## 1. Topic Overview

### Main Concept/Theme

In Term 3, the focus in Grade 7 Mathematics is on number patterns, algebraic expressions, equations, and geometry. The skills developed in this term are critical for understanding algebra and geometry at more advanced levels.

### Key Learning Objectives

- Recognize and describe number patterns.
- Understand and work with variables in algebraic expressions.
- Solve simple algebraic equations.
- Understand basic geometric concepts and properties of shapes.

## 2. Key Terms and Definitions

**Number Patterns**: Sequences of numbers following a specific rule.**Variable**: A symbol used to represent a number in equations and expressions.**Algebraic Expression**: A combination of numbers, variables, and operations.**Equation**: A mathematical statement showing that two expressions are equal.**Geometry**: The study of shapes, sizes, properties, and dimensions of objects.

## 3. Main Content Sections

### Number Patterns

**Identifying Patterns**: Learn to find the rule in a given number sequence.- Example: 2, 5, 8, 11… (increasing by 3 each time).
**Creating Patterns**: Practice creating your own number patterns based on a rule.**Arithmetic and Geometric Patterns**:**Arithmetic Pattern**: A sequence where the difference between consecutive terms is constant.**Geometric Pattern**: A sequence where each term is found by multiplying the previous term by a constant.

### Algebraic Expressions

**Components of Algebraic Expressions**:**Terms**: Parts of an expression separated by + or – signs.**Coefficient**: A number multiplied by a variable.- Example: In 3x + 5, 3 is the coefficient, x is the variable, and 5 is a constant.
**Simplifying Expressions**:- Combine like terms (terms with the same variable).
- Example: 2x + 3x = 5x.

### Solving Equations

**Understanding Equations**:- An equation has an equal sign (=) showing two expressions are equal.
- Example: 2x + 3 = 7.
**Solving Simple Linear Equations**:- Goal: Isolate the variable (get the variable alone on one side).
- Steps:
- Subtract or add to both sides to eliminate the constant.
- Divide or multiply to solve for the variable.

- Example:
- 2x + 3 = 7
- Subtract 3 from both sides: 2x = 4
- Divide by 2: x = 2

### Geometry

**Properties of Shapes**:**Triangles**: Types based on sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse).**Quadrilaterals**: Types like squares, rectangles, parallelograms, trapezoids.**Angle Relationships**:**Complementary Angles**: Sum to 90 degrees.**Supplementary Angles**: Sum to 180 degrees.**Perimeter and Area**:**Perimeter**: The distance around a shape.**Area**: The surface a shape covers.- Formulas for area:
- Rectangle: length × width
- Triangle: 1/2 × base × height

## 4. Example Problems or Case Studies

### Example Problems

**Number Pattern**:- Find the next three terms in the sequence: 3, 6, 9, 12…
- Solution: The pattern increases by 3. Next terms: 15, 18, 21.
**Solving Equations**:- Solve for x: 4x – 2 = 10
- Solution:
- Add 2 to both sides: 4x = 12
- Divide by 4: x = 3

### Case Study

**Pattern Application**:- Consider the daily savings of a person saving R5 more each day for a week starting with R10 on the first day. How much will they save on the 4th day?
- Solution: The sequence is 10, 15, 20, 25… On the 4th day, they will save R25.

## 5. Summary or Review Section

In Term 3, we’ve expanded our knowledge of patterns, algebra, and geometry. We learned to identify and create number patterns, simplified algebraic expressions and solved equations, and understood basic geometric properties.

## 6. Self-Assessment Questions

- Identify the next two terms: 7, 14, 21, 28…
- Simplify the expression: 5a + 3a – 2a.
- Solve the equation: 3x + 4 = 19.
- What is the area of a rectangle with a length of 8 cm and a width of 5 cm?
- Define supplementary angles.

## 7. Connections to Other Topics/Subjects

**Science**: Understanding patterns and algebra is essential when dealing with formulas and measurements.**Technology**: Algebra and geometry are foundational in programming and designing software.**Life Skills**: Managing personal finances often involves patterns and basic calculations.

This comprehensive guide should help you grasp the key concepts in Grade 7 Mathematics for Term 3. Keep practicing, and don’t hesitate to seek help if you need it! Happy studying!