Grade 3
  1. Number Sense and Numeration  1.1. Understanding Numbers  1.1.1. Reading and Writing Numbers up to 10,000  1.1.2. Place Value up to Thousands  1.1.3. Comparing and Ordering Numbers  1.1.4. Rounding Numbers to the Nearest Ten and Hundred  1.1.5. Skip Counting by 2s, 5s, 10s, and 100s up to 1,000  1.2. Operations with Whole Numbers  1.2.1. Addition and Subtraction up to 1,000  1.2.2. Multiplication Facts (up to 10 x 10)  1.2.3. Division Facts (up to 100)  1.2.4. Multiplication as Repeated Addition  1.2.5. Division as Equal Sharing  1.2.6. Word Problems with Addition, Subtraction, Multiplication, and Division  1.3. Estimation  1.3.1. Estimating Sums and Differences  1.3.2. Estimating Products and Quotients  1.4. Understanding Even and Odd Numbers
  2. Fractions and Decimals  2.1. Understanding Fractions  2.1.1. Identifying and Representing Fractions  2.1.2. Fractions of a Whole and Part of a Set  2.1.3. Comparing and Ordering Fractions with Like Denominators  2.1.4. Equivalent Fractions  2.1.5. Simple Fraction Word Problems  2.2. Introduction to Decimals  2.2.1. Tenths and Hundredths as Decimals  2.2.2. Relationship between Fractions and Decimals
  3. Measurement  3.1. Length  3.1.1. Measuring in Centimeters and Meters  3.1.2. Comparing and Ordering Lengths  3.1.3. Estimating Lengths  3.1.4. Converting Between Centimeters and Meters  3.2. Mass  3.2.1. Measuring in Grams and Kilograms  3.2.2. Estimating and Comparing Mass  3.3. Capacity  3.3.1. Measuring in Milliliters and Liters  3.3.2. Estimating and Comparing Capacity  3.4. Time  3.4.1. Telling Time to the Nearest Minute  3.4.2. Calculating Elapsed Time  3.4.3. Using a Calendar  3.4.4. Understanding A.M. and P.M.  3.5. Area and Perimeter  3.5.1. Calculating Perimeter of Simple Shapes  3.5.2. Estimating and Measuring Area of Shapes  3.5.3. Finding Area by Counting Squares
  4. Geometry  4.1. Properties of Shapes  4.1.1. Identifying 2D Shapes (Triangles, Quadrilaterals, Circles, etc.)  4.1.2. Identifying 3D Shapes (Cubes, Spheres, Cylinders, etc.)  4.1.3. Describing Attributes of 2D and 3D Shapes  4.1.4. Recognizing Parallel and Perpendicular Lines  4.2. Symmetry and Transformations  4.2.1. Recognizing Lines of Symmetry  4.2.2. Identifying Flips, Slides, and Turns  4.3. Angles  4.3.1. Understanding Right Angles  4.3.2. Comparing Angles (Acute, Right, Obtuse)
  5. Data Management and Probability  5.1. Data Collection and Organization  5.1.1. Collecting Data using Surveys and Experiments  5.1.2. Organizing Data using Tally Charts and Tables  5.2.1. Creating and Interpreting Pictographs  5.2.2. Creating and Interpreting Bar Graphs  5.2.3. Reading Simple Line Graphs  5.3. Probability  5.3.1. Understanding Basic Probability Terms (Certain, Possible, Impossible)  5.3.2. Predicting Outcomes  5.3.3. Simple Probability Experiments
  6. Patterns and Algebra  6.1. Patterns  6.1.1. Identifying and Extending Numeric Patterns  6.1.2. Identifying and Extending Shape Patterns  6.1.3. Creating Patterns Using Rules  6.2. Introduction to Algebra  6.2.1. Understanding Variables as Unknowns  6.2.2. Solving Simple Addition and Subtraction Equations  6.2.3. Using Patterns to Solve Problems
  7. Problem-Solving Skills  7.1. Strategies for Problem-Solving  7.1.1. Using Pictures or Diagrams  7.1.2. Identifying Patterns in Problems  7.1.3. Making Organized Lists  7.1.4. Guessing and Checking  7.1.5. Using Logical Reasoning  7.1.6. Breaking Down Problems into Steps

Grade 3 → Patterns and Algebra → Patterns ↓


Creating Patterns Using Rules


Patterns are present everywhere in our everyday lives - in the design of a carpet, the arrangement of tiles, or the repetition of beats in music. In mathematics, patterns play an important role and help us make predictions and solve problems. In Grade 3 mathematics, children learn to create patterns using rules, which is an important foundational skill in algebra. This helps them understand the regularity and predictability of patterns and discover the rules behind them.

