Standards: Connecticut has adopted the Common Core State Standards (CCSS) as the Connecticut State Standards (CSS).

Personalized Learning Resources: DreamBox, NWEA Assessment

Standard Assessments: Students take the NWEA Assessment three times a year and Smarter Balanced Assessment in the Spring.

CONTENT OBJECTIVES

Students will be able to . . .

• Solve multi-step and real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
• Create equations and inequalities in one variable and use them to solve problems.
• Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal definition of the relationship between the circumference and area of a circle.

CONTENT OBJECTIVES

Students will be able to . . .

• perform integer operations.
• find the distance between two integers on a number line.
• perform rational number operations.
• solve real-world problems.

CONTENT OBJECTIVES

Students will be able to . . .

• Solve linear equations in one variable.
• Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
• Solve linear equations… in one variable, including equations with coefficients represented by letters.
• Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers).
• Understand solving equations as a process of reasoning and explain the reasoning.
• Create equations… in one variable and use them to solve problems.

CONTENT OBJECTIVES

Students will be able to . . .

• Solve linear… inequalities in one variable, including equations with coefficients represented by letters.
• Create… inequalities in one variable and use them to solve problems.
• Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
• Represent constraints by… inequalities… and interpret solutions as viable or nonviable options in a modeling context.

CONTENT OBJECTIVES

Students will be able to . . .

• Understand that a function is a rule that assigns to each input exactly one output.
• Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line.
• Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
• Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
• 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.
• Use function notation, evaluate functions for inputs their domains, and interpret statements that use function notation in terms of a context.
• Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
• Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

CONTENT OBJECTIVES

Students will be able to . . .

• Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• 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).
• 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.
• Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
• Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
• Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

CONTENT OBJECTIVES

Students will be able to . . .

• Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables.
• Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
• Represent constraints by systems of equations and interpret solutions as viable or nonviable options in a modeling context.
• Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously.
• Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
• Solve real-world and mathematical problems leading to two linear equations in two variables.

CONTENT OBJECTIVES

Students will be able to . . .

• 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.
• Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ - y⁴ as (x²)² - (y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²).
• Factor a quadratic expression to reveal the zeros of the function it defines.
• Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
• Interpret parts of an expression, such as terms, factors, and coefficients.
• Solve quadratic equations in one variable

CONTENT OBJECTIVES

Students will be able to . . .

• Identifying the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx) and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
• Solve quadratic equations in one variable.
• 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).
• Evaluate square roots of small perfect squares.
• Use the method of completing the square to transform any quadratic equation in x into an equation of the form
• Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
• Use the structure of an expression to identify ways to rewrite it.