MATH 2030 – Content Standards

Title: Principles of Mathematics

Course Content Standards
The following standards are offered as guidelines for assessing student progress, judging the effectiveness of instructional programs and developing curricular units. Theses standards describe what a student should be able to demonstrate at the completion of the course.

Problem solving

Students will be able to apply and adapt a variety of appropriate strategies to solve problems including:

  • Solve problems that arise in mathematics and in other contexts.
  • Apply and adapt a variety of appropriate strategies to solve problems
  • Monitor and reflect on the process of mathematical problem solving
  • Construct number meanings through real-world experiences and the use of physical materials.
  • Relate the mathematical language and symbolism of operations to problem situations and informal language.
  • Interpret the multiple uses of numbers encountered in the real world.
  • Develop meaning for the basic operations by modeling and discussing a rich variety of problem situations.
  • Relate the mathematical language and symbolism of operations to problem situations and informal language.
  • Estimate and judge reasonableness of numerical results.
  • Relate mathematical symbols to mathematical ideas.
  • Relate subtraction to addition.
  • Recognize, extend, and create patterns.
  • Explore the use of variables and open sentences to express relations.
  • Extend the number system to fractions and decimals.
  • Relate algebraic ideas to geometric representations.
  • Relate multiplication to addition, arrays, and Cartesian products.
  • Relate division to subtraction and multiplication.
  • Explore the use of variables and open sentences to express relations.
  • Use models to represent mathematical ideas.
  • Represent situations and number patterns with tables, graphs, and verbal rules.
  • Use models to represent mathematical ideas.
  • Represent situations and number patterns with tables, graphs and verbal rules.
  • Understand the concepts of variable, expression, and equation.
  • Formalize situations and number patterns with tables, graphs, verbal rule, and equations and explore the interrelationships of those representations.
  • Analyze tables and graphs to identify properties and relationships.
  • Solve linear equations using concrete, informal, and formal methods.
  • Investigate inequalities and nonlinear equations informally.
  • Apply algebraic methods to solve a variety of mathematical problems.

Sets, Functions, and Reasoning

Students will be able to develop an understanding of sets and should represent, analyze and generalize a variety of patterns and functions using words, tables and graphs including:

  • Construct number meanings through real-world experiences and the use of physical materials.
  • Relate the mathematical language and symbolism of operations to problem situations and informal language.
  • Interpret the multiple uses of numbers encountered in the real world.
  • Develop meaning for the basic operations by modeling and discussing a rich variety of problem situations.
  • Relate the mathematical language and symbolism of operations to problem situations and informal language.
  • Estimate and judge reasonableness of numerical results.
  • Identify, describe, and draw lines, line segments, lines of symmetry, rays, angles, and parallel and perpendicular lines.
  • Relate numbers to points on a line.
  • Understand betweeness, closeness, rounding, and approximating.
  • Understand closeness, rounding, and approximating.
  • Recognize and describe mathematical relations and functions.
  • Explore concepts of operational inverses.
  • Expand the number system.
  • Use relations and functions to solve problems.
  • Recognize and describe relations and functions.
  • Represent data in tables and graphs.
  • Exhibit relationships graphically.
  • Use Venn diagrams and truth tables in problem solving involving set theory and logic.
  • Use inductive and deductive reasoning.
  • Use counting principles.

Whole Numbers

Students will be able to develop a sense of whole numbers and represent and use them in a number of ways including:

  • Construct number meanings through real-world experiences and the use of physical materials.
  • Understand our numeration system by relating counting, grouping and place value concepts.
  • Interpret the multiple uses of numbers.
  • Develop meaning for the four basic operations.
  • Relate the mathematical language and symbolism of operations to problem situations and informal language.
  • Identify fractions using physical models, both as parts of a whole and parts of a set.
  • Construct number meanings through real world experience and the use of physical materials.
  • Understand our numeration system by relating counting, grouping and place value concepts.
  • Interpret the multiple uses of numbers encountered in the real world.
  • Develop meaning for the basic operations by modeling and discussing a rich variety of problem situations.
  • Relate the mathematical language and symbolism of operations to problem situations and informal language.
  • Develop, represent, and use order relations for whole numbers, fractions and decimals (rational numbers) and integers.
  • Apply the basic operations to integers.
  • Understand how the basic arithmetic operations are related to one another.
  • Develop and use fractional exponents, negative exponents, and radicals.
  • Estimate and judge reasonableness of numerical results.

Number Theory

Students will be able to develop number theory concepts including:

  1. Construct number meanings through real world experience and the use of physical materials.
  2. Develop and apply number theory concepts (e.g., primes, factors, and multiples) in real-world and mathematical problem situations.
  3. Develop meaning for the basic operations by modeling and discussing a rich variety of problem situations.
  4. Estimate, and judge reasonableness of numerical results.
  5. Identify and Use Divisibility Tests
  6. Identify and Use Greatest Common Factors
  7. Identify and Use Least Common Multiples
  8. Interpret the multiple uses of numbers encountered in the real world.
  9. Investigate whether numbers are odd or even, prime or composite.
  10. Recognize, extend, and create patterns.
  11. Relate the mathematical language and symbolism of operations to problem situations and informal language.
  12. Use models to represent mathematical ideas.

