Grade 7 Mathematics Term 4 Summary (CAPS
Aligned)
1. Whole Numbers and Integers
Whole numbers: Counting numbers (0, 1, 2, 3, …). Integers: Positive and negative numbers.
Example: −3, −2, −1, 0, 1, 2, 3. Rules for integers: (+) + (+) = +, (−) + (−) = −, (+) × (+) = +, (+) × (−)
= −, (−) × (−) = +.
2. Fractions, Decimals and Percentages
Convert fractions to decimals: divide numerator ÷ denominator (e.g., ¾ = 0.75). Convert decimals to
percentages: multiply by 100 (0.75 × 100 = 75%). Simplify fractions by dividing numerator and
denominator by the same number.
3. Ratio and Rate
Ratio compares two quantities of the same kind (e.g., 2 red : 3 blue). Rate compares quantities of
different kinds (e.g., 60 km in 2 hours → 30 km/h). Simplify ratios by dividing both sides by the
same number.
4. Algebraic Expressions
Variable: a letter that represents an unknown value (e.g., 2x + 3). Like terms have the same
variable and power (2x + 3x = 5x). Substitution: replace variable with a number (if x = 4 → 2x + 3 =
11).
5. Geometry and Measurement
Perimeter: distance around a shape (Rectangle = 2(l + w)). Area: space inside a shape (Rectangle
= l × w, Triangle = ½ × base × height). Volume: amount of space a solid occupies (Cuboid = l × w ×
h).
6. Data Handling
Mean: add all numbers, divide by how many numbers. Median: middle number when data is in
order. Mode: number that appears most often. Range: highest − lowest value.
7. Practice Questions
1. Simplify: −8 + 12 = ___ 2. Convert ■ to a decimal. 3. 30 learners : 5 teachers → simplify ratio. 4.
Find the value of 3x + 2 when x = 4. 5. Find area of a rectangle with l = 8 cm, w = 5 cm. 6. Calculate
the mean of: 4, 6, 8, 10, 12
Answers
Aligned)
1. Whole Numbers and Integers
Whole numbers: Counting numbers (0, 1, 2, 3, …). Integers: Positive and negative numbers.
Example: −3, −2, −1, 0, 1, 2, 3. Rules for integers: (+) + (+) = +, (−) + (−) = −, (+) × (+) = +, (+) × (−)
= −, (−) × (−) = +.
2. Fractions, Decimals and Percentages
Convert fractions to decimals: divide numerator ÷ denominator (e.g., ¾ = 0.75). Convert decimals to
percentages: multiply by 100 (0.75 × 100 = 75%). Simplify fractions by dividing numerator and
denominator by the same number.
3. Ratio and Rate
Ratio compares two quantities of the same kind (e.g., 2 red : 3 blue). Rate compares quantities of
different kinds (e.g., 60 km in 2 hours → 30 km/h). Simplify ratios by dividing both sides by the
same number.
4. Algebraic Expressions
Variable: a letter that represents an unknown value (e.g., 2x + 3). Like terms have the same
variable and power (2x + 3x = 5x). Substitution: replace variable with a number (if x = 4 → 2x + 3 =
11).
5. Geometry and Measurement
Perimeter: distance around a shape (Rectangle = 2(l + w)). Area: space inside a shape (Rectangle
= l × w, Triangle = ½ × base × height). Volume: amount of space a solid occupies (Cuboid = l × w ×
h).
6. Data Handling
Mean: add all numbers, divide by how many numbers. Median: middle number when data is in
order. Mode: number that appears most often. Range: highest − lowest value.
7. Practice Questions
1. Simplify: −8 + 12 = ___ 2. Convert ■ to a decimal. 3. 30 learners : 5 teachers → simplify ratio. 4.
Find the value of 3x + 2 when x = 4. 5. Find area of a rectangle with l = 8 cm, w = 5 cm. 6. Calculate
the mean of: 4, 6, 8, 10, 12
Answers
