Probability Detectives: Predict, Test, and Explain!

Materials Needed

• 2 coins
• 1 standard six-sided die
• 10–20 small objects for a bag, such as buttons, blocks, or counters in different colors
• A small opaque bag or container
• Paper and pencils
• Colored pencils or markers
• Optional: a calculator, tablet, or spreadsheet for recording results

Learning Objectives

By the end of the lesson, Daniella and Alisia will be able to:

• Explain that probability describes how likely something is to happen.
• Use the words certain, likely, unlikely, and impossible correctly.
• Find simple probabilities by counting favorable outcomes and total possible outcomes.
• Compare a prediction with the results of an experiment.
• Explain why results from a small experiment may not exactly match a prediction.

Success Criteria

Daniella and Alisia are successful when they can:

• Place events on a probability scale from 0 to 1 or from impossible to certain.
• Write simple probabilities as fractions, such as 2 out of 6 or 2/6.
• Make a prediction before testing it.
• Record results clearly in a table.
• Use evidence from an experiment to explain what happened.

Introduction: The Mystery Prediction Challenge

Time: 10 minutes

Tell Daniella and Alisia:

Imagine you are planning a game booth at a school fair. You want to know which prizes people are most likely to win. How could probability help you?

Show or describe these events. Ask the children to decide whether each event is impossible, unlikely, equally likely, likely, or certain:

1. The sun will rise tomorrow.
2. A die will land on 6 when rolled.
3. A regular coin will land on heads.
4. A six-sided die will land on 8.
5. You will pick a red counter from a bag containing only red counters.

Have Daniella and Alisia explain their ideas. Encourage them to use the sentence frame:

“I think this is __________ because __________.”

Share the Lesson Goals

Explain:

Today we will become probability detectives. We will make predictions, test them with experiments, record what happens, and explain whether our results match our predictions.

Key Vocabulary and Probability Scale

Probability means how likely something is to happen.

• Impossible: It cannot happen. Probability is 0.
• Unlikely: It could happen, but it probably will not.
• Equally likely: There is an even chance of happening or not happening.
• Likely: It will probably happen.
• Certain: It must happen. Probability is 1.

Draw this scale on paper:

0 — Impossible —— Unlikely —— Equally Likely —— Likely —— Certain — 1

Ask Daniella and Alisia to place the five mystery events on the scale. They may write the event names, draw symbols, or use sticky notes.

Body: I Do, We Do, You Do

Part 1: I Do — Modeling a Die Probability

Time: 10 minutes

Use a standard six-sided die. Model the following question:

What is the probability of rolling a 4?

1. Count all possible outcomes: 1, 2, 3, 4, 5, and 6. There are 6 possible outcomes.
2. Count the favorable outcomes. Only one side shows 4, so there is 1 favorable outcome.
3. Write the probability: 1 out of 6, or 1/6.

Explain that:

Probability = number of favorable outcomes ÷ total number of possible outcomes

Model one more example:

What is the probability of rolling an even number?

• Even numbers are 2, 4, and 6.
• There are 3 favorable outcomes out of 6 possible outcomes.
• The probability is 3/6, which is also 1/2.

Quick Check

Ask:

• What is the probability of rolling a number less than 3? 2/6
• What is the probability of rolling a 7? 0, because it is impossible.
• What is the probability of rolling a number from 1 to 6? 6/6 or 1, because it is certain.

Part 2: We Do — Coin Flip Investigation

Time: 15 minutes

Work together to investigate coin flips.

Step 1: Make a Prediction

Ask Daniella and Alisia:

If we flip a fair coin 20 times, how many times do you predict it will land on heads?

Each child writes a prediction and explains it. A reasonable prediction is about 10 heads because heads and tails are equally likely.

Step 2: Run the Experiment

1. Decide who will flip the coin and who will record the result. Switch jobs halfway through.
2. Flip the coin 20 times.
3. Record each result using H for heads and T for tails.
4. Count the total number of heads and tails.

Result	Number of Times
Heads
Tails
Total flips	20

Step 3: Discuss the Results

Ask:

• Did you get exactly 10 heads?
• Was the number of heads close to your prediction?
• Why might the result not be exactly 10 heads and 10 tails?
• What do you think might happen if we flipped the coin 100 times?

Explain that probability gives a prediction, but random experiments do not always produce exact results. Over many trials, results often get closer to the predicted probability.

