Practice 5: Use appropriate tools strategically. 
Big Idea 1  Use Estimation Strategically
Added by JB 
Student behavior 
Reformulation: changes the numbers that are used to ones that are easy and quick to work with.
Compensation: make adjustments that lead to closer estimates. These may be done during or after the initial estimation.


Questions to ask  students or yourself 
 Do I need an exact answer?
 When do we estimate?
 Is there enough information to provide an exact answer?
 What are some of the errors that may be introduced by rounding?
 (what others of your own belong here?)



Big Idea 2  Select a tool that interacts with the underlying math 
Student behavior 
description
Students apply what has been uncovered with understanding a problem and select a tool
that can represent or interpret the problem to then generate a pathway toward the solution.
Tools can be used to allow students to experiment with mathematical objects, and apply approximation and estimation
strategies.


Questions to ask  students or yourself 
 Does the tool organize information?
 Does the tool demonstrate a concept?
 Does the tool parallel a common algorithm?
 Does the tool reveal a relationship?
 Does the tool fall short of helping to frame the problem?
 (what others of your own belong here?)



Big Idea 3  Select and Apply Technology Tools 
Student behavior 
Students can choose among tools that will help them identify a solution path,
and are able to use technological tools to explore and deepen their understanding of concepts.


Questions to ask  students or yourself 
 Have I selected the correct representation for the problem? What tools
that are available will help me produced my desired output? Examples, will using a graphing calculator or
spreadsheet help me represent a table better than what I can do with pen, paper, and a ruler?
 (what others of your own belong here?)



Big Idea 4  Use Internet and Online Resources Strategically 
Student behavior 
description
Mathematically proficient students are able to identify relevant external mathematical resources, such as web sites,
and use them to pose or solve problems.


Questions to ask  students or yourself 
 Where can I get reallife data that will help me prove/disprove a hypothesis?
 Where can I find examples of applying this in the realworld and what type of careers use these skills?
 Where can I find tools that may help me to represent my solution in another way to uncover additional meaning?



Really nice poster by:

MP 5 
Interpreting the Math Practice 
The Standard of Mathematical Practice as written: 
Mathematically proficient students consider the available tools when solving a mathematical problem.
These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet,
a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently
familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

The standard lists the practices of Mathematically proficient students 
Mathematically proficient students:
 consider the available tools when solving a mathematical problem.
These tools might include
 pencil and paper, concrete models, a ruler, a protractor
 a calculator, a spreadsheet,
 a computer algebra system, a statistical package, or dynamic geometry software.
 Are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about
when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.
For example, mathematically proficient high school students
 analyze graphs of functions and solutions generated using a graphing calculator.
 They detect possible errors by strategically using estimation and other mathematical knowledge.
 When making mathematical models, they know that technology can enable them to visualize the
results of varying assumptions, explore consequences, and compare predictions with data.
 Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources,
such as digital content located on a website, and use them to pose or solve problems.
 They are able to use technological tools to explore and deepen their understanding of concepts.


Evaluating teachers on MP5: Use appropriate tools strategically.
A teacher who is exemplary is meeting criteria in both the proficient and exemplary columns.

PROFICIENT (teacher mostly models) 
Task
 Lends itself to multiple learning tools.
 Gives students opportunity to develop fluency in mental computations.
Teacher
 Chooses appropriate learning tools for student use.
 Models error checking by estimation.


EXEMPLARY (students take ownership) 
Task
 Requires multiple learning tools (i.e., graph paper, calculator, manipulatives).
 Requires students to demonstrate fluency in mental computations.
Teacher
 Allows students to choose appropriate learning tools.
 Creatively finds appropriate alternatives where tools are not available.


