Standards Addressed:

Standard 1: Students develop number sense and use numbers and number relationships in problem-solving situations and communicate with appropriate mathematical language the reasoning used in solving these problems. (Number Sense)

Key Components

In order to meet this standard, students will

1.1 construct and interpret number meanings through real-world experiences and the use of hands-on materials;
1.2 represent and use numbers in a variety of equivalent forms (for example, fractions, decimals, percents, exponents, scientific notation);
1.3 know the structure and properties of the real number system (for example, primes, factors, multiples, relationships among sets of numbers); and
1.4 use number sense, including estimation and mental arithmetic, to determine the reasonableness of solutions.

Standard 2: Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate with appropriate mathematical language the reasoning used in solving these problems. (Algebra)

Key Components

In order to meet this standard, students will

2.1 identify, describe, analyze, extend, and create a wide variety of patterns in numbers, shapes, and data;
2.2 describe patterns using mathematical language;
2.3 solve problems and represent real-world situations mathematically;
2.4 compare and contrast different types of functions; and
2.5 describe the connections among representations of patterns and functions, including words, tables, graphs, and symbols.

As students in grades 9-12 extend their knowledge, they will

A. model real-world phenomena (for example, distance versus time relationships, population growth, growth functions for diseases, growth of minimum wage, automobile insurance tables) using functions, equations, inequalities, and matrices;
B. represent functional relationships using written explanations, tables, equations, and graphs and describe the connections among these representations;

Standard 3: Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate with appropriate mathematical language the reasoning used in solving these problems. (Data Analysis)

Key Components

In order to meet this standard, students will

3.1 solve problems by systematically collecting, organizing, describing, and analyzing data using surveys, tables, charts, and graphs;
3.2 make valid inferences, decisions, and arguments based on data analysis; and
3.3 use counting techniques, experimental probability, or theoretical probability, as appropriate, to represent and solve problems involving uncertainty.

C. fit curves to scatter plots, using informal methods or appropriate technology, to determine the strength of the relationship between two data sets and to make predictions;

Standard 6: Students link concepts and procedures as they develop, use, and explain computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers in problem-solving situations and communicate with appropriate mathematical language the reasoning used in solving these problems. (Computation)

Key Components

In order to meet this standard, students will

6.1 model, explain, and use the four basic operations-addition, subtraction, multiplication, and division-in problem-solving situations;
6.2 develop, use, and analyze algorithms; and
6.3 select and apply appropriate computational techniques (for example, approximate or exact) to solve a variety of problems and determine whether the results are reasonable.

C. select and use appropriate methods (for example, mental arithmetic, estimation, paper-and-pencil, calculator, and computer) for computing with real numbers in problem-solving situations and determine whether results are reasonable.

Cross Curricular Connections:

Exponential and logistic growth patters occur in many real world situations representing the sciences and social sciences. This module includes three such examples.

Glossary:

Students need to know the meaning of

• exponential growth (when the growth of a population is proportional to the population)
• logistic growth (when the population seems to level off; there is a certain "carrying capacity")
• carrying capacity (the limit toward which a population value tends)