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NCTM Afiliate Leaders Conference, Atlanta, Aug 2012

Focus in High School Mathematics: Reasoning and Sense Making

Focus in High School Mathematics: Reasoning and Sense Making is a conceptual framework to guide the development of future publications and tools related to 9–12 mathematics curriculum and instruction.  
 
FHSM-Stats-50x71  Focus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability

 		 FHSM_135024
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FHSM_ALG 

Focus in High School Mathematics: Reasoning and Sense Making in Algebra 
13525  Focus in High School Mathematics: Reasoning and Sense Making in Geometry 
13989  Focus in High School Mathematics: Fostering Reasoning and Sense Making for All Students

 
FHSM-Tech 

Focus in High School Mathematics: Technology 
Reasoning and Sense Making Examples 

The Reasoning and Sense Making Item Bank contains tasks that can be used in secondary classrooms to promote reasoning and sense making. Each example includes links to Focus in High School Mathematics: Reasoning and Sense Making (FHSM), Principles and Standards for School Mathematics (PSSM), and the Common Core State Standards (CCSS). 
Task  Purpose  
Horseshoes
in Flight  		 Students analyze the structure of algebraic expressions and a graph to determine what information each expression readily contributes about the flight of a horseshoe. This task is particularly relevant to students who are studying (or have studied) various quadratic expressions (or functions). The task also illustrates a step in the mathematical modeling process that involves interpreting mathematical results in a real-world context.
Taking a Spin   Although students are often asked to find the angles of rotational symmetry for given regular polygons, in this task they are asked to find the regular polygons for a given angle of rotational symmetry, a reversal that yields some surprising results. This task would be most appropriate with students who have at least some experience in exploring rotational symmetry.
Tidal Waves   Students analyze a problem faced by the captain of a shipping vessel. Students may use a range of functions to model the situation and reflect on their usefulness. Because trigonometric functions can be useful, this task would be particularly appropriate for students who have had an introduction to graphing sine and cosine functions.
Eruptions: Old Faithful* Students analyze data and make predictions.  They will create a variety of graphical displays to discover trends in the data, then use those graphs to support their predictions. This task is appropriate for students familiar with line graphs and other graphical displays of univariate data sets.
Fuel
for Thought* 		Students use mathematical reasoning to determine appropriate numerical measures and patterns in fuel consumption in order to inform consumer choice for vehicle purchasing. The task promotes a sophisticated use of number sense including careful attention to units. It is accessible to beginning high school students.
Bank Shot

 		 Students compare their own reasoning strategies and those of their classmates, focusing on the strategies’ usefulness in determining how to make certain bank shots in billiards. This task is intended to involve multiple geometric perspectives and would be appropriate for students with an understanding of similar triangles, rigid motions (reflections), and equations for lines and is designed to develop students’ understanding of these concepts.
Crow
 		 The distance formula is often presented as a “rule” for students to memorize. This task is designed to help students develop an understanding of the meaning of the formula. It would be appropriate as an introduction (or review) of the distance formula for students who are familiar with the Pythagorean theorem and coordinate systems.

*Please note that the Eruptions: Old Faithful and Fuel for Thought tasks are currently being revised.   

 Supporting Materials  See What's Inside 
Executive Summary (PDF)

PowerPoint Presentation

PowerPoint Presenter Guidelines

President's Letter (PDF)

FAQs (PDF)

Press Release

Article  (Education Week)
 		 Teacher's Guide (PDF)

Student's Guide (PDF)

Administrator's Guide (PDF)

Policymaker's Guide  (PDF)

Family's Guide (PDF)
Table of Contents PDF)

Sample Pages (PDF) from Chapter 6: Reasoning with Functions  

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