Jefferson County Schools
Jefferson County Schools

Mathematics - Foundations I

Mathematics

The Tennessee Mathematics Framework for grades 9 through 12 includes skills for many different High School level courses, and contains the following process standards:

MATHEMATICS AS PROBLEM SOLVING

The study of mathematics must emphasize Problem Solving opportunities which require various approaches to investigate, understand, and apply mathematical concepts.
The development of each learner’s ability to solve problems is essential if he or she is to be a productive citizen. We strongly endorse the first recommendation of An Agenda for Action (NCTM, 1980): "Problem solving must be the focus of school mathematics." To develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve. Some may be relatively simple exercises to be accomplished independently; some should involve small groups or an entire class working cooperatively; and some problems should also be open-ended with no single right answer.
"Mathematics as Problem Solving" emphasizes the learners’ use of a broad base of strategies to:
Investigate and understand mathematical content
Recognize and formulate problems from within and outside of mathematics
Use mathematical modeling and appropriate technology to solve a wide variety of problems, including real-world problems.
Generalize solutions and strategies, applying them to new problems
Increase confidence in their ability to use mathematics meaningfully and to become independent problem solvers.

MATHEMATICS AS COMMUNICATION

The study of mathematics must emphasize Communication by requiring opportunities to explain, conjecture, summarize, and defend one’s ideas orally, in writing, and through the use of technology.
The development of a learner’s power to think mathematically involves learning the signs, symbols, and terms of mathematics. This is best accomplished in problem situations in which students have an opportunity to read, write, and discuss ideas in which the use of the language of mathematics becomes natural. As students communicate their ideas, they learn to clarify, refine, and consolidate their answers.
"Mathematics as Communication" focuses on the learners’ development of using language and symbols to:
Reflect and clarify thinking about mathematical ideas and situations
Express mathematical ideas and relationships, orally, in writing, and with physical material, pictures, and diagrams
Understand and value the role of mathematical notation
Realize that representing, discussing, listening, writing, and reading mathematics are vital aspect of mathematics study and use
Use mathematical notation to formulate generalizations.

MATHEMATICS AS REASONING

The study of mathematics must emphasize Reasoning which requires critical thinking, logical argument, and justification of solutions, of thought processes, and of conjectures.
Making conjectures, gathering evidence, and building an argument to support such notions are fundamental to doing mathematics. In fact, a demonstration of good reasoning should be rewarded even more than the learner’s ability to find correct answers.
"Mathematics as Reasoning" concentrates on leading the learners to:
Make and test mathematical conjectures
Make, follow, and judge the value of mathematical arguments
Draw logical conclusions
Justify solution-finding processes and answers.

MATHEMATICAL CONNECTIONS

The study of mathematics must emphasize making Connections among the various topics within mathematics, between mathematics and other disciplines, and between mathematics and "real world" situations.
The mathematics curriculum is often viewed as consisting of several discrete stands; so topics tend to be taught in isolation. Unless the learners connect ideas both among and between areas of mathematics, they learn isolated skills rather than develop the ability to recognize general principles and procedures relevant to several areas. Connecting conceptual understanding to procedures will enable learners to apply, recreate, and invent new procedures when needed. Failure to connect conceptual understanding to procedures results in a view of mathematics as an arbitrary set of rules. Learners should have many opportunities to observe and work with the interaction of mathematics with other subjects and with everyday society. Problems become meaningful when they relate to the learners’ experiences. Mathematics must be integrated into contexts that give its symbols and processes practical meaning. The school environment is rich with opportunities to use mathematics in other subject areas as well as other subject area content in mathematics.
"Mathematical Connections" concentrate on enabling the learners to:
Appreciate mathematics as an integrated whole, linking conceptual and procedural knowledge within the discipline and relating multiple representations of concepts or procedures to one another.
Apply mathematical thinking and modeling to solve substantial problems that arise in other disciplines and curriculum areas, such as art, business, music, psychology, industrial arts, computer technology, social studies, and sciences, such as biology, chemistry, and physics.
Use, recognize, and value the varied roles of mathematics in their lives, cultures, and society.

