Topic: Algebra

Today’s lesson: algebraic expressions and substitution

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

  • Write algebraic expressions from word sentences
  • Use substitution to find values
  • Apply formulas to real-world situations

Starter Questions

Copy these questions and work them out:

Write using algebraic conventions:

  1. \(7 \times k\)
  2. \(m \times 13\)
  3. \(p \div 8\)

Write as algebra:

  1. Three more than a number
  2. A number minus five

Write as algebra:

  1. Double a number
  2. A number divided by four
  3. Six less than a number

Exercise 3.02

Work on these questions for 10 minutes:

  • Q1 column 1
  • Q4a, b
  • Q5a, b, c, d
  • Q6a, b, c

Whatever you don’t finish now is homework.

Algebra to number sentences

Write number sentences for these expressions. Example given.

  1. \(n-12\) “Twelve less than a number”
  2. \(4-x\)
  3. \(\frac{2x}{3}\)

What is Substitution?

Copy this definition:

Substitution means replacing a pronumeral with a number to find the value of an expression.

Example:

If \(n = 5\), find the value of \(3n + 2\)

\(3n + 2 = 3(5) + 2 = 15 + 2 = 17\)

What is a Formula?

Copy the definition and examples

A formula is a general rule that is written as an algebraic equation and shows the relationship between variables.

Examples:

  • Perimeter of rectangle: \(P = 2l + 2w\)
  • Area of square: \(A = s^2\)
  • Distance: \(d = st\) (distance = speed × time)

Substituting into a formula

Copy

Example 1: The formula for perimeter of a rectangle is \(P = 2l + 2w\).

If a rectangle has length = 8cm and width = 5cm, find the perimeter.

Example 2

The formula for area of a square is \(A = s^2\)

If a square has side length = 7m, find the area.

Real-World Example 3: Canteen Order

The total cost of my canteen order is \(C = 8n\) where \(n\) is the number of butter chickens I order.

If I order \(3\) butter chickens, what is the total cost?

Real-World Example 3: Canteen Order

The total cost of my canteen order is \(C = 8n\) where \(n\) is the number of butter chickens I order.

If I order \(3\) butter chickens, what is the total cost?

Solution:

\(C = 8n\)

\(C = 8(3)\) Remember this means \(8 \times 3\)

\(C = \$24\)

Guided Practice

Work through these together:

If \(a = 4\) and \(b = 3\), find the value of:

  1. \(2a + 5\)

  2. \(3b - 1\)

  3. \(ab\)

  4. \(\frac{a + b}{2}\)

Guided Practice: Formulas

Work through these together:

  1. Use \(P = 2l + 2w\) to find the perimeter when \(l = 12\) and \(w = 7\)

  2. Use \(A = s^2\) to find the area when \(s = 9\)

  3. Use \(C = 4.20n\) to find the cost of \(n = 5\) meat pies

Independent Practice

Attempt these, then we’ll review:

If \(x = 6\) and \(y = 2\), find:

  1. \(x + 4\)

  2. \(3y\)

  3. \(xy\)

  4. \(2x - y\)

  1. \(\frac{x}{y}\)

  2. \(x^2\)

  3. \(4x + 3y\)

  4. \(\frac{x + y}{4}\)