S4 Mathematics - Term 1

Topic 2: Equations and Inequalities

Lesson 2: Translating Words to Expressions

Duration: 40 minutes

Learning Outcomes

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

• Translate complex word statements into expressions
• Handle multiple operations in a single expression
• Apply formula building to solve word problems

Quick Review

Translate these:

1. "The sum of x and 5"
2. "3 less than n"
3. "Twice y"

Review Answers

1. x + 5
2. n - 3
3. 2y

Today's Challenge

Combine multiple operations in one expression

Then use formulas to solve problems

Two-Operation Example 1

"5 more than twice x"

Step 1: "twice x" = 2x
Step 2: "5 more than" = add 5

Answer: 2x + 5

Two-Operation Example 2

"3 times the sum of a and b"

Step 1: "sum of a and b" = a + b
Step 2: "3 times" = multiply by 3

Answer: 3(a + b)

Brackets needed!

Brackets Matter!

Different meanings, different expressions!

Multi-Step Translation Process

NCDC Example: Age Difference

"How many years older than Bayo is John?"

• John's age = 3(r + 1)
• Bayo's age = r + 1
• Difference = 3(r + 1) - (r + 1)

Simplifying the Difference

3(r + 1) - (r + 1)
= 3r + 3 - r - 1
= 2r + 2 or 2(r + 1)

More Complex Examples

"Half the difference of p and q"
= (p - q)/2

"The square of the sum of m and n"
= (m + n)²

Pair Practice

Translate these:

1. 7 less than triple k
2. Twice the difference of x and 4
3. The product of a and the sum of b and c

Answers

1. 7 less than triple k → 3k - 7

2. Twice the difference of x and 4 → 2(x - 4)

3. The product of a and the sum of b and c → a(b + c)

Solving Word Problems

The key skill: Setting up the equation correctly

1. Read carefully
2. Define your variable
3. Translate each condition
4. Solve and check

NCDC Problem: Ruth's Age

"In 6 years' time, John will be 6 years older than Bayo. How old is Ruth now?"

Given:

• Ruth = r, Bayo = r + 1, John = 3(r + 1)

Setting Up the Equation

In 6 years:

• John: 3(r + 1) + 6
• Bayo: (r + 1) + 6

Condition: John = Bayo + 6

3(r + 1) + 6 = (r + 1) + 6 + 6

Solving

3(r + 1) + 6 = (r + 1) + 12
3r + 3 + 6 = r + 1 + 12
3r + 9 = r + 13
2r = 4
r = 2

Checking the Answer

Ruth = 2, Bayo = 3, John = 9

In 6 years:

• Bayo = 9
• John = 15
• Difference = 6 ✓

Ruth is 2 years old now!

Another Problem: Alupo's Number

"Alupo thinks of a number. She adds 5, then multiplies by 3. Her result is 27."

Find the number.

Solution: Alupo's Number

Let the number be n

• Add 5: n + 5
• Multiply by 3: 3(n + 5)
• Result is 27: 3(n + 5) = 27

Solve: n + 5 = 9
n = 4

Check: 4 + 5 = 9, 9 × 3 = 27 ✓

Your Turn

"A number is doubled and then 7 is subtracted. The result is 15. Find the number."

Solution

Let the number be n

• Doubled: 2n
• Subtract 7: 2n - 7
• Result is 15: 2n - 7 = 15

Solve: 2n = 22, n = 11

Check: 11 × 2 = 22, 22 - 7 = 15 ✓

Summary: Multi-Step Translations

1. Work from inside out
2. Look for grouping words ("sum of", "difference of")
3. Use brackets when operations must happen first
4. Always simplify if possible

Summary: Problem Solving

1. Read carefully
2. Define your variable
3. Translate conditions to algebra
4. Solve the equation
5. Always check your answer!

Exit Questions

Translate:

1. 4 more than triple n
2. Half the sum of x and y
3. The square of 3 less than p

Answers

1. 4 more than triple n → 3n + 4

2. Half the sum of x and y → (x + y)/2

3. The square of 3 less than p → (p - 3)²

Homework

1. Translate: (a) 6 less than 4 times m, (b) Twice the sum of p and 5

2. A number n is tripled and 8 is added. Result is 29. Find n.

3. Okello is twice as old as Akello. In 5 years, sum of ages is 40. Find Akello's age now.

Next Lesson

Lesson 3: Building Formulas with Multiple Variables

We will work with:

• Formulas involving several variables
• Geometric and scientific formulas
• Real-world applications

Credits

Created: December 2025
Based on: NCDC Lower Secondary Mathematics Syllabus (2019)

Source: National Curriculum Development Centre (NCDC), Uganda