The Principles and Standards for School Mathematics describe the mathematical understanding, knowledge, and skills that students should acquire from prekindergarten through grade 12.

Algebra I is the Tennessee End-of-course test that must be passed before graduation to earn a high school diploma.

Foundations I

The Tennessee Mathematics Framework for grades 9 through 12 outlines skills to be taught in Foundations I.


Algebraic Concepts

    Inverse: Concept
The learner will be able to informally explain and model the concept of inverse in real world problem scenarios.
Strand Bloom's Scope Hours Source
Inverse Operations Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
  
    Algebraic Concepts: Measure/Estimate
The learner will be able to solve problems in measurement and estimation using algebraic thought processes.
Strand Bloom's Scope Hours Source
Algebraic Concepts Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Computation: Select/Use
The learner will be able to choose and/or apply suitable ways of computing with rational numbers (in various forms), and/or solving proportions (mentally, with computers, or calculators).
Strand Bloom's Scope Hours Source
Computation Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
  
    Variable: Describe
The learner will be able to describe the definition of a variable in an expression and equation.
Strand Bloom's Scope Hours Source
Variable Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Variable: Expression/Equation
The learner will be able to use the concept of variable to simplify expressions and obtain solutions to equations.
Strand Bloom's Scope Hours Source
Variable Application Master 2.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  

Data Interpretation

    Graphing: Apply/Technology
The learner will be able to apply suitable technology to represent and/or study data.
Strand Bloom's Scope Hours Source
Graphing Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
Unit Assessment Resources
- Facts Practice Test A, 100 Addition Facts, Saxon Math, Second, printable graph paper [Work Books].   http://geolab.seweb.uci.edu/graphing.phtml
  
    Graphs: Draw/Interpret
The learner will be able to draw and/or interpret graphs which model real world phenomena.
Strand Bloom's Scope Hours Source
Graphing Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
Instructional Resources
- gamequariam, graph interperation [On-line].  http://www.gamequarium.com/data.html
Unit Assessment Resources
- Facts Practice Test A, 100 Addition Facts, Saxon Math, Second, printable graph paper [Work Books].   http://geolab.seweb.uci.edu/graphing.phtml
  

Geometry

    Figures: Illustrate Understanding
The learner will be able to illustrate a comprehension of the properties and construction of geometric figures including angles, parallel lines, perpendicular lines, triangles, circles, and quadrilaterals.
Strand Bloom's Scope Hours Source
Figures Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Problem Solving: Applying Concepts
The learner will be able to apply learned geometry concepts in solving problems.
Strand Bloom's Scope Hours Source
Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Problem Solving: Properties/Formulas
The learner will be able to use geometric relationships, properties, and formulas to obtain solutions to real world problems.
Strand Bloom's Scope Hours Source
Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Circle: Understand Pi
The learner will be able to illustrate an understanding of pi.
Strand Bloom's Scope Hours Source
Circles Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
Instructional Resources
- circles, area & perimeter [On-line].  http://gomath.com/geometry/circle.php
  
    Spatial Thinking: Describe Position
The learner will be able to describe position using spatial sense with two-dimensional coordinate systems.
Strand Bloom's Scope Hours Source
Spatial Thinking Comprehension Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  

Measurement

    Problem Solving: Geometric
The learner will be able to use measurement ideas and relationships in geometric problem solving situations.
Strand Bloom's Scope Hours Source
Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
Instructional Resources
- gomath, triangle [On-line].  http://gomath.com/geometry/triangle.php
- gomath, parallelgram [online].  http://gomath.com/geometry/parallelogram.php
- gomath, trapezoid [On-line].  http://gomath.com/geometry/trapezoid.php
- gomath, rectangle [On-line].  http://gomath.com/geometry/rectangle.php
- gomath, square [On-line].  http://gomath.com/geometry/square.php
  
