# Probability Lesson Plan for the sum of two six-sided dice in table format

## Overview

Investigate the odds of rolling a certain sum with two six - sided dice.

## Intended learnings & learners thinkings

Title of Activity: Probability for the sum of two six-sided die Grade Level 5 + Name
Activity objective or outcome
Learners predict what will happen if they roll one die 36 times, roll one die 36 times, record data, organize data onto a graph, analyze the data, and explain the pattern they found and predict what would happen with different sided die.
Materials: Die, pencil, paper
Concepts Supporting Information Misconceptions Assessment
Probability
• A fair die has equal probability for each side. Or The probability of an outcome is the number of specific outcomes out of the total number of all possible outcomes of one event.
• The probability of a certain sum of two die is equal to the total number sum combinations for each possible sum out of the total number of all possible sums.
• The probability of a specific outcome is equal to the total number of ways to achieve the same outcome out of all the total number of different outcomes possible.
• The probability of an outcome is the number of specific outcomes out of the total number of all possible outcomes of one event.

• A die has six sides.
• The numbers on a die are 1 - 6.
• Each number appears only once.
• Each side has an equal chance of being rolled. (The die is fair.)
• The sums of the dice is: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
• There is one way for the dice to have a sum of 2, two for 3...six for 7 five for 8... For a total of 36.
• I can cause a certain number to be rolled (blowing, throw hard, throw a certain way...).
• It is magic.
• Diagnostic: What number(s) do you think will be the most likely to be rolled? The least likely?
• Summative: What is the probability for all possible rolls? How do you know?
• Generative: Have students predict the probability for certain sums if dice with a different amount of sides than six were rolled and summed. Spinners with unequal partitions and or different colors of sections and the probability of getting pairs of colors.
• Theoretical probability is determined with reasoning - by generating all the possible outcomes or combinations of outcomes in an event.
• Experimental probability is determined by repeating a certain event a number of times and collecting numerous results to determine the probability.
• Theoretical probability doesn't usually match the experimental probability.
• Theory is an idea used to explain or predict an event.
• Experiment is a test made to try to understand something.
The only way to figure probability is to crunch numbers. Explain how to find the experimental probability and theoretical probability of each of the following.

## Strategies to achieve educational learnings

Based on learning cycle theory & method
Exploration Procedure
2. What would be the distribution of the sums of two six sided dice rolled 36 times.
3. Record all predictions on the board.
5. What confidence they have in their answer and explain what gives them that confidence.
6. Rroll two dice 36 times, record the numbers and the sums for each roll.
Invention Procedure
2. How should the data be displayed?
3. Could chart the number of rolls for each sum 2 - 12 (2 - 12 horizontal axis, # rolls vertical axis). OR could write each addend above the sum. See graph data sheet
4. Display the data for all to see.
5. Ask questions to see how they interpret the data.
6. What pattern do you see from the data?
7. What sum turned up most?
8. What are the odds of each sum turning up?
9. Analyze the data by having them explain the pattern. It may be necessary to list every pair of addends for each sum 2 - 12 theoretical probability.
10. Have them communicate the pattern and compare the experimental probability with the theoretical probability.
Discovery Activity