division expressions.
Squared notation
\[ a^2 = a \times a \]
Squared means multiply by itself.
Squared with numbers
\[ n^2 \text{ when } n = 4 \]
Calculate squared expressions.
Cubed notation
\[ b^3 = b \times b \times b \]
Cubed means multiply three times.
Cubed with numbers
\[ n^3 \text{ when } n = 3 \]
Calculate cubed expressions.
Algebraic Terminology
Count the terms
\[ 3x + 2y – 5 \]
Count parts separated by + or -.
Identify coefficients
\[ 5x + 3 \]
Find the number multiplying a variable.
Identify constant terms
\[ 4x + 7 \]
Find the term with no variable.
Expression or equation?
\[ 3x + 5 \text{ vs } 2x = 8 \]
Distinguish expressions from equations.
Writing Single-Operation Expressions
Write addition expressions
\[ 5 \text{ more than } n \]
Translate ‘more than’ into addition.
Subtraction (variable first)
\[ 4 \text{ less than } n \]
‘Less than’ with variable first.
Subtraction (number first)
\[ n \text{ less than } 10 \]
Number reduced by a variable.
Write multiplication
\[ 6 \text{ times } n \]
Translate multiplication into algebra.
Write division
\[ n \text{ divided by } 4 \]
Translate division into fractions.
Writing Two-Step Expressions
Multiply then add/subtract
\[ 3n + 5 \]
Two-step: multiply first.
Add/subtract then multiply
\[ 2(n + 3) \]
Two-step: use brackets.
Divide then add/subtract
\[ \frac{n}{2} + 7 \]
Two-step: divide first.
Sum and product language
\[ \text{product of } 5 \text{ and } n \]
Understand sum, product, difference.
Expressions with Multiple Variables
Add/subtract two variables
\[ a + b \]
Combine two different variables.
Total cost expressions
\[ 3p + 2r \]
Cost of multiple items.
Coefficients with two variables
\[ 4a + 3b \]
Multiple variables with coefficients.
Expressions from Geometric Contexts
Perimeter of rectangle
\[ 2l + 2w \]
Perimeter with algebraic dimensions.
Perimeter of triangle
\[ a + b + c \]
Triangle perimeter expression.
Perimeter: mixed sides
\[ 3x + 12 \]
Algebraic and numeric sides.
Area of rectangle
\[ lw \]
Area with algebraic dimensions.
Special Cases and Conventions
Zero and identity properties
\[ n + 0 = n \]
Adding zero, multiplying by one.
Coefficient before variable
\[ 2n \text{ not } n2 \]
Write number before letter.
Alphabetical order
\[ ab \text{ not } ba \]
Write variables in alphabetical order.
Halves and doubles
\[ \text{half of } n = \frac{n}{2} \]
Common fractional relationships.
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