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 ↓


Identifying and Extending Numeric Patterns


In this simple guide, we will explore the fascinating world of numerical patterns in math. A numerical pattern is a sequence of numbers that follows a certain rule. By the end of this guide, you will be able to identify a pattern in a series of numbers and predict what comes next. We have simplified complex concepts to make them easier for third grade students to understand, providing both text and visual examples.

Understanding numerical patterns

Numerical patterns are essentially numbers that form a sequence with a particular regularity or rule. The rule can be simple, like adding or subtracting the same numbers over and over again, or a more complex operation.

Let's start by looking at a very simple numerical pattern:

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

Can you see what comes next in this series of numbers? This pattern follows a simple addition rule: each number increases by 2.

Example 1: Simple addition

Here's an example of how this simple addition pattern works:

2 4

In this pattern:

  • Start with 2
  • Add 2 to get 4
  • Add 2 again to get 6
  • Continue this pattern...

Expansion of the pattern

Once you identify the rule, you can extrapolate the pattern. Extrapolating the pattern means predicting which numbers will come next in the sequence.

Example 2: Counting with subtraction

Consider this pattern:

10, 9, 8, 7...

In this sequence, we start with 10 and subtract 1 each time:

10 9

This pattern continues by subtracting 1 from the previous number.

Example 3: Multiplication pattern

Sometimes the pattern involves actions like multiplication. Let's look at an example:

1, 3, 9, 27...

In this series:

  • Start from 1
  • Multiply by 3 to get 3
  • Multiply by 3 again to get 9
  • And so on...
1 3 9

Example 4: Partition pattern

Now, let's look at the partitioning pattern:

81, 27, 9, 3...

In this pattern:

  • Start at 81
  • Dividing by 3 gives 27
  • Dividing by 3 gives 9
  • Carry on like this...
81 27

Tips for finding patterns

To identify patterns, it is helpful to follow these tips:

  • Look at the difference or ratio between consecutive numbers.
  • Identify whether the pattern involves addition, subtraction, multiplication, or division.
  • Check if the numbers are increasing or decreasing in a specific way.
  • Write down any rules you discover.

Practice exercise

Try to recognize the pattern rule and predict the next number:

5, 10, 15, 20...

What is the rule? What happens next?

The rule here is to add 5 to the previous number. So, the next number will be:

25

Conclusion

Numerical patterns are an important part of understanding math. By practicing identifying, expanding, and predicting these patterns, you become better at problem-solving and logical thinking. We've covered a variety of simple numerical patterns associated with basic arithmetic operations. With practice, these concepts will become more natural, making it easier to tackle more complex patterns in the future.

Keep practicing the art of pattern recognition, and soon you'll be able to recognize patterns everywhere!


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Identifying and Extending Numeric Patterns

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