This document discusses how to analyze mathematical tasks for use in K-5 classrooms. It explains that to "unpack" a task means to carefully examine its components such as context, possible student interpretations, level of mathematics, number of possible solutions, and representations. Three sample tasks are presented and categories for analysis are listed, including context, interpretation, mathematics, answers, solutions, and other issues. Teachers are encouraged to unpack tasks to determine if they are "worthwhile", or well-designed to meet learning goals. The document models unpacking tasks and promotes reflection on how this process informs task selection.

1. Selecting, Designing & Using
Mathematical Tasks in the K-5 Classroom

2. Unpacking/Analyzing a Task
 What does it mean to ‘unpack’ a task?
 What might you consider in your analysis as you
‘unpack’ a task?
 How do you use this analysis to make a decision
about whether a task is worthwhile (what does it
mean to say a task is worthwhile)?

3. Unpacking Task 1
You have a dozen cookies and
want to share them among the
members of your family at supper.
How many cookies can each
person have?

4. Analysis of Task 1
Context: Is it a reasonable problem context? Might
students ever need to solve such a problem?
Interpretation: What are children’s possible
interpretations of the problem?
Mathematics: What is the difficulty level of the
mathematics involved? Is it the same for all students?
Who controls the difficulty level

5. Analysis of Task 1
Number of Answers: Are different answers possible?
If so, what answers are possible?
Representations or Solutions Paths: Are different
solution paths are possible? If so, what are they?
Other issues?

6. Unpacking Task 2
Our class has 28 students and Mrs.
Byrd’s has 24. If we want to arrange the
desks in groups with the same number
of desks in each group, which class has
more options? Use tiles to work on this
problem and show your answer.

7. Analysis of Task 2
Context:
Interpretation:
Mathematics:
Number of Answers:
Representations or Solutions Paths:
Other issues?

8. Unpacking Task 3
Use counters to solve and verify the following division
problems. Then write stories to accompany five of them.
32÷9= 19÷4= 42÷6= 56÷8=
25÷5= 15÷3= 21÷7= 65÷7=
Example for 35÷4: Shandra had 35 pencils and she wanted to
put 4 pencils each into some pencil boxes she had made as
gifts. How many boxes could she fill?
Share your stories with a friend and ask him or her to solve
the problems in your stories.

9. Analysis of Task 3
Context:
Interpretation:
Mathematics:
Number of Answers:
Representations or Solutions Paths:
Other issues?

10. Unpacking/Analyzing a Task
 What does it mean to ‘unpack’ a task?
 What might you consider in your analysis as you
‘unpack’ a task?
 How do you use this analysis to make a decision
about whether a task is worthwhile (what does it
mean to say a task is worthwhile)?

11. Reflect and Discuss
Examine Tasks H & L from the Place Value Task Card
Deck.
Unpack/analyze each task using categories suggested
by Ball’s work and/or adding your own additional
issues.
How does this analysis help you decide if Task H
and/or Task I are worthwhile?