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Matrix of Math Standards and Aeronautics Topics
6th-7th Grade Activities: PlaneMath Enterprises

Each of the lessons included in PlaneMath represent five or more of the National Council of Teachers of Mathematics (NCTM) Math Standards, as well as two or more general aeronautics topics. To help you plan your use of PlaneMath to teach or reinforce specific concepts, we have included the following matrices indicating the math standards and aeronautics topics that correspond to each lesson. To view the matrices for the 5th or the 6th-7th grade activities, please return to the main NCTM matrix page.

To jump to a particular standard and view its categories, use the following outline:

Process Standards

Content Standards

Aeronautical Content

NCTM Process Standards: 5th-8th

Standard 1: Mathematics as Problem Solving
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Investigate and formulate problems, develop and apply strategies X     X X X X X
Verify and interpret results X     X X X X X
Generalize solutions X       X X X X
Gain confidence using math meaningfully X     X     X X

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Standard 2: Mathematics as Communication
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Model situations in oral, written, pictorial, concrete, graphical and algebraic terms       X     X X
Reflect on and clarify mathematical thinking             X X
Develop a common understanding of mathematical ideas       X   X X X
Use reading, listening and viewing to interpret mathematical ideas X     X X X X X
Make conjectures and convincing arguments X       X X X X
Appreicate the value of mathematical notation       X       X

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Standard 3: Mathematics as Reasoning
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Recognize and apply inductive and deductive thinking               X
Use spatial reasoning: reasoning with graphics and proportions X     X X X X X
Make and evaluate mathematical conjectures and arguments X     X X X X X
Use math to validate own thinking                
Appreciate the power of mathematical reasoning             X X

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Standard 4: Mathematical Connections
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Integrate models and representations in problem solving X     X X X X X
Use mathematical ideas to further understanding of other mathematical ideas       X     X X
Apply mathematical thinking to problem-solving in other disciplines X     X X X X X
Value the role of mathematics in culture and society X     X X X X X

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NCTM Content Standards: 5th-8th

Standard 5: Number and Number Relationships
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Understand, represent and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, and scientific notation) in real-world and mathematical problem situations       X X X X  
Develop number sense for whole numbers, fractions, decimals, integers and rational numbers       X   X X X
Understand and apply ratios, proportions and percents in a wide variety of situations         X X X  
Investigate relationships among fractions, decimals and percents           X    
Represent numerical relationships in one- and two-dimensional graphs X       X   X X

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Standard 6: Number Systems and Number Theory
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Understand and appreciate the need for numbers beyond whole numbers                
Develop and use order relationships for whole numbers, fractions, decimals, integers and rational numbers           X   X
Extend their understanding of whole number operations to fractions, decimals, integers and rational numbers       X   X    
Understand how the basic arithmetic operations are related to one another             X  
Develop and apply number theory conceps (primes, factors, multiples) in real world mathematical problem situations                

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Standard 7: Computation and Estimation
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Compute with whole numbers, fractions, decimals, integers and rational numbers       X   X X X
Develop, analyze and explain procedures for computation and techniques for estimation       X       X
Develop, analyze and explain methods for solving proportions         X X X  
Select and use an appropriate method for computing from among mental arithmetic, paper and pencil, calculator and computer       X   X X X
Use computation, estimation and proportions to solve problems         X X X X
Use estimation to check the reasonableness of results       X       X

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Standard 8: Patterns and Functions
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Describe, extend, analyze and create a wide variety of patterns         X      
Describe and represent relationships with tables, graphs and rules X     X X      
Analyze functional relationships to explain how a change in one quantity results in a change in another X     X X     X
Use patterns and functions to representa dn solve problems         X      

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Standard 9: Algebra
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Understand the concepts of variable, expression and equation       X X X X  
Represent situations and number patterns with tables, graphs, verbal rules and equations, and explore the interrelationships of these representations X     X X X X X
Analyze tables and graphs to identify properties and relationships X     X X   X  
Develop confidence in solving linear equations using concrete, informal and formal methods       X   X X X
Investigate inequalities and non-linear equations informally         X      
Apply algebraic methods to solve a variety of real-world and mathematical problems       X X X X X

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Standard 10: Statistics
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Systematically collect, organize and describe data         X     X
Construct, read and interpret tables, charts and graphs X     X X   X X
Make inferences and convincing arguments that are based on data analysis       X     X X
Evaluate arguments that are based on data analysis       X       X
Develop an appreciation for statistical methods as powerful means for decision-making               X

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Standard 11: Probability
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Model situations by devising and carrying out experiments or simulations to determine probabilities               X
Model situations by constructing a sample space to determine probabilities                
Appreciate the power of using a probability model by comparing experimental results with mathematical expectations               X
Make predictions that are based on experimental or theoretical probabilities               X
Develop an appreication for the pervasive use of probability in the real world               X

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Standard 12: Geometry
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Identify, describe, compare and classify geometric figures       X X X    
Visualize and represent geometric figures with special attention to developing spatial sense     X X X X    
Explore transformations of geometric figures                
Represent and solve problems using geometric models       X X      
Understand and apply geometric properties and relationships       X   X    
Develop an appreciation of geometry as a means of describing the physical world       X X X    

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Standard 13: Measurement
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Extend understanding to the process of measurement           X X  
Estimate, make and use measurements to describe and compare phenomenon       X     X X
Select appropriate units and tools t measure to the degree of accuracy required in a particular situation           X X  
Understand the structure and use of systems of measurement                
Extend their understanding of the concepts of perimeter, area, volume, angle measure, capacity, weight and mass       X   X    
Develop the concepts of rates and other derived and indirect measurements                
Develop formulas and procedures for determining measures to solve problems           X X  

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Aeronautical Content
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History of Aerospace  
Innovations X     X X      
Inventors X              
Kinds of Aircraft  
Airplanes X X X X X X X X
Gliders               X
Four Principles of Airplane Design  
Aerodynamics (airflow around the vehicle) X     X X X   X
Structures and Materials   X   X   X   X
Propulsion (engine and power requirements)             X  
Stability and Control (how the vehicle handles as it flies) X X X X X     X
Four Forces of Flight  
Lift X       X X   X
Weight X           X X
Thrust X           X X
Drag X     X X X   X
Parts of an Airplane   X            
Instruments and Navigation   X X          

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