# Implement the design.

## Definition

Implementation should include- creating a model or prototype for the chosen solution to the design problem, using appropriate materials and processes
- determining the objectives for an engineering test of the solution
- testing the solution, using mathematical, conceptual, and/or physical modeling, simulating, and optimizing
- evaluating the test results.

## Process/Skill Questions

- Why should testing be considered before creating a model or prototype?
- How might one use a mathematical model to test a solution?
- What steps need to be taken if the model does not pass the engineering test?

## Related Standards of Learning

## English

### 11.5

The student will read, interpret, analyze, and evaluate a variety of nonfiction texts including employment documents and technical writing.

- Apply information from texts to clarify understanding of concepts.
- Read and correctly interpret an application for employment, workplace documents, or an application for college admission.
- Analyze technical writing for clarity.
- Paraphrase and synthesize ideas within and between texts.
- Draw conclusions and make inferences on explicit and implied information using textual support.
- Analyze multiple texts addressing the same topic to determine how authors reach similar or different conclusions.
- Analyze false premises, claims, counterclaims, and other evidence in persuasive writing.
- Recognize and analyze use of ambiguity, contradiction, paradox, irony, sarcasm, overstatement, and understatement in text.
- Generate and respond logically to literal, inferential, evaluative, synthesizing, and critical thinking questions about the text(s).

### 12.5

The student will read, interpret, analyze, and evaluate a variety of nonfiction texts.

- Use critical thinking to generate and respond logically to literal, inferential, and evaluative questions about the text(s).
- Identify and synthesize resources to make decisions, complete tasks, and solve specific problems.
- Analyze multiple texts addressing the same topic to determine how authors reach similar or different conclusions.
- Recognize and analyze use of ambiguity, contradiction, paradox, irony, overstatement, and understatement in text.
- Analyze false premises claims, counterclaims, and other evidence in persuasive writing.

## Mathematics

### AFDA.1

The student will investigate and analyze linear, quadratic, exponential, and logarithmic function families and their characteristics. Key concepts include

- domain and range;
- intervals in which the function is increasing or decreasing;
- absolute maxima and minima;
- zeros;
- intercepts;
- values of a function for elements in its domain;
- connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs;
- end behavior; and
- vertical and horizontal asymptotes.

### AFDA.2

The student will use knowledge of transformations to write an equation, given the graph of a linear, quadratic, exponential, and logarithmic function .

### AFDA.3

The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems using models of linear, quadratic, and exponential functions.

### AFDA.4

The student will use multiple representations of functions for analysis, interpretation, and prediction.

### AII.3

The student will solve

- absolute value linear equations and inequalities;
- quadratic equations over the set of complex numbers;
- equations containing rational algebraic expressions; and
- equations containing radical expressions.

### AII.6

For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will

- recognize the general shape of function families; and
- use knowledge of transformations to convert between equations and the corresponding graph of functions.

### AII.7

The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include< /br>

- domain, range, and continuity;
- intervals in which a function is increasing or decreasing;
- extrema;
- zeros;
- intercepts;
- values of a function for elements in its domain;
- connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs;
- end behavior;
- vertical and horizontal asymptotes;
- inverse of a function; and
- composition of functions algebraically and graphically.

### AII.8

The student will investigate and describe the relationships among solutions of an equation, zeros of a function,

*x-*intercepts of a graph, and factors of a polynomial expression.### AII.9

The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear, quadratic, and exponential functions.

### AII.10

The student will represent, create, and solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

### COM.1

The student will design and apply computer programs to solve practical problems in mathematics arising from business and applications in mathematics.

### COM.4

The student will design an algorithm to solve a given problem.

### COM.6

The student will translate mathematical expressions into programming expressions by declaring variables, writing assignment statements, and using the order of operations.

### COM.8

The student will implement conditional statements that include “if/then” statements, “if/then/else” statements, case statements, and Boolean logic.

### COM.14

The student will select and implement appropriate data structures, including arrays (one- and/or two-dimensional) and objects.

### COM.15

The student will define and use appropriate variable data types that include integer, real (fixed and scientific notation), character, string, Boolean and object.

### COM.17

The student will test a program using an appropriate set of data. The test data should include boundary cases and test all branches of a program.

### MA.2

The student will investigate and identify the characteristics of exponential and logarithmic functions to graph the function, solve equations, and solve practical problems.

### MA.3

The student will apply compositions of functions and inverses of functions to practical situations and investigate and verify the domain and range of resulting functions.

### MA.7

The student will perform operations with vectors in the coordinate plane and solve practical problems using vectors.

### MA.10

The student will use parametric equations to model and solve practical problems.

### MA.11

The student will use matrices to organize data and will add and subtract matrices, multiply matrices, multiply matrices by a scalar, and use matrices to solve systems of equations.