Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Algebra ↓


Patterns and Sequences


Patterns and sequences are fundamental concepts in algebra and mathematics in general. They form the basis for understanding complex mathematical ideas and can be seen in numbers, shapes, and other elements of mathematics. In this guide, we will explore patterns and sequences, focusing on how they are introduced in grade 6 mathematics.

Understanding the pattern

A pattern is a repeated arrangement or design. Patterns can be found everywhere, in nature, music, art, and mathematics. In mathematics, patterns help us make predictions and understand the rules that govern numbers and operations.

Let's look at a simple number pattern:

2, 4, 6, 8, 10, ...

In this pattern, each number is 2 more than the previous number. It is called an arithmetic pattern because you can find the next number by adding the same amount each time.

Visualization of patterns

Visual aids can make it easier to understand patterns. Let's use a visual example to see how patterns can be organized.

Notice how these squares are arranged in a straight line. The pattern is of the same shape and style repeated across a row. This is an example of a repeating pattern, and you can guess that the next shape will be another square.

Understanding sequences

A sequence is a list of numbers or items in a specific order. Each item in the sequence is called a term. Sequences are special types of patterns. Unlike simple patterns, sequences often have specific rules for how they proceed.

Arithmetic sequence

One of the simplest types of sequences in math is an arithmetic sequence. In an arithmetic sequence, you add the same values from one term to get to the next.

For example:

3, 6, 9, 12, 15, ...

Here, to go from one term to the next, you add 3. The rule for this sequence can be written as:

Next term = Current term + 3

If you continue this pattern the sequence will increase by 3 each time.

Geometric progression

Another common type of sequence is the geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Let's examine a geometric sequence:

2, 4, 8, 16, 32, ...

In this example, each term is multiplied by 2 to get the next term.

Next term = Current term × 2

Multiplication makes the numbers grow rapidly.

Finding the nth term

Often in sequences, we want to find the value of a particular term without listing all the terms. This can save a lot of time and effort, especially in long sequences.

Finding the nth term in an arithmetic sequence

The formula for the nth term in an arithmetic sequence is:

a n = a 1 + (n - 1)d

- a n is the nth term - a 1 is the first term - n is the term number - d is the common difference

Example: Find the 10th term of the arithmetic sequence: 5, 8, 11, 14, ...

Here, a 1 = 5 and d = 3 (because each term increases by 3).

a 10 = 5 + (10 - 1) × 3 = 5 + 27 = 32

Hence the 10th term is 32.

Finding the nth term in a geometric sequence

The formula for the nth term in a geometric sequence is:

a n = a 1 × r n-1

- a n is the nth term - a 1 is the first term - r is the common ratio - n is the term number

Example: Find the 6th term of the geometric sequence: 3, 6, 12, 24, ...

Here, a 1 = 3 and r = 2 (since each term is multiplied by 2).

a 6 = 3 × 2 6-1 = 3 × 2 5 = 3 × 32 = 96

Hence the sixth term is 96.

Discovering real-world patterns and sequences

Patterns and sequences are not just limited to theoretical exercises; they have applications in the real world as well. Understanding these concepts can help in various fields such as science, finance, and technology.

Patterns in nature

Nature is full of patterns, and many of them can be explained using sequences. For example, the arrangement of leaves on a stem, called a phyllotaxis pattern, often follows the Fibonacci sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

In this sequence, each number is the sum of the two numbers before it.

Sequences in finance

In finance, sequences help predict market trends and interest rates. An example of this can be the calculation of compound interest, which is based on a geometric sequence.

A = P(1 + r/n) nt

- A is the amount accumulated after n years along with interest. - P is the principal (initial amount of money) - r is the annual interest rate (decimal) - n is the number at which interest is compounded per unit year - t is the time for which the money is invested in years

Key concepts to remember

  • Pattern: A repeated design or recurring arrangement.
  • Sequence: A specific sequence of numbers, where each item is called a term.
  • Arithmetic sequence: Sequence where the difference between the terms remains constant.
  • Geometric sequence: A sequence in which each term is found by multiplying the previous term by a fixed number.
  • Finding the nth term: Use formulas to find a specific term without listing all the terms.

Understanding patterns and sequences is an important step in developing algebraic thinking. These concepts form a foundation for more advanced mathematics and help develop problem-solving skills. By mastering the fundamentals, students can unlock a deeper appreciation for the beauty and utility of mathematics in everyday life.


Grade 6 → 2.3


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