observe, describe, and illustrate the Sun, Moon, stars, and objects in the sky such as clouds.

construct null and alternative hypothesis statements about a population parameter;

Earth and space. The student knows that the natural world includes earth materials and systems that can be observed. The student is expected to:

explain the meaning of the p-value in relation to the significance level in providing evidence to reject or fail to reject the null hypothesis in the context of the situation;

describe and classify rocks by the observable properties of size, shape, color, and texture;

interpret the results of a hypothesis test using technology-generated results such as large sample tests for proportion, mean, difference between two proportions, and difference between two independent means; and

observe and describe weather changes from day to day and over seasons; and

identify evidence that supports the idea that air is all around us and demonstrate that wind is moving air using items such as a windsock, pinwheel, or ribbon.

describe the potential impact of Type I and Type II Errors.

The student is expected to observe and generate examples of practical uses for rocks, soil, and water.

Bivariate data. The student applies the mathematical process standards to analyze relationships among bivariate quantitative data. The student is expected to:

Organisms and environments. The student knows that plants and animals depend on the environment to meet their basic needs for survival. The student is expected to:

analyze scatterplots for patterns, linearity, outliers, and influential points;

observe and identify the dependence of plants on air, sunlight, water, nutrients in the soil, and space to grow; and

transform a linear parent function to determine a line of best fit;

compare different linear models for the same set of data to determine best fit, including discussions about error;

observe and identify the dependence of animals on air, water, food, space, and shelter.

compare different methods for determining best fit, including median-median and absolute value;

Organisms and environments. The student knows that organisms resemble their parents and have structures and undergo processes that help them interact and survive within their environments. The student is expected to:

describe the relationship between influential points and lines of best fit using dynamic graphing technology; and

identify the structures of plants, including roots, stems, leaves, flowers, and fruits;

identify and interpret the reasonableness of attributes of lines of best fit within the context, including slope and y-intercept.

identify the different structures that animals have that allow them to interact with their environment such as seeing, hearing, moving, and grasping objects;

identify and record the changes from seed, seedling, plant, flower, and fruit in a simple plant life cycle; and

identify ways that young plants resemble the parent plant.

Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

apply mathematics to problems arising in everyday life, society, and the workplace;

use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

create and use representations to organize, record, and communicate mathematical ideas;

analyze mathematical relationships to connect and communicate mathematical ideas; and

display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Patterns and structure. The student applies mathematical processes to connect finite differences or common ratios to attributes of functions. The student is expected to:

determine the patterns that identify the relationship between a function and its common ratio or related finite differences as appropriate, including linear, quadratic, cubic, and exponential functions;

classify a function as linear, quadratic, cubic, and exponential when a function is represented tabularly using finite differences or common ratios as appropriate;

determine the function that models a given table of related values using finite differences and its restricted domain and range; and

determine a function that models real-world data and mathematical contexts using finite differences such as the age of a tree and its circumference, figurative numbers, average velocity, and average acceleration.

Patterns and structure. The student applies mathematical processes to understand the connections among representations of functions and combinations of functions, including the constant function, \(f(x) = x\), \(f(x) = x^2\), \(f(x) = \sqrt{x}\), \(f(x) = 1/x\), \(f(x) = x^3\), \(f(x) = \sqrt[3]{x}\), \(f(x) = bx\), \(f(x) = |x|\), and \(f(x) = log_b (x)\) where \(b\) is 10 or \(e\); functions and their inverses; and key attributes of these functions. The student is expected to:

compare and contrast the key attributes, including domain, range, maxima, minima, and intercepts, of a set of functions such as a set comprised of a linear, a quadratic, and an exponential function or a set comprised of an absolute value, a quadratic, and a square root function tabularly, graphically, and symbolically;

Scientific and engineering practices. The student asks questions, identifies problems, and plans and safely conducts classroom, laboratory, and field investigations to answer questions, explain phenomena, or design solutions using appropriate tools and models. The student is expected to:

compare and contrast the key attributes of a function and its inverse when it exists, including domain, range, maxima, minima, and intercepts, tabularly, graphically, and symbolically;

ask questions and define problems based on observations or information from text, phenomena, models, or investigations;

verify that two functions are inverses of each other tabularly and graphically such as situations involving compound interest and interest rate, velocity and braking distance, and Fahrenheit-Celsius conversions;

use scientific practices to plan and conduct simple descriptive investigations and use engineering practices to design solutions to problems;

represent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations such as combining a 20% discount and a 6% sales tax on a sale to determine \(h(x)\), the total sale, \(f(x) = 0.8x\), \(g(x) = 0.06(0.8x)\), and \(h(x) = f(x) + g(x)\);

identify, describe, and demonstrate safe practices during classroom and field investigations as outlined in Texas Education Agency-approved safety standards;

model a situation using function notation when the output of one function is the input of a second function such as determining a function \(h(x) = g(f(x)) = 1.06(0.8x)\) for the final purchase price, \(h(x)\) of an item with price \(x\) dollars representing a 20% discount, \(f(x) = 0.8x\) followed by a 6% sales tax, \(g(x) = 1.06x\); and

use tools, including hand lenses, goggles, heat-resistant gloves, trays, cups, bowls, beakers, sieves/sifters, tweezers, primary balance, notebooks, terrariums, aquariums, stream tables, soil samples (loam, sand, gravel, rocks, and clay), seeds, plants, windsock, pinwheel, student thermometer, demonstration thermometer, rain gauge, straws, ribbons, non-standard measuring items, flashlights, sandpaper, wax paper, items that are magnetic, non-magnetic items, a variety of magnets, hot plate, aluminum foil, Sun-Moon-Earth model, and plant and animal life cycle models to observe, measure, test, and compare;

compare and contrast a function and possible functions that can be used to build it tabularly, graphically, and symbolically such as a quadratic function that results from multiplying two linear functions.