Topic: Algebra

Today’s lesson: words to algebraic expressions

By the end of this lesson, you will be able to:

  • Translate word phrases into algebraic expressions
  • Identify key mathematical vocabulary in word problems
  • Write expressions for real-world situations

Warm-up: Individual Practice

Work individually. Use your notes from last lesson if needed.

Simplify these expressions:

  1. \(6x + 2x\)
  2. \(9a - 4a\)
  3. \(3 \times 5m\)
  1. \(\frac{20p}{4}\)
  2. \(7n \times 2\)
  3. \(4k + k\)

Copy this vocabulary chart:

Word/Phrase Example
\(\times\) times, multiply by, product of “4 times a number” = \(4n\)
\(\div\) divided by, quotient, per “a number divided by 3” = \(\frac{n}{3}\)
\(-\) more than, plus, sum “5 more than a number” = \(n + 5\)
\(+\) less than, minus, difference “3 less than a number” = \(n - 3\)

Important Word Order

Copy these examples - order matters!

  • “5 more than a number” means \(n + 5\)
  • “5 less than a number” means \(n - 5\)
  • “a number divided by 4” means \(\frac{n}{4}\)
  • “4 divided by a number” means \(\frac{4}{n}\)

BUT WATCH OUT: - “subtract a number from 4” means \(4 - n\) (not \(n - 4\))

Key: Read carefully - sometimes the number comes second!

Worked Example 1: Think-Pair-Share

Attempt these yourself. Then discuss with person next to you

Let \(n\) represent “a number”. Write expressions for:

  1. Three times the number
  2. The number plus 7
  1. The number divided by 2
  2. 4 less than the number

Worked Example 1: Solutions

Let’s check your answers:

  1. Three times the number \(3n\)

  2. The number plus 7 \(n + 7\)

  1. The number divided by 2 \(\frac{n}{2}\)

  2. 4 less than the number \(n - 4\)

Fraction Language

Copy these fraction patterns:

  • “Half of a number” = \(\frac{n}{2}\)
  • “One-third of a number” = \(\frac{n}{3}\)
  • “One-quarter of a number” = \(\frac{n}{4}\)
  • “Two-thirds of a number” = \(\frac{2n}{3}\)

Pattern: “One-[fraction name] of” means divide by the bottom number

Consecutive Numbers

Copy these patterns:

If \(n\) is a number, then:

  • The next consecutive number is \(n + 1\)
  • The previous consecutive number is \(n - 1\)
  • The number two more is \(n + 2\)
  • The number three less is \(n - 3\)

Example: If the number is 7, the next consecutive number is 8, which is \(7 + 1\)

Guided Practice:

Attempt these questions then discuss with person next to you

Let \(x\) represent “a number”. Write expressions for:

  1. Half of the number
  2. 6 more than the number
  3. The previous consecutive number
  4. Subtract the number from 10
  1. The number multiplied by 8
  2. 9 divided by the number
  3. Two-thirds of the number

Guided Practice: Solutions

  1. Half of the number \(\frac{x}{2}\)

  2. 6 more than the number \(x + 6\)

  3. The previous consecutive number \(x - 1\)

  4. Subtract the number from 10 \(10 - x\)

  1. The number multiplied by 8 \(8x\)

  2. 9 divided by the number \(\frac{9}{x}\)

  3. Two-thirds of the number \(\frac{2x}{3}\)

Your Turn: Individual Practice

Work individually. Use your vocabulary chart if needed.

Let \(m\) represent “a number”. Write algebraic expressions for:

  1. Five times the number
  2. The number divided by 6
  3. 4 more than the number
  4. The number minus 10
  5. One-quarter of the number
  6. The next consecutive number

Extension for fast finishers: Create your own word problem for the expression \(3m + 7\)

Real-World Connections

Let’s connect to real situations:

Example: “Sarah has some money. She spends $5 and has \(m\) left.”

  • Let \(x\) = the money Sarah started with
  • Expression: \(x - 5 = m\), so \(x = m + 5\)

Your turn: Write an expression for each:

  • “Tom’s age in 3 years time” (if Tom is \(t\) years old now)
  • “The cost of 4 identical items” (if each item costs \(c\) dollars)

Extension: Write a real-world scenario for the expression \(2n - 15\)

Challenge Questions: Pair Work

Work with your partner for 5 minutes

Let \(p\) represent “a number”. Write expressions for:

  1. Three more than twice the number
  2. Half of the number, minus 4
  1. The sum of the number and its next consecutive number
  2. Five less than one-third of the number

Challenge Solutions

Let’s check the challenge questions:

  1. Three more than twice the number Answer: \(2p + 3\)

  2. Half of the number, minus 4 Answer: \(\frac{p}{2} - 4\)

  1. The sum of the number and its next consecutive number Answer: \(p + (p + 1) = 2p + 1\)

  2. Five less than one-third of the number Answer: \(\frac{p}{3} - 5\)

Exit Ticket

Complete individually before you leave

Let \(n\) represent “a number”. Write algebraic expressions for:

  1. Seven times the number
  2. The number divided by 5
  3. 8 less than the number
  4. One-third of the number
  5. Subtract the number from 12

On the back: Write one thing you learned today and one thing you found challenging.

Exercise 3.02

Complete subquestion parts a,c,e,…

Do 20 subquestions in total. If it’s making sense, jump ahead to harder questions and do more of those.

Summary

What we learned today:

  • Key mathematical vocabulary helps translate words to algebra
  • Word order is important in mathematics
  • Consecutive numbers follow patterns
  • Fractions have special language patterns
  • Real-world situations can be written as algebraic expressions

Next Lesson

Coming up:

  • Collecting like terms with multiple variables
  • Simplifying more complex expressions
  • Solving simple equations