Math

• To understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required)

A The student will be able to understand what an "input" (X) value is.

B. The student will be able to understand what an "output" (X) value is.

C. The student will be understand a function has one and only one "output value" for each "input value"

D. The student will be able to identify functions from tables, coordinates and graphs (extension * and from equations)

• Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line, give examples of functions that are not linear. For example, the function A = s given the area of a square, as a function of its side length, is not linear because it's graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

A. The student will recognize equations in the form of Y = mx + b as functions that form straight lines (linear)

B. The student will recognize "Y" as an output value for a linear function. (Y = mx + b)

C. The student will recognize "m" as a slope/rate of change for a linear function. (Y = mx + b)

D. The student will recognize "b" as an initial value/y--intercept for a linear function (Y = mx + b)

E. The student will recognize "x" as an "input value" for a linear function. (Y = mx + b)

F. The student will recognize ( X, Y ) is an Ordered Pair/Linear Pair/Coordinate/Point for a graphed function.

• Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

A. The student will understand and apply the academic vocabulary "Increase", "Decrease" as they relate to graphs, equations, quatities, etc.

B. The student will understand the academic vocabulary "linear" and "nonlinear" as they relate to graphs, equations, etc.

C The student will be able to analyze graphs and make mathematical decisions based on this analysis.

D. The student will be able to sketch, explain & apply the meaning (in context) of the parts of a graph (i.e. slope, rate of change, output, input, equation, y-intercept)

• 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).

A. The student will be able to identify equations with "one solution" from multi-step equations reduced to

their simplest form (x = a),

B. The student will be able to identify equations with "no-solutions" from multi-step equations reduced to

their simplest form ( a ≠ b)

C. The student will be able to identify equations with "infiniely many solutions" from multi-step equations

reduced to their simplest form ( a = a).

• Understand the definition of a function in relation to domain and range.

• Write a linear equation from a word problem and graph with labels.

• Understand that the intersection of the two linear equations (lines) is the solution5.

• Understand how to graph an inequality and be able to pull at least one real-world solution

• Use rigid motions to transform figures and determine the effect of a transformation on a figure using the definition of Congruence.

• Determine the criteria for congruent triangles using rigid motions.

• Justify theorems/properties about triangles, lines, and angles