    Area/Volume: Length/Problems
The learner will be able to apply the ideas of length, area, and volume to approximate and solve real world problems with focus on parallelograms, triangles, right rectangular prisms, circles, and right cylinders.
Strand Bloom's Scope Hours Source
Perimeter/Area/Volume Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
  
    Measurement: Estimation/Computation
The learner will be able to describe the concepts and methods applied in estimation, measurement, and computation.
Strand Bloom's Scope Hours Source
Measurement: Estimation Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
  

Number Theory

    Connecting: Rational Numbers
The learner will be able to connect physical, graphical, verbal, and symbolic illustrations of rational numbers.
Strand Bloom's Scope Hours Source
Connecting Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
  
    Number Systems: Illustrate Understanding
The learner will be able to illustrate understanding of the subsets, elements, properties, and operations of the rational number system.
Strand Bloom's Scope Hours Source
Number Systems Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
Instructional Resources
- Purple Math, number systems [On-line].  http://purplemath.com/modules/numtypes.htm
  
    Number Forms: Apply/Notation
The learner will be able to apply mathematical notations appropriately.
Strand Bloom's Scope Hours Source
Number Forms Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
Instructional Resources
- purple math, GCF & LCM [online].  http://purplemath.com/modules/lcm_gcf.htm
- math.com, GCF [On-line].  http://www.math.com/school/subject1/lessons/S1U3L2GL.html
- math.com, LCM [On-line].  http://www.math.com/school/subject1/lessons/S1U3L3GL.html
  
    Number Theory Concepts: Apply
The learner will be able to use number theory concepts in mathematical problem scenarios.
Strand Bloom's Scope Hours Source
Number Theory Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
Instructional Resources
- math.com, ratios & proportions [online].  http://www.math.com/school/subject1/lessons/S1U2L1GL.html
  
    Number Theory: Problem Solving
The learner will be able to use number theory concepts to solve problems.
Strand Bloom's Scope Hours Source
Number Theory Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  

Numeration

    Number Lines: Describe Position
The learner will be able to apply spatial sense to describe position and to represent operations.
Strand Bloom's Scope Hours Source
Number Lines Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Patterns: Spatial/Identify/Continue/Make
The learner will be able to identify, continue, and/or make spatial patterns.
Strand Bloom's Scope Hours Source
Patterns: Identify/Describe/Continue Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
Instructional Resources
- patternmania, sequencing [On-line].  http://primarygames.com/patterns/start.htm
  
    Patterns: Number/Identify
The learner will be able to identify number patterns.
Strand Bloom's Scope Hours Source
Patterns: Number Knowledge Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Patterns: Number/Create
The learner will be able to create patterns using numbers.
Strand Bloom's Scope Hours Source
Patterns: Number Synthesis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Patterns: Number/Extend
The learner will be able to extend patterns of numbers.
Strand Bloom's Scope Hours Source
Patterns: Number Synthesis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Patterns: Geometric/Identify
The learner will be able to identify geometric patterns.
Strand Bloom's Scope Hours Source
Patterns: Geometric Knowledge Master 0.5 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Patterns: Geometric/Extend/Make
The learner will be able to extend and make geometric patterns.
Strand Bloom's Scope Hours Source
Patterns: Geometric Synthesis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Estimation Strategies: Predicting
The learner will be able to apply estimation strategies to forecast computational results.
Strand Bloom's Scope Hours Source
Estimation Strategies Application Master 2.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  

Percents

    Problem Solving: Real World
The learner will be able to illustrate an understanding of percent in obtaining solutions to real world problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
Instructional Resources
- Purple Math, percent-fractions-decimals [On-line].  http://purplemath.com/modules/percents.htm
Unit Instructional Resources
- math.com, percents [On-line].  http://www.math.com/school/subject1/lessons/S1U1L7GL.html
  

