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 and Algebra is an important foundational topic in Grade 3 Maths that introduces young learners to the idea of sequences, the concept of variables, and simple equations. It promotes logical thinking and problem-solving through identifying and expanding patterns in both numbers and shapes. By understanding these concepts, students can better understand more complex mathematical ideas in the future.

Patterns

Patterns are arrangements of objects, numbers or shapes that follow a particular sequence or rule. Recognizing patterns helps us predict what comes next in a sequence, understand concepts logically and find order in mathematics and the world around us.

Number patterns

Number patterns are sequences of numbers that follow a specific rule. For example, you might have a sequence where each number increases by 2. The sequence starts at 2 and goes on:

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

To identify the rule of a number pattern, look at how the numbers change from one to the next. In the example above, the rule is "add 2" because each number is obtained by adding 2 to the previous number.

Let's look at another pattern:

5, 10, 15, 20, 25, ...

In this sequence, the rule is "add 5." Recognizing these simple arithmetic progressions helps build understanding and confidence in handling numerical sequences.

Visual example of number patterns

In this visual pattern, the order of colors follows a pattern. It can also be related to numbers, where each "block" is considered a step in the sequence.

Shape pattern

Motif patterns consist of a series of shapes that are repeated according to a certain rule. For example, a pattern may consist of alternating shapes such as:

Circle, Triangle, Circle, Triangle, Circle, Triangle, ...

Such identification helps students understand geometric representations and symmetry, as well as enhances their observation skills.

Visual example of a motif pattern

Algebra

Algebra at the grade 3 level introduces students to the basic idea of using symbols or letters to represent unknown numbers. This is a simple introduction to using algebraic thinking to solve problems and understand relationships between numbers.

Understanding variables

In algebra, a variable is a symbol or letter that stands in place of a number. For example:

x + 5 = 10

Here, "x" is the variable. Students learn that they can find out what "x" is by solving the equation.

Solving simple equations

Solving equations involves finding the value of the variable that makes the equation true. Using the equation above:

x + 5 = 10

We can subtract 5 from both sides to solve for x:

x + 5 - 5 = 10 - 5
x = 5

This shows that when x equals 5, the equation is balanced.

Visual example of solving equations

X , 5 , 10

In this visual example, shapes and numbers demonstrate solving an equation by visualizing each component. The strategy of balancing both sides through actions such as subtraction or addition helps students understand the concept.

Introduction to simple word problems

Word problems help students understand how algebra can be applied in real life. By translating words into mathematical expressions, they develop critical thinking skills.

Example:

Sam has 3 apples. Then he buys more apples until he has 7 apples. How many apples did he buy?

We can let x represent the number of apples bought by Sam. Then the equation is:

3 + x = 7

To solve for x, subtract 3 from both sides:

x = 7 - 3
x = 4

So, Sam bought 4 apples.

Creating and expanding patterns

An important aspect of studying patterns is learning how to create and extend patterns. Students can express their creativity and use logic to create new sequences or extend existing sequences by figuring out the rule.

Examples of creating patterns

  • Create a number pattern in which 4 is added to each number, starting from 1. The pattern is: 1, 5, 9, 13, 17, ...
  • Create a shape pattern using squares and circles that alternates with each successive shape: square, circle, square, circle...

Examples of extended patterns

Given the pattern 10, 20, 30, 40, ..., students can recognize the rule as "add 10" and expand it as follows:

50, 60, 70, ...

Factors that amplify the pattern

Many sequences in real life repeat according to strict rules or change slightly as they evolve. Understanding these factors varies depending on the type of pattern (e.g., arithmetic or geometric progression).

Interactive exercises to reinforce learning

Exercise 1: Find the rule

Look at the sequence and find the pattern rule: 3, 6, 9, 12, ...

Exercise 2: Complete the pattern

Fill in the blanks: 15, ___, 25, ___, 35

Exercise 3: Solve equations

What is x in this equation? x - 4 = 10

Exercise 4: Create your own pattern

Think of a number pattern rule and create your own sequence. Write down the first five numbers of your pattern.

Conclusion

Understanding patterns and algebra at the Grade 3 level lays a strong foundation for higher-level mathematics in the future. It encourages children's problem-solving skills, logical thinking, and the ability to connect mathematical concepts to real-world situations. By working on identifying, creating, and extending patterns and solving equations, students gain confidence and competence in basic algebra, which benefits their academic journey.


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Patterns and Algebra

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