ALT IPP Pre-work:
Estimated Time Needed to Complete: 45 minutes
Directions:
Complete all IPP facilitation pre-work to a degree where you could facilitate. Pre-work includes:
- Read phase 0 and come prepared to ask questions about effective planning for Phase 0 (read in the IPP document
and the prepared Phase 0 for the model protocol)
- Do the problem using 2-3 strategies and/or representations
- Read the entire protocol and be able to articulate the steps of the protocol
- Please scan and email your representations/strategies and solutions to Will Roble + Anne Pearson by June 18th
Phase 0
Content Standards:
- 8.EE.B – Understand the connections between proportional relationships, lines and linear equations
- 8.EE.5 – Graph proportional relationships, interpreting the unit rate as the as the slope of the graph. Compare two
different proportional relationships represented in different ways
- 8.F.4 – Construct a function to model a linear relationship between two quantities. Determine the rate of change
and initial value of the function from a description of a relationship or from two (x,y) values, including reading these
from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the
situation it models, and in terms of its graph or a table of values.
Practice Standards:
- SMP1 – Make sense of problems and persevere in solving them
- SMP2 – Reason abstractly and quantitatively
- SMP3 – Construct viable arguments and critique the reasoning of others
- SMP4 – Model with mathematics
- SMP6 – Attend to precision
Criteria for selecting the exercise:
- Draws thinking towards mathematics to be used and learned; is relatively narrowly focused on a strategy,
concept or skill
- May be difficult or easy, complex or simple, but never puzzling
- The path(s) towards the solution is(are) often apparent1
- Incorporates the following Key Cognitive Strategies (Conley):
o Problem Formation: requires planning and use of reasoning skills
o Research: lends itself to strategic selection and use of tools
o Interpretation: requires planning and use of reasoning skills; requires understanding, identification
and/or application of one or more concepts and skills
o Communication: requires students to demonstrate evidence of their thinking, fluency and conceptual
understanding through use of models, work shown and/or written explanations; requires evidence to be
provided and may require development of logical argument for concepts or steps
o Precision & Accuracy: requires attention to appropriate rules of precision when tending to work in
written, oral, or symbolic form
Problem: Anna and Jason have summer jobs stuffing envelopes for two different
companies. Anna earns $1.53 for every 17 envelops she finishes. Jason recorded his
earnings in the table to the right. Who makes more from stuffing the same number
of envelopes? How can you tell?
1
Paul Zeitz, The Art and Craft of Problem Solving p. ix
Number of
envelopes
11
22
33
Earnings
$0.88
$1.76
$2.64