Probability/Statistics

    Problem Solving: Application
The learner will be able to use the ideas of probability and statistics in many different problem solving contexts.
Strand Bloom's Scope Hours Source
Problem Solving Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Graphing: Select/Create/Study
The learner will be able to select, create, and study suitable graphical illustrations for a set of data including pie charts, histograms, stem and leaf plots, scatterplots and/or box and whisker plots.
Strand Bloom's Scope Hours Source
Graphing Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Measure of Central Tendency: Interpret
The learner will be able to interpret a group of data using the suitable measure of central tendency.
Strand Bloom's Scope Hours Source
Measures of Central Tendency Analysis Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
Instructional Resources
- statistics, Mean-Median-Mode [On-line].  http://www.robertniles.com/stats/mean.shtml
  
    Simulations: Approximate Probability
The learner will be able to approximate probability using simulations.
Strand Bloom's Scope Hours Source
Event Simulation Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
Instructional Resources
- math goodies, probability [On-line].  http://www.mathgoodies.com/lessons/vol6/intro_probability.html
  
    Data Management: Technology
The learner will be able to use suitable technology to collect data.
Strand Bloom's Scope Hours Source
Data Management Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  

Problem Solving

    Investigations: Individual/Groups
The learner will be able to explore problems individually or in cooperative groups.
Strand Bloom's Scope Hours Source
Investigations Master TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
Unit Instructional Resources
- Problem solving steps, problem solving steps and examples [On-line].  http://www2.hawaii.edu/suremath/intro_algebra.html
- I can't do word word problems, 3 step problem solving process [On-line].  http://www2.hawaii.edu/suremath/mathTopics.html
- Request-Response-Result, request-response-result techinque [On-line].  http://www2.hawaii.edu/suremath/essentialRRR.html
  
    Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.
Strand Bloom's Scope Hours Source
Solution Evaluation Master 1.5 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19, p. 20
Unit Instructional Resources
- Problem solving steps, problem solving steps and examples [On-line].  http://www2.hawaii.edu/suremath/intro_algebra.html
- I can't do word word problems, 3 step problem solving process [On-line].  http://www2.hawaii.edu/suremath/mathTopics.html
- Request-Response-Result, request-response-result techinque [On-line].  http://www2.hawaii.edu/suremath/essentialRRR.html
  

Rational and Irrational Numbers

    Problem Solving: Rational/Real World
The learner will be able to use rational numbers in real world scenarios.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 0.5 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
  

Technology

    Problem Solving: Technology
The learner will be able to appropriately use technology to solve problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 19
  

Whole Numbers

    Subtraction Story Problems: Regrouping
The learner will be able to solve real world story problems by determining that subtraction is needed to solve the problems, regrouping, and subtracting the appropriate numbers.
Strand Bloom's Scope Hours Source
Subtraction Story Problems Application Master 1.0 TN: Curriculum Framework (9-12), January 30, 1998, Foundations I, p. 20
  
    Add or subtract whole numbers
The learner will be able to use appropriate technology to add or subtract whole numbers.
Strand Bloom's Scope Hours Source
Add/Subtract Whole Numbers Master 2.0 Jefferson County Schools(a)
Instructional Resources
- math.com, add & sub integers [On-line].  http://www.math.com/school/subject1/lessons/S1U1L11GL.html
  
    Multiply or divide whole numbers
The learner will be able to use appropriate technology to multiply or divide whole numbers.
Strand Bloom's Scope Hours Source
Add Whole Numbers Master 2.0 Jefferson County Schools(a)
Instructional Resources
- math.com, mul & div integers [online].  http://www.math.com/school/subject1/lessons/S1U1L12GL.html
  

© 2003 by Jefferson County Schools and EdVISION Corporation.  All Rights Reserved. Made with Curriculum Designer by EdVISION Corporation.