033. Algebra Terminology and Expressions

Learning Intentions

• To know the basic terminology of algebra
• Identify coefficients, terms and constant terms within expressions
• write expressions from word descriptions

Pre-requisite Summary

• Understand that letters can be used to represent numbers
• Recall the operations addition, subtraction, multiplication and division
• Know that multiplication can be written without a multiplication sign in algebra, for example
• Be able to read simple mathematical symbols and brackets
• Understand that an expression is a combination of numbers, variables and operations
• Know that like terms have the same variable part
• Be able to distinguish between numbers attached to variables and numbers standing alone
• Be able to translate simple verbal phrases into arithmetic operations

Worked Examples

Worked Example 1

a) Define the terms variable, coefficient, term and constant term.

b) Identify the variable in .

c) State the coefficient, the terms and the constant term in .

Worked Example 2

Identify the coefficients, terms and constant terms in:

a)

b)

c)

Worked Example 3

Write an expression for each description:

a) more than

b) times

c) less than

Worked Example 4

Write an expression for each description:

a) the sum of and

b) twice plus

c) minus

Worked Example 5

For the expression :

a) list all terms

b) identify each coefficient

c) state the constant term

Worked Example 6

For each word description, write an expression and then identify its terms:

a) more than twice

b) less than

c) the sum of and

Problems

Problem 1

a) Define the terms variable, coefficient, term and constant term.

b) Identify the variable in .

c) State the coefficient, the terms and the constant term in .

Problem 2

Identify the coefficients, terms and constant terms in:

a)

b)

c)

Problem 3

Write an expression for each description:

a) more than

b) times

c) less than

Problem 4

Write an expression for each description:

a) the sum of and

b) twice plus

c) minus

Problem 5

For the expression :

a) list all terms

b) identify each coefficient

c) state the constant term

Problem 6

For each word description, write an expression and then identify its terms:

a) more than twice

b) less than

c) the sum of and

Exercises

Understanding and Fluency

Exercise 1.

State the meaning of each term:

a) variable

b) coefficient

c) constant term

Exercise 2.

Identify the variable, terms and constant term in:

a)

b)

c)

Exercise 3.

Identify the coefficients in:

a)

b)

c)

Exercise 4.

List the terms and state the constant term in:

a)

b)

c)

Exercise 5.

Write an expression for each description:

a) more than

b) times

c) less than

Exercise 6.

Write an expression for each description:

a) the sum of and

b) twice plus

c) minus

Exercise 7.

Write an expression for each description and identify the terms:

a) more than

b) less than

c) the sum of and

Exercise 8.

Mixed practice:

a) In , state the coefficient of

b) In , state the constant term

c) In , list the terms

Reasoning

Exercise 9.

Explain why is called the coefficient in .

Exercise 10.

A student says the coefficient in is . Explain the mistake.

Exercise 11.

Explain why the number in is called a constant term.

Exercise 12.

A student writes “ less than ” as . Explain why this is incorrect.

Problem-solving

Exercise 13.

A phone plan costs a fixed $12 plus $3 for each gigabyte used. Write an expression for the total cost.

Exercise 14.

A taxi fare is a fixed $6 plus $2 for each kilometre . Write an expression for the fare and identify the constant term.

Exercise 15.

A school buys notebooks at $4 each and pays a $5 delivery fee. Write an expression for the total cost.

Exercise 16.

A person saves $10 each week for weeks and already has $25. Write an expression for the total amount saved.

Exercise 17.

A rectangle has length and width less than . Write an expression for the width.

Exercise 18.

A shop sells pens for $2 each. A customer also buys a notebook for $7. Write an expression for the total cost if pens are bought.

Potential Misunderstandings

• Students may think a variable is always a specific unknown value rather than a symbol that can represent a number
• Students may confuse a coefficient with a constant term
• Students may think a term must contain a variable, ignoring constant terms
• Students may not Recognise that a single variable such as has coefficient
• Students may list parts of a term separately, for example treating as two terms instead of one
• Students may reverse word descriptions such as “ less than ” and write instead of
• Students may confuse “sum” with multiplication or subtraction
• Students may not recognise that subtraction creates a negative term in an expression

Next: 034. Substituting into Algebraic Expressions