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 ↓


Solving Simple Addition and Subtraction Equations


In this lesson, we will learn how to solve simple addition and subtraction equations. This is an essential skill for understanding how algebra works. We will explore different ways to solve these equations and notice some interesting patterns along the way. Let's get started!

Understanding the equations

An equation is like a balance. It shows that two things are equal. Equations often have an unknown value that we want to find. This unknown value is often represented by a letter, such as x or y. Solving an equation means figuring out which value makes the equation true.

Example of a simple equation

Consider the equation:

x + 3 = 7
x + 3 = 7

This equation is like a puzzle. x is the missing number that makes x + 3 equal to 7 When solving equations, we try to find out what the unknown number is.

Solving sum equations

Let's start by solving simple addition equations. The goal is to find the unknown number that completes the equation.

Step-by-step example

Let us solve the following equation:

x + 4 = 10
x + 4 = 10

To solve this equation, we need to find out what number x must be so that when we add 4, we get 10 Here is how we can solve it step by step:

  1. Look at the equation: x + 4 = 10.
  2. Think about what number added to 4 makes 10.
  3. Subtract 4 from 10: 10 - 4.
  4. The result is 6.
  5. So x = 6 because 6 + 4 = 10.

Therefore, the solution of x + 4 = 10 is x = 6.

Envisioning a solution

X , 4 , 10

In the visualization, we have isolated the components of the equation. The sum of x and 4 must equal 10.

Solving subtraction equations

Next, let's learn how to solve a subtraction equation by finding the value of the unknown number.

Step-by-step example

Consider the following equation:

y - 5 = 3
y - 5 = 3

To solve this equation, we want to know what the number y is, so that when we subtract 5, we get 3 Let's solve it step by step:

  1. Look at the equation: y - 5 = 3.
  2. Think about what number you need to subtract 5 from to get 3.
  3. Add 3 to 5: 3 + 5.
  4. The result is 8.
  5. So y is 8 because 8 - 5 = 3.

Therefore, the solution of y - 5 = 3 is y = 8.

Envisioning a solution

Y , 5 , 3

The figure shows that subtracting y from 5 gives a remainder of 3.

Using patterns to solve equations

Sometimes, it is helpful to look for patterns when solving equations. Recognizing patterns can make it easier to find a solution quickly.

Pattern example

Consider the two equations:

a + 6 = 11 b - 4 = 2
a + 6 = 11 b - 4 = 2

Let's look at the pattern:

  1. For a + 6 = 11, we find a by subtracting 6 from 11: 11 - 6 = 5 So, a = 5.
  2. For b - 4 = 2, we add 4 to 2 to find b: 2 + 4 = 6 So, b = 6.

We see a pattern: in addition equations, we subtract; in subtraction equations, we add.

Practice problems

Let's practice solving some equations ourselves. Try solving the following:

  1. x + 5 = 12
  2. y - 8 = 7
  3. z + 9 = 15
  4. a - 3 = 4

Solve each problem step by step:

  1. For x + 5 = 12, subtract 5 from 12: 12 - 5 = 7 So, x = 7.
  2. For y - 8 = 7, add 8 to 7: 7 + 8 = 15 So, y = 15.
  3. For z + 9 = 15, subtract 9 from 15: 15 - 9 = 6 So, z = 6.
  4. For a - 3 = 4, add 3 to 4: 4 + 3 = 7 So, a = 7.

By practicing, we get better at recognizing which operations to use to solve these equations.

Conclusion

Today, we discovered how to solve simple addition and subtraction equations. We learned to look at equations as simple puzzles where we find the unknown value that makes the equation true. Remember, addition equations are solved by subtracting, while subtraction equations are solved by adding. With practice, solving these equations becomes a simple and enjoyable task.

Keep practicing, and soon solving equations will become second nature to you!


Grade 3 → 6.2.2


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Understanding Variables as Unknowns
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Using Patterns to Solve Problems

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Solving Simple Addition and Subtraction Equations

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