Read and Discuss the Story. This lesson is based
upon the book A Three Hat Day by Laura Geringer.
It tells the story of R.R. Pottle the Third, a man who
truly loves hats and possesses a wonderful collection.
He is also unhappy and lonely, but a happy ending
is in store as his love of hats leads to finding his
true love.
Have students predict what they think the story
might be about based upon the title and cover illustration.
Ask students to justify their predictions, and
accept all reasonable responses. Have students listen
for evidence to prove or disprove their predictions as
you read the story aloud.
After reading, allow time for students to share reactions
to the story and discuss evidence of proof and
disproof of the predictions. Help students understand
that disproof is good critical thinking and that a
"correct" prediction is not "better" than a disproving
one.
Show the cover illustration and ask:
- Which hat did R.R. Pottle put on first? Which came
second and third? (First he put on the bathing
cap, next the fire helmet, and third was the sailor
hat.)
- Suppose R. R. Pottle wanted to cheer himself up
by putting on the same three hats in a different
order. What is another hat combination using the
bathing cap, fire helmet, and sailor hat? Can you
draw it for us? (Answers will vary. Possible
response: First the sailor hat, then the fire helmet,
and finally the bathing cap. See Figure 1.)
- If he changed the order of the three hats each day,
how many days do you think R. R. Pottle could
wear a new hat combination? Make a prediction.
(Predictions will vary.)
Review Math Practices. Display and refer students
to the Math Practices page in the Reference section
of the Student Activity Book. Focus on Math
Practices 2 and 5, Find a strategy and Show my
work. Use prompts similar to the following to discuss
ways to select good tools, use efficient strategies,
and show work so someone else can understand
the thinking.
- What tools and strategies could you use to find all
the different hat combinations? (Possible
response: We could use three different color
cubes or other counters and move them around in
different orders.) [See Figure 2.]
- How could you show your work on paper? (We
could draw them in stacks of three different colors.)
- Are there other ways to draw or show the three different
hats? (Possible responses: We could draw
pictures of each of the hats. We could write symbols
like numbers to show each hat like 1, 2, 3 on
paper and keep changing the order.)
- How can you tell which hat is which if you use
symbols? (We have to show which symbol stands
for each hat and always use the same number for
each hat, like 1 means the bathing cap, 2 means
the fire helmet,
3 means the sailor hat.)
[See Figure 3.]
- Are there other symbols you could use to represent
the hats? (Possible responses: We could use
letters like B for bathing cap, F for fire helmet,
and S for sailor hat. [See Figure 4.] We could just
draw a mark like a tally mark with three different
colors to show the hats.) [See Figure 5.]
- Which method seems easiest—drawing each hat
for every combination or using symbols or counters?
(Responses will vary.)
- How could you organize your work to be sure you
found all the combinations without repeating the
order? (Possible responses: Write each combination
in columns or rows or draw boxes on the
paper for each way. We have to check carefully at
the end to see if any are the same.)
Find Three Hat Combinations. Direct students to
the Three Hat Combinations page in the Student
Activity Book. Explain that this is where they will
record their solutions. They should include R. R.
Pottle's first hat combination—the bathing cap, fire
helmet, and sailor cap. Remind them to show their
work clearly so that others can understand their
thinking.
Have students work in pairs to find a solution to the
problem. Allow students to experiment and use the
tools and strategies of their choice. Many may use
trial and error. As students work, make note of any
using a systematic approach.
Use the Three Hat Combinations page in the Student Activity
Book with the Feedback Box to assess students' abilities to
find efficient strategies for solving the problem [MPE2] and
show and explain their thinking [MPE5].
