Cryptology & Mathematics: Secret Codes & Number Secrets
Course Objectives

Cryptology & Mathematics: Secret Codes & Number Secrets, is a unit designed for gifted students in fourth through sixth grade. This gifted curriculum provides a range of skill development opportunities, from novice gifted to advanced gifted students.

These course objectives are taken from the National Council of Teachers of Mathematics (NCTM) Standards for Mathematics and North Carolina Standard Course of Study, NC Department of Public Instruction and serve as specific reference points for national and state mathematics standards.

NCTM Standards for Mathematics

NC Standard Course of Study: Mathematics

# NCTM Standards for Mathematics

### Number and Operations Standard for Grades 3–12

Students should

• understand numbers, ways of representing numbers, relationships among numbers, and number systems;
• understand meanings of operations and how they relate to one another;
• compute fluently and make reasonable estimates;
• understand various meanings of multiplication and division;
• understand the effects of multiplying and dividing whole numbers;
• describe classes of numbers according to characteristics such as the nature of their factors;
• use number-theory arguments to justify relationships involving whole numbers;
• represent the idea of a variable as an unknown quantity using a letter or a symbol.

### Algebra Standard for Grades 3-12

Students should

• Understand patterns, relations, and functions.

### Problem Solving Standard for Grades 3-12

Students should

• build new mathematical knowledge through problem solving,
• 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.

### Geometry Standards for Grades 3-12

Students should

• describe a motion or a series of motions that will show that two shapes are congruent,
• use geometric models to solve problems in other areas of mathematics, such as number and measurement.

### Reasoning and Proof Standards for Grades 3-12

Students should

• Make and investigate mathematical conjectures.

### Communication Standards for Grades 3-12

Students should

• organize and consolidate their mathematical thinking through communication;
• communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
• analyze and evaluate the mathematical thinking and strategies of others;
• use the language of mathematics to express mathematical ideas precisely.

### Connections Standards for Grades 3-12

Students should

• recognize and use connections among mathematical ideas,
• recognize and apply mathematics in contexts outside of mathematics.

### Representation Standards for Grades 3-12

• Use representations to model and interpret physical, social, and mathematical phenomena.

# NC Standard Course of Study

### Sixth-Grade Mathematics, Competency Goal 1: The learner will understand and compute with rational numbers.

1.04     Students will develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.

• Analyze computational strategies
• Describe the effect of operations on size
• Estimate the results of computations
• Judge the reasonableness of solutions

1.05     Students will develop fluency in the use of factors, multiples, exponential notation, and prime factorization.

1.07     Students will develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

### Sixth-Grade Mathematics, Competency Goal 5: The learner will demonstrate an understanding of simple algebraic expressions.

5.01     Students will simplify algebraic expressions and verify the results using the basic properties of rational numbers.

• Distributive
• Order of operations

5.02     Students will use and evaluate algebraic expressions.

5.03     Students will solve simple (one- and two-step) equations or inequalities.

### Seventh-Grade Mathematics, Competency Goal 5: The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.

5.04     Develop fluency in the use of formulas to solve problems

Eight- Grade Mathematics, Competency Goal 4: The learner will understand and use graphs and data analysis.

4.01     Collect, organize, analyze, and display data  (including scatterplots) to solve problems

4.03     Identify misuses of statistical and numerical data

### Eighth Grade Mathematics, Competency Goal 5: The learner will understand and use linear relations and functions.

5.04     Solve equations using the inverse relationships of addition and subtraction, multiplication and division, and squares and square roots

### Other Mathematical Objectives, Adapted from NCSCOS:

Students should

• understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
• identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems;
• understand and use properties of operations, such as the distributivity of multiplication over addition;
• use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals;
• understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems;
• Use factors, multiples, prime factorization, and relatively prime numbers to solve problems;
• describe, extend, and make generalizations about geometric and numeric patterns;
• express mathematical relationships using equations;
• recognize and generate equivalent forms for simple algebraic expressions and solve linear equations;
• investigate how a change in one variable relates to a change in a second variable;
• investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
• predict and describe the results of sliding, flipping, and turning two-dimensional shapes;
• design investigations to address a question and consider how data-collection methods affect the nature of the data set;
• collect data using observations, surveys, and experiments;
• represent data using tables and graphs such as line plots, bar graphs, and line graphs;
• describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed;
• propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions;
• Apply and adapt a variety of appropriate strategies to solve problems;
• Create and use representations to organize, record, and communicate mathematical ideas.