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


Patterns are all around us. They are an essential part of understanding math and help us understand the world. In grade 3 math, we begin to explore patterns as part of algebra and mathematics. This exploration helps us develop critical thinking and problem-solving skills.

Introduction to patterns

Patterns are repeated arrangements of numbers, shapes, or objects. When you see a pattern, you can often predict what will happen next. Recognizing patterns helps children strengthen their understanding of numbers and their relationships.

Number patterns

Number patterns are sequences of numbers that follow a particular rule. One of the simplest types of number patterns is when the numbers increase or decrease by the same amount each time. Let's look at an example:

1, 3, 5, 7, 9, 11, ...

In this pattern, each number is 2 more than the number before it. We say that the rule of this pattern is "add 2" to get the next number.

Let's look at another example:

10, 8, 6, 4, 2, 0, ...

This time, each number is 2 less than the number before it. Here, the rule is "subtract 2."

Identifying and creating number patterns

To identify a number pattern, look at the differences between the numbers. Ask yourself: What do I have to do to get from one number to the next? Is there a quantity that is constantly being added or subtracted? Let's consider another example:

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

To recognize the pattern, note that each number is 2 more than the previous number.

Now, let's try to create our own pattern. We'll start with the number 3 and create a pattern by adding 5 each time:

3, 8, 13, 18, 23, ...

Odd and even number patterns

Numbers can be classified as odd or even. Even numbers can be divided evenly by 2. Examples of even numbers are 2, 4, 6, 8, etc. On the other hand, odd numbers cannot be divided evenly by 2. Examples of odd numbers are 1, 3, 5, 7, etc.

Let's look at examples of odd and even patterns:

Odd Pattern: 1, 3, 5, 7, 9, ... Even Pattern: 2, 4, 6, 8, 10, ...

Visual patterns using shapes

Patterns don't just exist in numbers; they can also be found in shapes. A shape pattern is a sequence of shapes that repeat according to a rule. Let's explore this idea:

This pattern has a blue square followed by a red circle. This pattern continues with the same sequence of blue squares and red circles.

Mounting pattern

Some patterns can be increasing or decreasing. Increasing patterns are sequences in which each part gets larger or smaller according to a specific rule. For example, consider the following pattern:

In this visual pattern, each step becomes a larger square. The rule is that each square grows by 10 units in width and height.

Creating your own mounting patterns

Creating increasing patterns is as simple as choosing a rule and applying it. Let's create a number pattern that increases by adding the numbers of the digits of the previous term:

1, 2, 4, 8, 16, 23, 28, 38, ...

The rule here is that the digits of the previous term are added to the same term to get the next number.

Discovering patterns with tables and charts

Using tables and charts can help visualize and organize patterns, making them easier to understand. A table can show how a pattern works for a set of numbers or objects:

Duration Number
1 4
2 7
3 10
4 13

In this table, for each term there is a corresponding number, where we add 3 to the previous number.

Patterns in everyday life

Patterns are not just confined to math classes; they exist all around us in nature, music, art, and architecture. Recognizing patterns helps us understand complex structures and systems, both natural and man-made.

Consider the patterns in the petals of a flower or the shell of a snail. These natural patterns can be observed and studied in the same way as mathematical patterns.

Conclusion

Understanding patterns is an important part of learning math. Being able to recognize, predict, and create patterns lays the foundation for algebraic thinking. As students explore patterns in numbers, shapes, and everyday situations, they develop important skills that will help them solve problems and understand the world around them.

Encourage young learners to notice patterns and play with them. Through creativity and exploration, they will deepen their appreciation for the beauty and usefulness of patterns everywhere.


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Patterns

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