Students will:

• Come up with questions that need you to collect or find two sets of related data.
• Decide what variables (things you can measure) could help explain a problem or answer your questions.
• Choose a good way to collect a sample that represents the larger group, which could include randomly picking items or people to answer your question.
• Examine the connections between two sets of numerical data shown in a scatterplot.
• Draw conclusions from your analysis of the data and clearly share your findings.
• Describe why a set of data could or could not be meaningfully displayed in a scatterplot, using terms like: categorical, quantitative, univariate, bivariate, relationship between data sets, correlation, or causation. (Honors)

Given a scatterplot with a correlation that is neither linear nor quadratic, describe characteristics of the pattern. The pattern might be described by more than one function. (Honors)

Students will:

• Identify and understand the domain (input values), range (output values), zeros (where the function equals zero), slope (rate of change), and intercepts (where the graph crosses the axes) of a linear function. Also, explain what these characteristics mean in real-world situations.
• Explore and describe how changing the basic function y = x affects the slope and y-intercept of a linear function.
• Graph a linear function in two variables, both by hand and using technology, including graphs that represent real-life situations.
• Compare and explain the differences and similarities of linear functions when they are shown as equations, graphs, tables, and in real-life contexts.
• When given a table of data pairs or a scatterplot with up to 30 points, use technology to decide if a straight line or a curve best fits the relationship and find the equation for it.
• Use technology to create either a straight line or curve that best represents the data, and discuss the pros and cons of the model.
• Use the straight line model to predict outcomes and check how accurate these predictions are, including using technology to help.
• Explore what the slope (rate of change) and y-intercept (starting point) of the line mean in the given context.
• Examine the connections between two sets of numbers shown in a scatterplot.
• Draw conclusions from your analysis of the data and clearly share your findings.
• Given a restriction to the domain of a linear function in context, find the corresponding range and explain what it means in the context of the function. (Honors)

Identify the domain and range of the best fit line in the context of the problem. Given the context, explain the relationship of the domain and range and the validity of predictions. (Honors)

Students will:

• Write a linear equation or inequality with one variable to represent a real-life situation.
• Solve multi-step linear equations with one variable, including real-world problems, by using math properties like equality and real numbers.
• Solve multi-step linear inequalities with one variable and graph the solution on a number line, including real-world examples, by applying math properties like equality and inequality.
• Rearrange formulas or equations to solve for a specific variable by using equality properties.
• Determine if a linear equation with one variable has one solution, no solution, or an infinite number of solutions.
• Check possible solutions for multi-step linear equations and inequalities using algebra, graphs, and technology to ensure the answers make sense. Explain the method used and interpret the solutions for real-world problems.
• Solve problems using an equation or inequality where the variable in a contextual situation can be defined in different ways; compare and contrast the equation/inequality, solution, and interpretation of the solution based on the definition of the variable. (Honors)
• Compare and contrast different but equivalent solutions to literal equations. Describe situations in which different forms might be most useful. (Honors)

Justify a method of solving an equation or inequality (including compound inequalities) using the properties of real numbers, the properties of equality, and the properties of inequalities. (Honors)

Students will:

• Create two linear equations with two variables that represent a real-world situation.
• Use math rules and equality properties to solve a system of two linear equations with two variables, both by hand and on a graph.
• Determine if a system of two linear equations has one solution, no solution, or an infinite number of solutions.
• Create a linear inequality with two variables to represent a real-world situation.
• Show the solution to a linear inequality with two variables on a graph.
• Create two linear inequalities with two variables to represent a real-world situation.
• Show the solution set for a system of two linear inequalities with two variables on a graph.
• Check possible solutions for a system of two linear equations, a linear inequality with two variables, or a system of two linear inequalities by using algebra, graphing, or technology. Explain the solution process and interpret the solutions in real-life contexts.
• Solve a system of equations with 3 lines. Verify the solution to the system. (Honors)

Solve a system of equations with 3 variables using both reasoning and algebraic methods. (Honors)

Students will:

• Create two linear equations with two variables that represent a real-world situation.
• Use math rules and equality properties to solve a system of two linear equations with two variables, both by hand and on a graph.
• Determine if a system of two linear equations has one solution, no solution, or an infinite number of solutions.
• Create a linear inequality with two variables to represent a real-world situation.
• Show the solution to a linear inequality with two variables on a graph.
• Create two linear inequalities with two variables to represent a real-world situation.
• Show the solution set for a system of two linear inequalities with two variables on a graph.
• Check possible solutions for a system of two linear equations, a linear inequality with two variables, or a system of two linear inequalities by using algebra, graphing, or technology. Explain the solution process and interpret the solutions in real-life contexts.
• Solve a system of equations with 3 lines. Verify the solution to the system. (Honors)

Solve a system of equations with 3 variables using both reasoning and algebraic methods. (Honors)

Students will:

• Translate real-world situations into algebraic expressions and vice versa.
• Evaluate algebraic expressions that include absolute values, square roots, and cube roots when given specific values to replace the variables, without needing to simplify the denominator.
• Explore patterns to understand and explain the laws of exponents, including multiplying, dividing, and raising powers of numbers.
• Simplify and find equivalent expressions with multiple variables and ratios of monomials using the laws of exponents.
• Simplify and find equivalent radical expressions, such as square roots of whole numbers, in their simplest form.
• Simplify and find equivalent radical expressions, like cube roots of integers.
• Add, subtract, and multiply square and cube roots in numeric expressions.
• Create and justify equivalent numerical expressions for radicals using rational exponents, limited to exponents of 1/2 and 1/3 (e.g., √5 = 5^(1/2), √(8^3) = 8^(1/3) = (2^3)^(1/3) = 2).
• Solve equations with variables in the exponent, limit to expressions on each side of the equation that will simplify to the same base. (Honors)
• Compare and contrast different methods of simplifying square roots and cube roots of numerical expressions; describe orally and/or in writing when different methods are efficient. Include square roots and cube roots of algebraic expressions when comparing and contrasting. (Honors)
• Simplify a radical by rationalizing an irrational monomial denominator. (Honors)

Describe how the laws of exponents can be used to decompose a fractional power with a denominator of 2 or 3 and generate equivalent expressions. (Honors)

Students will:

• Determine and identify the domain (all possible x-values), range (all possible y-values), zeros (where the function crosses the x-axis), slope, and intercepts of a linear function, whether it's presented as an equation or a graph. Understand what these characteristics mean in real-world situations.
• Write the equation of a line that is parallel or perpendicular to a given line and passes through a specific point.
• Graph a linear function with two variables, using technology if needed, including situations that relate to real-world examples.
• Given an algebraic or graphical representation of a linear function, find the value of f(x) for any given x in the domain, and find the value of x when given any value of f(x) in the range.
• Compare and contrast linear functions when they are represented in different forms, such as algebraic equations, graphs, tables, or real-world situations.
• Given a pictorial representation of a pattern, represent the pattern with a function; justify the symbolic representation of the function by connecting parts of the function with the pictorial representations (Honors)

Determine the curve of best fit using an exponential function. (Honors)

Students will:

• Find the sum and difference of polynomial expressions in one variable by using different methods, including hands-on objects, pictures, and symbolic models.
• Find the product of polynomial expressions in one variable using different methods, such as hands-on objects, pictures, symbolic models, the distributive property, and area models. The expressions should have no more than five terms.
• Completely factor first- and second-degree polynomials in one variable with whole number coefficients. After factoring out the greatest common factor (GCF), the leading coefficients should have no more than four factors.
• Find the quotient when dividing polynomials by a monomial or binomial divisor, or a completely factored divisor.
• Show that quadratic expressions are equal, using different methods like hands-on models, verbal explanations, symbolic forms, and graphs.
•  Factor completely first- and second-degree polynomials in two variables. (Honors)

Factor completely third- and fourth-degree polynomials that can be factored using other methods. (Honors)

Students will:

• Find the sum and difference of polynomial expressions in one variable by using different methods, including hands-on objects, pictures, and symbolic models.
• Find the product of polynomial expressions in one variable using different methods, such as hands-on objects, pictures, symbolic models, the distributive property, and area models. The expressions should have no more than five terms.
• Completely factor first- and second-degree polynomials in one variable with whole number coefficients. After factoring out the greatest common factor (GCF), the leading coefficients should have no more than four factors.
• Find the quotient when dividing polynomials by a monomial or binomial divisor, or a completely factored divisor.
• Show that quadratic expressions are equal, using different methods like hands-on models, verbal explanations, symbolic forms, and graphs.
• Solve quadratic equations (equations that involve squaring a number) by completing the square. (Honors)
• Compare different methods for solving the same quadratic equation, check the solutions for accuracy, and explain which method is best depending on how the equation is set up. (Honors)

Look at a picture that shows a pattern, create a math function to represent that pattern, and explain how the parts of the function match up with the picture to show why it works. (Honors)

Students will:

• Create two linear equations with two variables to represent a real-life situation.
• Use the rules of numbers and equality to solve a system of two linear equations with two variables, both by hand and with graphs.
• Decide if a system of two linear equations has one solution, no solution, or an infinite number of solutions.
• Write a linear inequality with two variables to represent a real-life situation.
• Show the solution of a linear inequality with two variables on a graph.
• Create a system of two linear inequalities with two variables to represent a real-life situation.
• Show the solution set of a system of two linear inequalities with two variables on a graph.
• Check the possible solution(s) to a system of two linear equations, a linear inequality with two variables, or a system of two linear inequalities by using algebra, graphs, and technology. Explain how you found the solution and interpret it for real-life problems.
• Create questions that involve collecting or acquiring data that involves two variables (bivariate data).
• Decide which variables could help explain a real-life problem or situation or answer your questions.
• Choose the best way to collect a sample that represents a larger group, possibly by using a random sampling method, to answer your question.
• Using a table of ordered pairs or a scatterplot with up to 30 data points, use technology to figure out if a linear or quadratic function best fits the relationship, and if so, find the equation of the best-fitting curve.
• Use technology to apply linear and quadratic regression methods to write a linear or quadratic function that represents the data, and describe the strengths and weaknesses of the model.
• Use a linear model to predict outcomes and evaluate how strong and accurate these predictions are, including the use of technology.
• Explore and explain what the slope (rate of change) and y-intercept (starting point) of a linear model mean in the real world.
• Analyze the relationship between two numerical variables shown in a scatterplot.
• Draw conclusions from the analysis of two-variable data and clearly explain the results.

Look at a picture that shows a pattern, create a math function to represent that pattern, and explain how the parts of the function match up with the picture to show why it works. (Honors)

In this unit, teachers will provide differentiated opportunities for students to review previous content and/or explore content at a deeper level.