## Description

- Overview:
- Modeling Our World with Mathematics Unit 1: Health & Fitness Topic 1 - A Healthier You!

- Subject:
- Mathematics
- Level:
- High School
- Material Type:
- Module
- Author:
- Hannah Hynes-Petty, Washington OSPI OER Project, Washington OSPI Mathematics Department, Barbara Soots
- Date Added:
- 09/29/2020

- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Format:
- Downloadable docs

## Standards

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: (+) Know and apply that the Binomial Theorem gives the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Degree of Alignment: Not Rated (0 users)

Cluster: Reason quantitatively and use units to solve problems

Standard: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*

Degree of Alignment: Not Rated (0 users)

Cluster: Perform arithmetic operations on polynomials

Standard: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand the relationship between zeros and factors of polynomial

Standard: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

Degree of Alignment: Not Rated (0 users)

Cluster: Understand the relationship between zeros and factors of polynomial

Standard: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Degree of Alignment: Not Rated (0 users)

Cluster: Use polynomial identities to solve problems

Standard: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

Degree of Alignment: Not Rated (0 users)

Cluster: Use polynomial identities to solve problems

Standard: (+) Know and apply that the Binomial Theorem gives the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)

Degree of Alignment: Not Rated (0 users)

Cluster: Rewrite rational expressions

Standard: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Degree of Alignment: Not Rated (0 users)

Cluster: Rewrite rational expressions

Standard: (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Degree of Alignment: Not Rated (0 users)

Cluster: Create equations that describe numbers or relationship

Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*

Degree of Alignment: Not Rated (0 users)

Cluster: Create equations that describe numbers or relationship

Standard: Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*

Degree of Alignment: Not Rated (0 users)

Cluster: Create equations that describe numbers or relationship

Standard: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.*

Degree of Alignment: Not Rated (0 users)

Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Standard: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Standard: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve equations and inequalities in one variable

Standard: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Degree of Alignment: Not Rated (0 users)

Cluster: Represent and solve equations and inequalities graphically

Standard: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Degree of Alignment: Not Rated (0 users)

Cluster: Understand the concept of a function and use function notation.

Standard: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Degree of Alignment: Not Rated (0 users)

Cluster: Understand the concept of a function and use function notation.

Standard: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Degree of Alignment: Not Rated (0 users)

Cluster: Interpret functions that arise in applications in terms of the context

Standard: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

Degree of Alignment: Not Rated (0 users)

Cluster: Interpret functions that arise in applications in terms of the context

Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

Degree of Alignment: Not Rated (0 users)

Cluster: Interpret functions that arise in applications in terms of the context

Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze functions using different representations

Standard: Graph linear and quadratic functions and show intercepts, maxima, and minima.*

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze functions using different representations

Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Degree of Alignment: Not Rated (0 users)

Cluster: Build a function that models a relationship between two quantities

Standard: Write a function that describes a relationship between two quantities.*

Degree of Alignment: Not Rated (0 users)

Cluster: Summarize, represent, and interpret data on a single count or measurement variable

Standard: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).*

Degree of Alignment: Not Rated (0 users)

Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Standard: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*

Degree of Alignment: Not Rated (0 users)

Cluster: Interpret linear models

Standard: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.*

Degree of Alignment: Not Rated (0 users)

Cluster: Interpret linear models

Standard: Distinguish between correlation and causation.*

Degree of Alignment: Not Rated (0 users)

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# Tags (3)

- Modeling Our World With Mathematics
- Washington Office of Superintendent of Public Instruction
- wa-math

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