132r. Review Algebra Terms and Expressions

Learning Intentions

• To know the basic terminology of algebra
• Identify coefficients, terms and constant terms within expressions, including in situations where coefficients are zero or negative
• write expressions from word descriptions

Pre-requisite Summary

• Know that letters can be used to stand for numbers
• Understand that operations such as addition, subtraction and multiplication can be written Use symbols
• Know that multiplication may be written without the sign, for example
• Be able to read simple mathematical phrases carefully
• Understand that a number on its own can be a term
• Know that positive and negative numbers can both appear in expressions

Worked Examples

Worked Example 1

State the meaning of each algebra term:

a) variable or pronumeral

b) coefficient

c) term

d) constant term

Worked Example 2

Identify the coefficients, terms and constant term in each expression:

a)

b)

c)

Worked Example 3

Identify the coefficients, terms and constant term in each expression, including negative coefficients:

a)

b)

c)

Worked Example 4

Identify the coefficients, terms and constant term in each expression, including zero coefficients:

a)

b)

c)

Worked Example 5

Write an algebraic expression for each description:

a) more than a number

b) times a number

c) less than a number

Worked Example 6

Write an algebraic expression for each description:

a) the sum of a number and

b) times a number , then subtract

c) a number decreased by

Problems

Problem 1

State the meaning of each algebra term:

a) variable or pronumeral

b) coefficient

c) term

d) constant term

Problem 2

Identify the coefficients, terms and constant term in each expression:

a)

b)

c)

Problem 3

Identify the coefficients, terms and constant term in each expression, including negative coefficients:

a)

b)

c)

Problem 4

Identify the coefficients, terms and constant term in each expression, including zero coefficients:

a)

b)

c)

Problem 5

Write an algebraic expression for each description:

a) more than a number

b) times a number

c) less than a number

Problem 6

Write an algebraic expression for each description:

a) the sum of a number and

b) times a number , then subtract

c) a number decreased by

Exercises

Understanding and Fluency

Exercise 1.

State the meaning of each term:

a) variable

b) coefficient

c) term

d) constant term

Exercise 2.

Identify the terms in each expression:

a)

b)

c)

d)

Exercise 3.

Identify the coefficient of the variable in each expression:

a)

b)

c)

d)

Exercise 4.

State the constant term in each expression:

a)

b)

c)

d)

Exercise 5.

Identify the coefficients, terms and constant term in each expression:

a)

b)

c)

d)

Exercise 6.

Write an algebraic expression for each description:

a) more than a number

b) times a number

c) less than a number

d) the sum of a number and

Exercise 7.

Write an algebraic expression for each description:

a) a number decreased by

b) times a number

c) times a number , then add

d) less than a number

Exercise 8.

Match each expression to a description:

a)

b)

c)

d)

Reasoning

Exercise 9.

Explain why has a negative coefficient.

Exercise 10.

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

Exercise 11.

Noah says that the constant term in is . Is he correct? Explain.

Exercise 12.

Explain why still has a constant term even though the coefficient of is zero.

Exercise 13.

A student writes “ less than a number ” as . Describe the error.

Problem-solving

Exercise 14.

A rectangle has width cm and length that is cm longer than the width. Write an expression for the length.

Exercise 15.

A taxi fare has a fixed charge of $ plus $ for each kilometre travelled, . Write an expression for the total fare.

Exercise 16.

A student scores marks on a test, then gains extra marks. Write an expression for the new score.

Exercise 17.

A shop sells notebooks for $ each. Write an expression for the cost of buying notebooks.

Exercise 18.

A temperature is and then drops by . Write an expression for the new temperature.

Exercise 19.

A bag contains red marbles and more blue marbles than red marbles. Write an expression for the number of blue marbles.

Potential Misunderstandings

• Students may think a coefficient is any number in an expression
• Students may confuse a term with a variable
• Students may think the constant term must always be positive
• Students may ignore a negative sign when identifying a coefficient
• Students may think a zero coefficient means the term does not exist at all
• Students may confuse the constant term with the coefficient
• Students may reverse phrases such as “less than” when writing expressions
• Students may think means instead of
• Students may not recognise that a number on its own is also a term

Next: 133r. Review Evaluating and Comparing Algebraic Expressions