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 using symbols
• Know that multiplication may be written without the $\times$ sign, for example $3x$
• 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) $3x+5$
b) $7a-2$
c) $4m+6n+9$

Worked Example 3

Identify the coefficients, terms and constant term in each expression, including negative coefficients:
a) $-5x+8$
b) $2p-3q-7$
c) $-4y-6$

Worked Example 4

Identify the coefficients, terms and constant term in each expression, including zero coefficients:
a) $0x+9$
b) $3a+0$
c) $0m-5n+4$

Worked Example 5

Write an algebraic expression for each description:
a) $6$ more than a number $x$
b) $4$ times a number $y$
c) $9$ less than a number $k$

Worked Example 6

Write an algebraic expression for each description:
a) the sum of a number $n$ and $12$
b) $3$ times a number $p$, then subtract $5$
c) a number $t$ decreased by $8$

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) $5x+4$
b) $8b-1$
c) $2r+3s+6$

Problem 3

Identify the coefficients, terms and constant term in each expression, including negative coefficients:
a) $-3x+7$
b) $4p-2q-9$
c) $-6z-5$

Problem 4

Identify the coefficients, terms and constant term in each expression, including zero coefficients:
a) $0x+11$
b) $7c+0$
c) $0u-4v+3$

Problem 5

Write an algebraic expression for each description:
a) $8$ more than a number $x$
b) $5$ times a number $y$
c) $4$ less than a number $k$

Problem 6

Write an algebraic expression for each description:
a) the sum of a number $n$ and $15$
b) $2$ times a number $p$, then subtract $6$
c) a number $t$ decreased by $10$

Exercises

Understanding and Fluency

1. State the meaning of each term:
   a) variable
   b) coefficient
   c) term
   d) constant term

2. Identify the terms in each expression:
   a) $3x+4$
   b) $7a-5$
   c) $2m+6n+8$
   d) $-4y+9$

3. Identify the coefficient of the variable in each expression:
   a) $5x+2$
   b) $-3p+7$
   c) $9k-4$
   d) $0t+6$

4. State the constant term in each expression:
   a) $4x+9$
   b) $-2a-7$
   c) $6m+3n+5$
   d) $8q+0$

5. Identify the coefficients, terms and constant term in each expression:
   a) $6x-1$
   b) $-5r+4$
   c) $3p-2q+8$
   d) $0m+12$

6. Write an algebraic expression for each description:
   a) $5$ more than a number $x$
   b) $3$ times a number $y$
   c) $7$ less than a number $n$
   d) the sum of a number $k$ and $11$

7. Write an algebraic expression for each description:
   a) a number $p$ decreased by $4$
   b) $6$ times a number $t$
   c) $2$ times a number $m$, then add $9$
   d) $10$ less than a number $w$

8. Match each expression to a description:
   a) $x+8$
   b) $4y$
   c) $k-3$
   d) $2p+5$

Reasoning

9. Explain why $-3x+4$ has a negative coefficient.

10. A student says that in $5x+7$, the coefficient is $7$. Explain the mistake.

11. Noah says that the constant term in $4a-6$ is $6$. Is he correct? Explain.

12. Explain why $0x+9$ still has a constant term even though the coefficient of $x$ is zero.

13. A student writes “$3$ less than a number $x$” as $3-x$. Describe the error.

Problem-solving

14. A rectangle has width $w$ cm and length that is $5$ cm longer than the width. Write an expression for the length.

15. A taxi fare has a fixed charge of $\mathrm{\$}4$ plus $\mathrm{\$}2$ for each kilometre travelled, $k$. Write an expression for the total fare.

16. A student scores $m$ marks on a test, then gains $6$ extra marks. Write an expression for the new score.

17. A shop sells notebooks for $\mathrm{\$}3$ each. Write an expression for the cost of buying $n$ notebooks.

18. A temperature is $t^{\circ }\text{C}$ and then drops by $8^{\circ }\text{C}$. Write an expression for the new temperature.

19. A bag contains $x$ red marbles and $5$ 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 $3x$ means $3+x$ instead of $3\times x$
• Students may not recognise that a number on its own is also a term