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 → Data Management and Probability → Probability ↓


Simple Probability Experiments


Probability is a part of mathematics that helps us figure out the likelihood of something happening. When we talk about a "probability experiment," it means we're looking at something we can measure or test to find out how likely it is to happen. In simple probability experiments, we often focus on things like tossing a coin, throwing dice, or choosing a card from a deck.

What is probability?

Probability is a way of expressing how likely or unlikely something is to happen. This probability is usually expressed as a number between 0 and 1. If the probability is 0, the event will not happen. If the probability is 1, the event is certain to happen. Most probability values lie somewhere in between.

Here is the formula for probability:

Probability = (number of favourable outcomes) / (total number of possible outcomes)

Let us examine this with some examples.

Example 1: Tossing a coin

When you flip a coin, there are two possible outcomes: it can land on heads or it can land on tails. Each outcome is equally likely. Therefore, the probability of flipping heads is:

Probability of getting heads = 1 (favorable outcomes) / 2 (probable outcomes) = 0.5

Similarly, the probability of getting tails is:

Probability of tails = 1/2 = 0.5

This is a simple probability experiment because there is only one step – the coin toss – and each outcome is equally likely.

Visual example: coin toss

H Tea

In this illustration, we see that a coin can either fall on 'H' which is heads, or on 'T' which is tails, which shows the two possible outcomes.

Example 2: Throwing a dice

Consider a standard six-sided die. When you roll the die, there are six possible outcomes. You can roll a 1, 2, 3, 4, 5, or 6. If you want to know the probability of rolling a 3, you can use the probability formula.

Probability of 3 coming up = 1 (favourable outcome) / 6 (possible outcomes) = 1/6 ≈ 0.1667

If you want to calculate the probability of getting an even number (2, 4, or 6), you count the number of favorable outcomes (which is 3) and divide by the total number of outcomes (which is 6):

Probability of getting an even number = 3/6 = 1/2 = 0.5

Visual example: dice roll

1 2 3 4 5 6

In this illustration, each number on the die represents one of the six possible outcomes when the die is thrown.

Example 3: Choosing a card

Consider a deck of 52 cards. There are 4 suits: hearts, diamonds, clubs and spades, and each suit has 13 cards. If you draw a card from the deck, you can think about the probability of drawing an ace.

Probability of getting an ace = 4 (favourable outcomes) / 52 (possible outcomes) = 1/13 ≈ 0.0769

Let's say you want to draw a card that is shaped like a heart:

Probability of drawing a heart = 13 (favourable outcomes for hearts) / 52 (possible outcomes) = 1/4 = 0.25

Visual example: card draw

A♠ A♥ A♦ A♣ 10♥

Here, the illustration shows the aces of each suit and a random heart card, illustrating the variety of possible outcomes when cards are drawn from a full deck.

Understanding outcomes in probability

Outcomes are all the possible things that can happen in a probability experiment. When we say "favorable outcome," it means the result we are looking for. For example, if the outcome we want is to roll a 4 on a die, then rolling a 4 is the favorable outcome.

Simple events

A simple event is an event that has only one outcome. For example, rolling a 3 on a six-sided die or getting heads when tossing a coin are simple events. In each scenario, only one specific thing happens.

Complex events

Unlike simple events, complex events have two or more outcomes. An example of this would be rolling an even number (2, 4, or 6) on a die or picking a face card (king, queen, or jack) from a deck of cards.

Example 4: Choosing marbles

Imagine you have a bag containing 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble?

Total marbles = 5 (red) + 3 (blue) + 2 (green) = 10
Probability of choosing a blue marble = 3 (favourable outcomes) / 10 (total marbles) = 0.3

If you want to know the probability of choosing a red or green marble:

Probability of choosing red or green marble = (5+2) / 10 = 7/10 = 0.7

Conclusion

Probability helps us understand how likely something is to happen. To find the probability, we look at the number of favorable outcomes and divide it by the total number of possible outcomes. Simple probability experiments like tossing a coin, throwing dice, and picking cards are great ways to learn the basics of probability. You can use probability to predict outcomes, make plans, or make informed decisions.

By understanding these basic concepts, you'll be able to understand how probability plays a role in the world around you, from sports to everyday decisions.


Grade 3 → 5.3.3


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Simple Probability Experiments

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