Part 3: We Do — The Mystery Bag

Time: 15 minutes

Place colored objects in a bag. For example:

• 5 blue counters
• 3 red counters
• 2 yellow counters

Do not let Daniella and Alisia look inside the bag.

Predict the Probability

Ask them to calculate:

• Probability of picking a blue counter: 5/10
• Probability of picking a red counter: 3/10
• Probability of picking a yellow counter: 2/10
• Probability of picking a green counter: 0/10, because there are no green counters

Test the Prediction

1. Mix the objects in the bag.
2. Without looking, pick one object.
3. Record its color.
4. Return it to the bag before the next turn. This keeps the probabilities the same each time.
5. Repeat 20 times.

Color	Predicted Probability	Actual Number Picked
Blue	5/10
Red	3/10
Yellow	2/10

Discuss whether the actual results were close to the predictions. Ask the children to use evidence from their table.

Part 4: You Do — Create a Fair Game

Time: 15–20 minutes

Daniella and Alisia will design a simple game of chance. They may choose one of these options:

• A dice game
• A coin-flipping game
• A spinner game drawn on paper
• A mystery-bag game

Game Design Rules

1. Give the game a fun name.
2. Write clear instructions.
3. State what a player must do to win.
4. Calculate the probability of winning.
5. Decide whether the game is fair. A fair game gives players equal chances of winning.
6. Test the game at least 10 times.
7. Record the results in a table.

Example:

In “Lucky Six,” a player rolls a die. The player wins if the die shows 5 or 6. There are 2 winning outcomes out of 6, so the probability of winning is 2/6, or 1/3.

Choice and Creativity

They may:

• Draw a game board.
• Use toys or counters as game pieces.
• Create a pretend carnival game.
• Explain their game aloud instead of writing every detail.
• Use a digital spinner or spreadsheet if available.

Assessment

Formative Assessment During the Lesson

• Listen for correct use of probability vocabulary.
• Ask Daniella and Alisia to explain how they counted favorable outcomes.
• Check their coin-flip and mystery-bag tables.
• Ask them to predict which color or number is most likely and explain why.
• Have them show answers with fingers, drawings, fractions, or words.

Summative Assessment: Probability Detective Exit Challenge

Give Daniella and Alisia this challenge:

A bag contains 4 green counters, 2 purple counters, and 4 orange counters.

1. How many counters are in the bag altogether?
2. What is the probability of picking a purple counter?
3. What is the probability of picking a green or orange counter?
4. Which color is most likely to be picked?
5. Is picking a red counter impossible, unlikely, likely, or certain? Explain.

Expected answers:

• 10 counters
• 2/10, or 1/5
• 8/10, or 4/5
• Green and orange are equally likely.
• Picking red is impossible because there are no red counters.

Simple Success Rubric

Skill	Developing	Secure	Excellent
Vocabulary	Uses some words correctly.	Uses probability words correctly.	Explains the words with examples.
Calculating Probability	Needs help counting outcomes.	Finds simple probabilities correctly.	Explains and simplifies probabilities.
Recording Results	Records some results.	Creates a clear table.	Compares results and predictions thoughtfully.
Game Design	Creates a game with support.	Creates and tests a playable game.	Explains whether the game is fair using probability.

Differentiation and Support

For Learners Who Need More Support

• Use real objects and pictures before introducing fractions.
• Begin with the words impossible, possible, and certain.
• Provide sentence frames such as “There are ___ favorable outcomes out of ___ total outcomes.”
• Use smaller numbers, such as a bag with 5 objects.
• Allow answers to be spoken, drawn, or shown with objects.

For Learners Ready for More Challenge

• Ask them to simplify fractions, such as 3/6 to 1/2.
• Compare two games and decide which gives a player a better chance of winning.
• Calculate experimental probability from the results.
• Change the number of objects in the mystery bag to make a color more or less likely.
• Design a game in which one player has a 1/4 chance of winning.

Conclusion: Tell What We Learned

Time: 5–10 minutes

Ask Daniella and Alisia to complete these statements:

• Probability tells us __________________________.
• An impossible event has a probability of __________________.
• A certain event has a probability of __________________.
• To find a simple probability, I count __________________ and __________________.
• Our experiment results were similar to or different from our prediction because __________________.

Review the main ideas:

• Probability describes how likely an event is.
• Some events are impossible, while others are certain.
• Simple probability compares favorable outcomes with all possible outcomes.
• Experiments help us compare predictions with real results.
• Random results may change each time, especially in small experiments.

Finish with a final question:

If you could use probability to help make one real-life decision, what would it be?