S4 Mathematics - Term 1

Topic 2: Equations and Inequalities

Lesson 1: Introduction to Building Formulas

Duration: 40 minutes

Learning Outcomes

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

• Understand the relationship between words and algebra
• Identify key words that indicate operations
• Build simple formulas from word statements

A Formula You Already Know

The area of a rectangle:

"The area is found by multiplying length by width"

↓

A = l × w

Words become formulas!

Today's Goal

Learn to turn word statements into algebraic formulas

This skill is called:

Building Formulas from Word Statements

Key Words Chart

Addition Key Words

Key Words: sum, plus, more than, increased by, total, added to

Examples:

• "The sum of a and b" → a + b
• "x increased by 5" → x + 5
• "3 more than y" → y + 3

Subtraction Key Words

Key Words: difference, minus, less than, decreased by, fewer than

Examples:

• "The difference of p and q" → p - q
• "x decreased by 7" → x - 7
• "5 less than n" → n - 5

Watch Out! Order Matters

"5 less than x" means x - 5 ✓

NOT 5 - x ✗

Think: "Start with x, then take away 5"

Multiplication Key Words

Key Words: product, times, of, multiplied by, twice, triple

Examples:

• "The product of m and n" → mn
• "Twice the number k" → 2k
• "Triple the value of z" → 3z

Division Key Words

Key Words: quotient, divided by, per, ratio, half of

Examples:

• "x divided by 4" → x ÷ 4 or x/4
• "Half of y" → y/2
• "The ratio of a to b" → a/b

Equals Key Words

Key Words: is, equals, gives, results in, the same as

Examples:

• "The sum of x and 3 is 10" → x + 3 = 10
• "Twice n equals 14" → 2n = 14

Practice: Translate These

Write algebraic expressions:

1. The sum of m and 7
2. n decreased by 4
3. Triple the value of k
4. Half of z

Answers

1. The sum of m and 7 → m + 7
2. n decreased by 4 → n - 4
3. Triple the value of k → 3k
4. Half of z → z/2

Building Complete Formulas

Process:

1. Read carefully - identify the relationship
2. Assign letters (variables) to quantities
3. Use key words to determine operations
4. Write the formula

Example: Cost of Mangoes

Statement: "The cost C of buying n mangoes at 500 shillings each"

Step 1: Cost = number × price per mango
Step 2: C = cost, n = number of mangoes
Step 3: Multiplication (each = per item)
Step 4: C = 500n

NCDC Curriculum Example

"Bayo is one year older than Ruth. If Ruth is r years old, what is Bayo's age?"

Solution:

• Bayo's age = Ruth's age + 1
• Ruth's age = r
• Bayo's age = r + 1

Extended Example

"John's age is 3 times Bayo's age"

• We know Bayo's age = r + 1
• John's age = 3 × Bayo's age
• John's age = 3(r + 1)

Note the brackets!

Ages Relationship Visualized

Practice Problem 1

"A taxi charges UGX 3,000 plus UGX 500 per kilometre."

Write a formula for total cost C for k kilometres.

Solution to Practice 1

• Base charge: 3,000
• Per kilometre: 500 × k
• Total cost: base + distance charge

C = 3000 + 500k

Practice Problem 2

"The perimeter P of a square is 4 times its side length s."

Write the formula.

Solution to Practice 2

• Perimeter = 4 × side
• P = perimeter, s = side length

P = 4s

Summary: The Process

1. Read - understand the relationship
2. Assign - choose letters for variables
3. Identify - find key words for operations
4. Write - build the formula

Summary: Key Words

Exit Questions

Write expressions or formulas for:

1. The sum of p and 12
2. 7 less than twice n
3. Earnings E for h hours at UGX w per hour

Answers to Exit Questions

1. p + 12

2. 2n - 7 (twice n, then subtract 7)

3. E = wh

Homework

Write formulas for:

1. Cost T of x books at UGX 8,000 each
2. Amina's age if she is 5 years older than Bosco (age b)
3. Perimeter P of rectangle with length L and width W
4. Taxi fare F: UGX 2,000 base + UGX 400 per km for d km
5. Triangle area A: half base b times height h

Next Lesson

Lesson 2: Translating Words to Expressions

We will practice with:

• More complex word problems
• Multiple operations in one formula
• Real-world Ugandan contexts

Credits

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

Source: National Curriculum Development Centre (NCDC), Uganda