Integers and Fractions

Students will be able to develop a sense of integers and fractions and use them in a number of ways, including:

  1. Apply operations for the real number systems to a variety of mathematical situations.
  2. Apply the basic operations to integers.
  3. Apply understanding of whole number operations to fractions.
  4. Compare numbers to each other in terms of greater than, less than, or equal to and explore different representations of the same number.
  5. Construct number meanings through real world experience and the use of physical materials.
  6. Develop concepts of fractions and mixed numbers.
  7. Develop meaning for the basic operations by modeling and discussing a rich variety of problem situations.
  8. Develop, represent, and use order relations for whole numbers, fractions (rational numbers) and integers.
  9. Estimate, and judge reasonableness of numerical results.
  10. Expand the number system.
  11. Explore concepts of operational inverses.
  12. Identify fractions using physical models, both as parts of a whole and parts of a set.
  13. Interpret the multiple uses of numbers encountered in the real world.
  14. Investigate relationships among fractions, decimals, and percents.
  15. Perform arithmetic operations with rational numbers.
  16. Recognize, extend, and create patterns.
  17. Relate division to subtraction and multiplication.
  18. Relate mathematical symbols to mathematical ideas.
  19. Relate numbers to points on a line.
  20. Relate subtraction to addition.
  21. Relate the mathematical language and symbolism of operations to problem situations and informal language.
  22. Understand and apply ratios, proportions to a wide variety of situations.
  23. Understand and appreciate the need for numbers beyond the whole numbers.
  24. Understand betweeness, closeness, rounding, and approximating.
  25. Use models to represent mathematical ideas.

Decimals, Rational and Irrational Numbers

Students will be able to develop a sense of decimals, rational numbers and irrational numbers and use them in a number of ways, including:

  1. Apply fractions and decimals to problem situations, including money.
  2. Apply operations for the real number systems to a variety of mathematical situations.
  3. Apply understanding of whole number operations to fractions and decimals.
  4. Compare numbers to each other in terms of greater than, less than, or equal to and explore different representations of the same number.
  5. Construct number meanings through real world experience and the use of physical materials.
  6. Develop and use fractional exponents, negative exponents, radicals.
  7. Develop concepts of fractions and decimals with standard symbols.
  8. Develop concepts of fractions, mixed numbers and decimals.
  9. Develop meaning for the basic operations by modeling and discussing a rich variety of problem situations.
  10. Develop the real number system.
  11. Develop, represent, and use order relations for whole numbers, fractions and decimals (rational numbers) and integers.
  12. Estimate, and judge reasonableness of numerical results.
  13. Explore concepts of operational inverses.
  14. Explore the properties of rational numbers
  15. Extend the number system to fractions and decimals.
  16. Interpret the multiple uses of numbers encountered in the real world.
  17. Investigate relationships among fractions, decimals, and percents.
  18. Perform arithmetic operations with real numbers.
  19. Recognize, extend, and create patterns.
  20. Relate numbers to points on a line
  21. Relate the mathematical language and symbolism of operations to problem situations and informal language.
  22. Understand the Pythagorean Theorem by relating it to rational and irrational numbers.
  23. Understand and apply ratios, proportions, and percents to a wide variety of situations.
  24. Understand and appreciate the need for numbers beyond the whole numbers.
  25. Understand betweeness, closeness, rounding, and approximating.
  26. Understand our numeration system by relating counting, grouping and place value concepts.
  27. 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.
  28. Understand our decimal system by relating grouping and place value concepts.
  29. Use percentages, orders of magnitude, ratios, and proportions to express relationships between quantities.

Statistics

Students will be able to develop an understanding of statistics and should be able to analyze data and make inferences about the real world including:

  1. Apply measures of central tendency.
  2. Apply measures of variability.
  3. Apply measures of relative standing.
  4. Collect, organize, and describe data.
  5. Construct and draw inferences from charts, tables, and graphs.
  6. Construct, read, and interpret displays of data, including picture, bar, circle, and line graphs.
  7. Construct, read, and interpret tables, charts, and graphs.
  8. Explore concepts of sampling.
  9. Formulate and solve problems that involve collecting, organizing, and analyzing data.
  10. Make inferences and convincing arguments and evaluate arguments that are based on data analysis.
  11. Recognize statistical methods and probability models as powerful decision-making tools.
  12. Understand and apply measures of central tendency, variability, and correlations.
  13. Use line fitting to predict from data.
  14. Use descriptive and inferential statistics.