Download Tina_s_Texting_Tragedy_sp_4_sp_5c

Domain:
Statistics & Probabiity Standard Code: 6.SP.4 & SP.5.c Teachers:
Liz Roberts, Sherry Hammond, Candis Clayton
Adapted from: Smith, Margaret Schwan, Victoria Bill, and Elizabeth K. Hughes. “Thinking Through a Lesson Protocol: Successfully Implementing High-Level Tasks.”
Mathematics Teaching in the Middle School 14 (October 2008): 132-138.
PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK
Students will be able to display numerical data to give meaning; give quantitative measures (mean,
What are your mathematical goals for
median, center, spread, interquartile range) as well as, describe patterns and deviations.
the lesson? (i.e., what do you want
students to know and understand about
mathematics as a result of this lesson?)




What are your expectations for
students as they work on and
complete this task?
What resources or tools will
students have to use in their
work that will give them
entry into, and help them
reason through, the task?
How will the students work—
independently, in small groups, or
in pairs—to explore this task?
How will students record and
report their work?
How will you introduce students to the
activity so as to provide access to all
students while maintaining the
cognitive demands of the task?
Expectations: All students will be engaged and on-task.
Materials/Resources/Tools: pencils, paper, task sheet, calculator, & any manipulatives students may
choose to help them solve the problem.
Groupings: Students will work either with partners or in groups no larger than 4.
Recording: Students will record the information on their task sheet & in math journal.
Launch: Questions for students—
1. How many of you have cell phones?
2. How many of you are allowed to send and receive text messages?
3. How many texts do you think you send each month? (estimate)
Show a video clip of “texting grandma”
http://www.youtube.com/watch?v=ySR3hpieiQc
Explain story/task & give task sheets to students.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
Sub-task A
As students work independently or in
What is the task asking you?
small groups, what questions will you
What do you already know about the task?
ask to—
How could you represent the data? Could you draw a picture or a graph, etc.?
 help a group get started or make
What have we done in the past that could help you with this task?
progress on the task?
For struggling students: What does “unlimited texting” mean?
 focus students’ thinking on the
Sub-task B
key mathematical ideas in the
How can you show the highs/lows/differences in numbers of texts each day?
task?
 assess students’ understanding of What does average mean? How do you figure that out?
key mathematical ideas, problem- What was the least number of texts and what was the most number of texts?
What info is needed? What info is not needed?
solving strategies, or the
What have we done in the past that could help you with this task?
representations?
 advance students’ understanding What do the parts of your picture, chart, plot mean?
For struggling students: How do you make a “box & whiskers plot”? What parts do we need?
of the mathematical ideas?
How do we find the average? What is a quartile? What is an outlier?
For advanced students, demonstrate at least one more way to represent/prove your answer(s).
Sub-task C
How many texts will Tina’s mom need to pay for from the month?
Is there anything else the task is asking you?
How will you ensure that students
remain engaged in the task?
See above questions.
 What assistance will you give or
what questions will you ask a
student (or group) who becomes
quickly frustrated and requests
more direction and guidance is
solving the task?
For advanced learners who finish early--Present additional task as follows:
 What will you do if a student (or
1. Change the number of free texting minutes to 350 per month
group) finishes the task almost
2. Cost of texting 351-500 messages is $.25
immediately? How will you
3. Cost of texting from 501-up messages is $.35
extend the task so as to provide
4. Now how much money would Tina need to earn to pay her mom back?
additional challenge?
PART 3: SHARING AND DISCUSSING THE TASK
This task could have a variety of pathways to the solution.
How will you orchestrate the class
discussion so that you accomplish your
Students will be chosen to present and defend their solutions (based upon the methods they
mathematical goals?
used) to demonstrate a variety of solution pathways. Students will be asked to listen/watch
 Which solution paths do you want
and record different methods in their math journals.
to have shared during the
class discussion? In what order will
Solution Pathways: histogram, dot plots, box & whisker plot, algorithm, and other ideas.
the solutions be presented? Why?
 What specific questions will you ask
Order of presentation: struggling students or students with limited/basic understanding,
so that students will—
students with “popular” solution pathways, students demonstrating abilities to think “outside
1. make sense of the
the box” or abstractly with more complex solution pathways.
mathematical ideas that you
want them to learn?
Questions:
2. expand on, debate, and question
1. What did you know before that helped you solve this investigation?
the solutions being shared?
2. Which solution pathway made the most sense to you and why?
3. make connections among the
Which method was most helpful in solving the task?
different strategies that are
3.
How were the strategies similar? How were they different?
presented?
4. What patterns did you notice?
4. look for patterns?
5. What is one more situation where you could use a box & whisker plot?
5. begin to form generalizations?
What will you see or hear that lets you
know that all students in the class
understand the mathematical ideas that
you intended for them to learn?
All students need to participate during the “exploration”.
Students need to recognize and use correctly median, mean, upper/lower quartiles,
cluster(s), and outliers.
Students need to associate quartiles with “25%” and describe the various parts of their data
using appropriate vocabulary.
SP.4 and SP.5.c
Tina’s Texting Tragedy
Sub-task A
Tina’s mom is mad, really mad! She signed her daughter up for a cell phone on the family plan. She didn’t sign her up for unlimited texting. But you
guessed it, Tina texted a lot. When her mom got the bill, she was furious. The bill listed the number of texts Tina sent each day. How can her mom
display the data from the bill to show Tina how serious and upset she is?
Number of texts sent each day
Sun
17
23
20
33
30
Mon
20
17
18
14
17
Tues
22
19
34
5
39
Wed
18
15
22
10
Thur
8
17
19
45
Fri
19
7
11
17
Sat
23
38
22
26
Sub-task B
What was the average number of texts Tina sent every day? Create a box-and-whiskers graph to chart the daily numbers of text messages. Show the
median, upper and lower quartiles. What does each quartile represent? Identify any outliers and clusters and what they represent.
Sub-task C
Tina’s mom’s plan allows for 200 texts a month for free, but any texts after that cost $.25 each. How much will Tina have to earn to pay her mom for
all those extra texts? How many will Tina want to limit herself to each day in the future to make sure this never happens again?