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 ↓


Introduction to Algebra


Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities. This helps us solve problems and understand patterns in numbers. In Grade 3, we begin to explore the basic ideas of algebra, such as using symbols for numbers, finding patterns, and understanding relationships between numbers.

What are the patterns?

Patterns exist all around us, whether we notice them or not. A pattern is something that repeats in a predictable way. It can be a sequence of shapes, colors, numbers, or any other type of object.

Visual example of the pattern

◯ △ ★ ◯ △ ★ ◯ △ ★
◯ △ ★ ◯ △ ★ ◯ △ ★

In this pattern, a sequence of shapes—a circle, triangle, and star—is repeated. Once you know the beginning of the sequence, you can predict what comes next.

Number patterns

Let's look at some number patterns. A number pattern is a sequence of numbers that follows a certain rule.

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

This pattern is formed by adding 2 each time. We start with 1 and keep adding 2 to get the next number.

Algebraic thinking: Using symbols

In algebra, we often use symbols (such as letters) for numbers. This can make it easier to write and solve problems. For example, the letter x can be used for a number we don't know yet.

Use of symbols in equations

Let's look at an example. Suppose we have this equation:

x + 3 = 7
x + 3 = 7

Here, x represents a number we don't know. Our job is to figure out what x is. To do this, we can think of what number adds up to 3 to give 7. The answer is 4, because:

4 + 3 = 7
4 + 3 = 7

So, x = 4.

Solving problems algebraically

Algebra helps us solve problems by modeling the problem using equations. Let's take a look at a simple problem.

Example problem

We have 5 apples, and we want to divide them equally among our friends. If each friend gets x apples and we have 5 friends, we can use this equation:

5x = 5
5x = 5

This means that we divide the apples equally among 5 friends.

Solving equations

To find out how many apples each friend will get, solve the equation:

x = 5 / 5 x = 1
x = 5 / 5 x = 1

Each friend will get 1 apple.

More practice with patterns and algebra

Continue the pattern

An important skill is to identify and continue number patterns. Let's practice with some examples.

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

The rule is to add 2 each time, so that the next number is 10.

10, 7, 4, 1, ...
10, 7, 4, 1, ...

The rule here is to subtract 3 each time, so that the next number is -2.

Writing equations from problems

Let's practice writing equations to represent simple problems. If there are n cookies and we pack them in boxes of 10, we get the equation:

n = 10b
n = 10b

where b is the number of boxes.

Example: If we have 50 cookies and each box contains 10, then:

n = 10 * 5 n = 50
n = 10 * 5 n = 50

We know that we will need 5 boxes to pack all 50 cookies.

Understanding variables

A variable is a symbol, usually a letter, used to represent a number. In math, variables are used to represent unknown values in equations and expressions. In our apples example, the variable x was used to represent the unknown number of apples each friend would receive.

Using variables

Let's look at another example of using variables in algebra. Think about how you could use variables to solve this problem:

Problem: You have some pencils and want to give them equally to 4 friends. If you have 12 pencils, how many will each friend get?

Solution: You can write the problem as an equation:

p = 12 / 4
p = 12 / 4

Where p represents the number of pencils each friend gets. Solving the equation gives:

p = 3
p = 3

So each friend will get 3 pencils.

Simple word problems using algebra

Word problems are a great way to apply your algebra skills to real-world situations. By substituting the information given in the problem into an equation, you can often find the solution to the problem.

Example word problem

Problem: You have 24 candies and you want to divide them equally among 3 friends. How many candies will each friend get?

The equation for this problem is:

c = 24 / 3
c = 24 / 3

where c is the number of candies for each friend. Solving this gives:

c = 8
c = 8

Each friend will get 8 candies.

Invisible numbers and algebra

In algebra, sometimes we work with numbers that are not immediately obvious. These are called "invisible numbers" and they help us form equations. For example, think of the equation:

y + 5 = 10
y + 5 = 10

We need to subtract 5 from 10 to find the invisible number y :

y = 10 - 5 y = 5
y = 10 - 5 y = 5

The invisible number is 5.

Creating your own patterns

Once you become proficient at identifying patterns, it's fun to create your own patterns! Here are some steps to help you create patterns:

  1. Choose a starting number.
  2. Set a rule (such as addition or subtraction).
  3. Apply the rules to create your pattern.

Let's try to make a pattern starting with 3 and adding 4:

3, 7, 11, 15, 19, ...
3, 7, 11, 15, 19, ...

Making patterns from letters

We can also create patterns using symbols or letters. For example:

A, B, C, A, B, C, A, ...
A, B, C, A, B, C, A, ...

This pattern is repeated after every three letters. Such patterns can help in learning and remembering the sequence.

Ways to get better at algebra

Practicing regularly improves your algebra skills. Here are some ways to get better:

  • Practice problems regularly.
  • Explore different patterns and sequences.
  • Use visual aids to understand concepts.
  • Discuss problems with friends to get different perspectives.

Algebra can be challenging at first, but with practice it becomes easier to understand and use.

Practice problems

Here are some practice problems to test your skills:

  1. Continue the pattern: 5, 10, 15, 20, 25, ...
  2. Solve for n: 3n = 12
  3. If you have 16 marbles and you want to divide them equally among 4 friends, how many marbles will each friend get?
  4. Create a pattern starting with 8 and subtracting 2 each time.

Check your answers and review any mistakes to improve your understanding!

Conclusion

Algebra is a powerful tool that helps us understand numbers and solve real-world problems. By learning to recognize patterns, use symbols, and create equations, you can gain a deeper understanding of math. As you practice, you'll find that algebra becomes an indispensable part of your problem-solving toolkit. Keep exploring, practicing, and having fun with algebra!


Grade 3 → 6.2


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Creating Patterns Using Rules
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Introduction to Algebra

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