Understanding by Design
Title:
Subject/Course:
Topic:
Grades:
Designers:
PROBABILITY
Math
Probability
6
Joanne Mohan, Amy Brown, Kim Grubich, Jill Martin
Stage 1 - Desired Results
Established Goals: Students pose questions and collect , organize, represent, interpret and analyze data
to answer those questions. Students develop and evaluate inferences, predictions and arguments that are
based on data.
Benchmark H: Find all possible outcomes of simple experiments or problem situations, using methods
such as lists, arrays, and tree diagrams.
Benchmark I: Describe the probability of an event using ratios, including fractional notation.
Benchmark J: Compare experimental and theoretical results for a variety of simple experiments.
Benchmark K: Make and justify predictions based on experimental and theoretical probabilities.
Understandings:
Students will understand that…
Experiments can be designed to answer questions.
Answers are justified based upon the data that is
collected and organized
Outcomes and probability can be determined
through interpreting and analyzing data
Inferences, predictions and arguments are based
upon the data collected
Essential Questions:
 How is an experiment designed to test
probability?
 What organizational tools are best to
represent the data?
 How is probability assigned using fractions,
ratios, and percents?
 How are inferences and predictions made
and justified based upon data?
 .How do I determine the difference between
theoretical and experimental results?
Theoretical and experimental results of an
experiment may vary.
Probability can be expressed as fractions, ratios or
percents.
Students will know...
 Vocabulary: Theoretical and experimental data
outcome; probability
 The results of an experiment may or may not
support the theoretical data.
 What a logical inference is
Students will be able to....
 Find possible outcomes using lists, arrays, tree
diagrams and other appropriate organizers
 Make logical inferences from statistical data
 Design an experiment to test theoretical
probability
 Justify the results of an experiment
 Represent all possible outcomes of simple
experiments as fractions, ratios or percents.
Stage 2 – Assessment Evidence
Performance Tasks:
In teacher assigned groups of 3 or 4, develop and create a fair
game for one player. Use a tree diagram to state the
theoretical probability. Present your findings as a fraction,
ratio, and percent. Explain why this game is fair. Make a
prediction based upon your theoretical probability. Have at
least 25 different people play your game and record the
results. Present the experimental results as a fraction, ratio
and percent. Write a summary statement comparing your
theoretical results with the experimental results. Show the tree
diagram, data, prediction and summary statement in poster
format.
Other Evidence
Journal entry- What are the components of a fair
game.
Quiz(zes)- Probability/Tree Diagrams/Predictions
Journal Entry- Given an unfair game (Lucky Coin
Toss), students will explain why it is not fair and
change the rules to make it fair.
Stage 3 – Learning Plan
Introductory Activities
Days 1 - 3
Collections of Math Lessons (introductory activities) probability investigations, pg 65 – 79
Probability Reference Page for students – Dale Seymour
Marilyn Burns: 50 Problem Solving Activities: Probability Tile Games
HW day 3: Exploring Probability – Dale Seymour pg 3
E.M: 7.1, Probability of Equally Likely Outcomes (spinners, dominos and dice)
Days 4 - 12
Go over Investigations 1 – 7 in How Likely Is It? Connected Mathematics) Over 9-10 days
1. A First Look at Chance
2. More Experiments with Chance
3. Using Spinners to Predict Chances
Marilyn Burns ATM – different types of spinners, pp 64 – 75; 261-271
4. Theoretical Probabilities
Everyday Mathematics 7.4, Using Tree Diagrams to find expected outcomes
7.5, Using Tree Diagrams to calculate probabilities
Three Door Puzzle (sieve or tree diagram type activity)
TI Explorations grades 6 and 7: “Probably not!” (theoretical v empirical – advanced
activity)
5. Analyzing Games of Chance
TI Explorations grades 5 and 6:”Hey, that’s not fair!” (or is it?) (fair vs. unfair)
Why aren’t there more reds in my bag?
Dale Seymour Exploring Statistics in the Elementary Grades book 2 pp 68 – 93
E.M.: 7.7 Fair and Unfair games
6. More About Games of Chance
7. Probability and Genetics
Extra materials:
Marilyn Burns: About Teaching Mathematics::
pp 59 – 61 overview of ways to collect data “big ideas”
Creative Publications (short warm up type activities)