Monday, April 22, 2013

Creating a Rigorous Task and Making Sample Tasks Your Own

This week I am sharing a resource I created for a workshop focused on identifying language objectives together with mathematical content and practice standards objectives. It is based on the Buttons Task (grade 6 Statistics and Probability) found at  illustrativemathematics.org (illustrative Mathematics is an initiative of the Institute for Mathematics & Education funded by the Bill & Melinda Gates Foundation)

This is an example of how a task found on-line (or elsewhere) can be modified for broader learning objectives and rigor while embedding [student directions] to encourage mathematical discourse.

If you are interested in a copy of the file email your request to: ngordon@doe.mass.edu

Content Standard:
STATISTICS AND PROBABILITY 6.SP.1
Develop understanding of statistical variability. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
Context for language use:
The Jar of Buttons task requires READING the definitions and questions, WRITING, recording reasoning and questions. Additionally there is well SPEAKING AND LISTENING with the oral discourse activities such as turn and talk.

A Jar Full of Buttons
Zeke likes to collect buttons and he keeps them in a jar.
Occasionally Zeke empties the buttons out of the jar so
he can see all of his buttons at once.
http://3.bp.blogspot.com/-EdImtqVkA5A/TbY9TQOY8KI/AAAAAAAAqSw/kY3ijntbEJM/s1600/spilled-jar-of-buttons.jpg

PART ONE: Review in your group the following definition:
A statistical question is one that anticipates an answer based on data that vary. 

Example: “How many minutes do 6th grade students typically spend on homework each week?” is a statistical question. We expect 6th grade students’ time spent on homework would vary from student to student or week to week. 

Non-example: “How much time did Juana spend studying last night?” is not a statistical question since the answer is based on a single number individually complete the table below. 

PART TWO: Which of the questions in the table below are statistical questions? Explain why it is or is not a statistical question.

QUESTION

Statistical Q?
Yes or No
Why or Why Not?
 I. What is the typical number of holes for the buttons in the jar?


 II. How many buttons are in the jar?


 III. How large is the largest button in the jar?


 IV. If Zeke grabbed a handful of buttons, what are the chances that all of the buttons in his hand are round?


V.  What is a typical size for the buttons in the jar?


 VI. How many buttons have four holes?


VII. How are these buttons distributed according to color?



PART THREE:  When everyone has recorded his or her answers, compare with your partner/group. Share reasoning if there are any disagreements. 

Individually write TWO new “button questions”. One should be a statistical questions and the other one not statistical. Be prepared to share your thinking and explain why it is or is not a statistical question.

PART FOUR:  Trade your two questions with your partner/in your group and see if they agree with your classifications.  OR Hand in your two Question as exit ticket 

Solutions
Statistical questions I, III, IV and VII
Possible statistical question:  What is the distribution of button shapes in the jar?
Possible non-statistical question:  How many more buttons are in the jar this week?

Adapted from Illustrative Mathematics http://www.illustrativemathematics.org/illustrations/104

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