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Thinking in Data and Probability Session 3
Remember to read the Baroody article.
Bring your vandewalle books.
8:00-9:00
Opening Activity - Sticks and Stones - Illuminations
Set up 2 game boards on the floor for 4-6 players in each game.
 Provide 3 sticks colored on one side and blank on the other
to each group and game pieces for each individual.
 Post the game rules on the walls.
 Post the data chart on the wall nearest each group and
provide sticky notes to each player.
 After each toss, place the sticky note above the appropriate
column.
 Discussion - Which is more likely?
 Discuss whole group. We will revisit this later in the phases
of learning.
Sticks
Stones
Chart Paper
Sticky notes
Goals for today:
 Develop an understanding of probability and the probability
of an event.
 Use data to make predictions as a way to analyze the data.
 Discover how children’s probability sense grows gradually
with experience.
 Recognize that investigation and exploration should
permeate probability instruction.
 Discover the value of learning probability and statistics as
real applications of mathematics.
9:00-9:30
What is probability? What does the terminology probability of an
event mean?
Make a list of the topics and ideas that come to mind when you think
of probability, including both everyday uses of probability and
mathematical or school uses.
What does probability have to do with statistics? Think about ways
that statistics might use probability, and vice versa.
What do we see in common? Compile a common list for our definition
of probability and its relationship to statistics.
Randomness, fair/unfair, Game of chance
(Math Matters Chapter 14) and (vandewalle K-3 pg. 332- act. 12.1)
Probability Intro Smartboard notebook
Part 5 was
centered around
session 10 of
Annenberg
Chart paper
9:30-9:45
LEVEL 1 Thinking:
Probabilistic thinking begins when children start to differentiate
between whether an event will always happen, sometimes
happen, or never happen.
Children often lack the ability to distinguish between definite
events and possible events. Personal preferences will affect their
decisions even though the obvious outcome is visible - 3 white
marbles and 1 red. Which is more likely ? Red because it is my
favorite color.
They may also make predictions about the likelihood of an event
based on facts that do not directly affect the event - familiarity
causes thinking about the event to be more likely.
Scenario - If you have won several raffles, you will probably think
your chance of winning a raffle is higher than someone who has
never won a raffle.
Thus the need to have students investigate probabilities first hand
through data collection and experimentation. Students need to
confront their misconceptions if we are to help them make sense
of mathematics.
9:45-10:00
10:00-11:00
Break
Making sense of probability - Phase 1- Phase 1 Menu
Provide task assignment sheet and have all tasks posted around the
room with appropriate materials available for each.
Phase 1 Menu - Tasks to help students move to level 2
 You have 1 hour to complete the tasks and respond to the
accompanying reflection questions.
 Each task focuses on one or more of the guidelines for
laying the conceptual groundwork for probability.
 Think as a student might as you approach these tasks.
 Work in pairs as determined by the cards you selected
when entering the room.
 Respond to the reflection questions for Probability Phase 1.
Tasks:
 Race to the Top
 Probability Number Line
 Fair or Unfair
11:00-11:15
Phase 1 Tasks Discussion
Refer to reflection questions
Refer to assessment note on pg. 335 vandewalle.
11:15-11:30
Level 2: Transitional (Nonsystematic Sense of the Possible) - refer
to level handout.
Lunch
11:30-12:30
Blank paper for
drawing
Number line and
items cut out for
placing on the
number line
Misconceptions
Recording Sheet
for the Phases
12:30-1:30
Phase 2 Menu - Tasks to help students move to level 3
 You have 1 hour to complete the activities and
respond to the accompanying reflection questions.
 Each task moves students toward more precise means
of analyzing probability situations and informally
solving problems.
 Complete the following tasks as a student might do
them.
 Respond to the reflection questions for discussion.
Tasks:
 Take a Chance
 Two Coins
 Three Coins
Coin
Handouts for
discussion and
tasks
dice
1:30-1:45
Phase 2 Task Discussion
Refer to Reflection Questions
Level 3: Informal Quantitative (Semi-Systematic Sense of the
Possible)
Reflection
questions
2:00-3:00
Phase 3 Menu - Tasks to help students move to level 4
 You have 1 hour to complete the activities and respond to
the accompanying reflection questions.
 Each task encourages students to adopt more formal
procedures.
 Complete the following tasks as a student might do them.
 Respond to the reflection questions for discussion.
Tasks
 Cube Confusion
 Foul Forecast
 A Love Story
 The Marble Argument
Marbles
Cubes
Paper for
making a table,
graphic, or other
more formal
procedure
3:00-3:15
Phase 3 Discussion
Refer to Reflection Questions
1:45-2:00
Back to Sticks and Stones
 Individually determine the number of options for throw determine the probability of each throw.
 Why more moves for certain throws?
 What might you use to determine the possibilities? Tree
Diagram? A table?
 Rewrite the rules so that distance is in alignment with
probability.
Back to the cards you drew:
 What was the likelihood of being with the partners you had
3:15-3:45
today? What could you do to figure that out?
Time to plan a task to fit your grade level and student level of
probabilistic thinking
What understandings and misconceptions do you think your
students will be bringing to your class?
3:45-4:15
4:15-4:30
5 Practices to Orchestrate Productive Mathematical Discussions
What is this?
How will this help as we work together to improve student
learning?
Closure
Exit Card:
 Which task did you select for your class?
 What level are you trying to move your students to?
 What specific ideas from the phase discussions will you
focus on?
Homework
 Complete the planned task prior to next meeting
 Bring student work and plan to share the task and the
outcomes with the group
 Read the Orchestrating Productive Mathematical
Discussion article
 When I visit to coach next, we will be following the 5
practices as we pre and post conference.
Article
Handouts