What are Critical Learning Concepts (CLC's)?
CLC's are the concepts that I believe are the most important concepts for a student to have learned by the end of a school year. I teach mostly 7th and 8th graders, so I have the 7th grade and 8th grade CLC's below. 7th grade is mostly about operating with negative numbers for the first time, proportional relationships, circles, and probability. 8th grade is mostly about understanding the ins and outs of rational numbers, solving linear equations, writing linear expressions/equations, writing/solving linear inequalities, Pythagorean theorem, and systems of equations.
Pre-Algebra 7
7.1.1.1: Understand what a Rational Number is.
7.1.2.4: Problems that involve operations with rational numbers and positive integer exponents including interest problems.
7.2.2.1: Represent proportional relationships with a table, graph, verbal description, symbols. Determine Unit rate/slope.
7.2.2.2: Solve problems involving proportional relationships
7.2.3: Simplify numerical and algebraic expressions using order of operations and algebraic properties. Include rational numbers and whole number exponents.
7.2.4.1: Represent relationships with equations that involve positive and negative rational numbers and solve for the value of a variable by subbing in given values.
7.3.1: Understand where pi comes from and calculate circumference and area of circles and sections of circles as well as surface area and volume of cylinders.
7.3.2.4: Graph and describe translations and reflections of shapes on xy plane and determine location of the vertices of these shapes
7.4.3.2: Calculate probability as a fraction of sample space or as a fraction of area and express as a percent, decimal and fraction
Algebra 1
8.1.1.1: Understand what a rational and irrational number is and understand the closure properties for irrational and rational numbers.
8.1.1.4: Know and apply properties of positive and negative integer exponents to generate equivalent numerical expressions.
8.2.1.1: Understand what a function is and use function notation (f(x) for example) to represent that function.
8.2.2.2: Identify graphical properties of linear functions including slopes and intercepts.
8.2.2.1: Represent linear functions with tables, verbal descriptions, symbols, equations and graphs, and translate from one representation to another.
8.2.3.1: Evaluate algebraic expressions including expressions with radicals and absolute values for given values.
8.2.4.2: Solve multi-step equations in one-variable and solve for a single variable.
8.2.4.3: Express linear equations in slope-intercept, point slope, and standard form and be able to translate between these forms.
8.2.4.5: Solve linear inequalities using properties of inequalities and graph the solutions on a number line.
8.2.4.7: Represent relationships using systems of linear equations and solve systems of linear equations using symbols, graphs, and numerically.
8.3.1.1: Understand and apply the Pythagorean theorem
8.3.2.1: Understand the relationship between slopes of parallel lines and slopes of perpendicular lines.
8.4.1: Be able to display data in a scatter plot, find a line of best fit, and make predictions for points not in the data.
Algebra 2
9.2.1.3: Finding the domain in multiple representations.
9.2.1.5: Identify the vertex, line of symmetry and intercepts of the parabola corresponding to aquadratic function, using symbolic and graphical methods, when the function is expressed in the form f(x) = ax^2 + bx + c, in the form f(x) = a(x-h)^2 + k, or in factored form.
9.2.1.6: Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.
9.2.2.6: Sketch graphs of common nonlinear functions and know how to use graphing technology to graph them.
9.2.3.4: Add, subtract, multiply, divide and simplify algebraic fractions.
9.2.4.1: Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratics using all methods.
9.2.4.6: Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically.
9.2.4.7: Solve equations that contain radical expressions. Recognize that extraneous solutions may arise when using symbolic methods.
9.4.1.3: Use scatterplots to analyze patterns and describe relationships. Determine regression line using technology.