Understanding the pattern

A pattern is a sequence of numbers, shapes or colours that follows a particular rule. Every pattern is made up of elements or units that are repeated according to a set rule.

Types of patterns

Third grade students mainly learn two types of patterns: number patterns and shape patterns.

Number patterns

Number patterns are sequences of numbers that follow a specific rule.

  • Example 1: 2, 4, 6, 8, 10, ... Here the rule is to add 2 to each number to get the next number.
  • Example 2: 5, 10, 15, 20, ... In this pattern, the rule is to add 5 to each number to get the next number.

Shape pattern

Shape patterns are sequences of shapes that follow a specific transformation or arrangement rule.

  • Example: ▲ ◼️ ▲ ◼️ ▲ ◼️ ... This pattern alternates between triangles and squares.

Creating patterns using rules

When we create patterns using rules, we set up a system or method to repeat elements in a specific way. Let's see how we can create patterns using some simple rules:

Examples of number patterns

Example 1: Adding a constant number (Arithmetic sequence)

Start at 3, add 3

This means you start with the number 3 and keep adding 3 to get the next numbers in the pattern.

  • 3 (start)
  • 3 + 3 = 6
  • 6 + 3 = 9
  • 9 + 3 = 12
  • ...and so on.

Pattern: 3, 6, 9, 12, 15, ...

Example 2: Subtracting a constant number

Start at 20, subtract 4

This time, you'll start with 20 and subtract 4 from each number to arrive at the next number.

  • 20 (start)
  • 20 - 4 = 16
  • 16 - 4 = 12
  • 12 - 4 = 8
  • ...and so on.

Pattern: 20, 16, 12, 8, 4, 0, -4, ...

Example 3: Doubling the numbers

Start at 1, double the number

In this pattern, starting from 1, each number is doubled to get the next number.

  • 1 (start)
  • 1 × 2 = 2
  • 2 × 2 = 4
  • 4 × 2 = 8
  • ...and so on.

Pattern: 1, 2, 4, 8, 16, ...

Visual patterns using shapes

Example 1: Repeating shapes

Visual patterns often involve repeating a specific arrangement of shapes.

Consider the pattern:

...

Rule: Repeat a circle followed by a star symbol. This creates a simple alternating pattern.

Example 2: Increasing number of shapes

Visual patterns may also include increasing or decreasing the number of shapes in a specific way.

Pattern example:

...

Rule: Start with one circle and add another circle each time.

The importance of rules in patterns

Rules are very important because they define how the pattern will continue. Without clear rules, the pattern cannot be followed or extended correctly.

Making predictions with patterns

Understanding the rule allows us to predict future elements in the pattern. For example, knowing the "add 2" rule allows us to extend the pattern 2, 4, 6 to the next element, which is 8.

Creating your own patterns

Creating patterns helps children understand logical thinking and the importance of structure. Let's try creating some new patterns!

Example 1: Multiplication of numbers

Start at 2, multiply by 2 each time

Multiplying by 2, we get this sequence:

  • 2
  • 2 × 2 = 4
  • 4 × 2 = 8
  • 8 × 2 = 16
  • ...and so on.

Pattern: 2, 4, 8, 16, 32, ...

Example 2: Combining number patterns

You can create complex patterns by combining different rules.

Start at 5, alternate between adding 5 and subtracting 2
  • 5 (start)
  • 5 + 5 = 10
  • 10 - 2 = 8
  • 8 + 5 = 13
  • ...and so on.

Pattern: 5, 10, 8, 13, 11, 16, ...

Exercises and drills

Practice is important to master creating patterns using the rules. Below are some exercises to try:

Exercise 1: Identifying the rule

Look at the pattern and try to identify the rule.

Pattern: 3, 6, 12, 24, ...

What is the rule? (Hint: every number ...)

  • If you discover that each number is double the previous one, you are right!

Exercise 2: Expanding the pattern

Complete the following patterns by finding the rule and predicting the next numbers:

Pattern: 10, 20, 30, ___, ___

Consider this: what are we adding each time?

Exercise 3: Creating your own pattern

Create a pattern using the rule of "subtract 1, then add 2." Write down the first five digits in your pattern.

Conclusion

Understanding how to form patterns using rules is a foundational skill in math that helps young learners prepare for more advanced concepts. By working through number and shape patterns, children learn to recognize sequences and predict future events. This not only enhances their math skills but also develops critical thinking and problem-solving abilities.

Encouraging children to experiment with creating their own patterns helps them build confidence and develop a deeper understanding of the beauty and structure inherent in mathematics.


Grade 3 → 6.1.3


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Identifying and Extending Shape Patterns
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Creating Patterns Using Rules

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