중학교 및 고등학교 수학 주제에 대한 개인 또는 소규모 그룹 튜터링

Private tutoring covers learner and family requested needs.  Math For The Middles educators have over 12 years of tutoring experience.  With a range of talented and gifted programs like Summer Institute for the Gifted to focusing on academic and math esteem growth in students who seek accountability and academic support. The structure of private tutoring includes learners sharing their needs an informal exit ticket "assessment" to review and reinforce taught learning concepts. Guided instruction is included but learners will be expected to "do math" during tutoring.  We believe the only way to learn math is to do math.  Please message for the specific topics you would like to taught.  If you're learner is enrolled in a formal school system please share school based resources to ensure cohesiveness of your school's expectations.   Below is a long list of topics that may be covered.  This course is customizable to meet more than once a week and match your families needs.  


High School Topics
-Algebra 1
-Geometry
-Algebra 2



Middle School Math Topics from 6th to 8th Grade
Rational Numbers, Properties of Exponents and Square Roots
•	Add, subtract, multiply, and divide rational numbers (positive and negative decimals, fractions, and integers)
•	Develop transition from conceptually understanding rational numbers to developing rules and procedural fluency of rational operations
•	Convert fractions to decimals using division
•	Define rational and irrational numbers
•       Calculate unit rates with complex fractions
•	Solve multi step ratio and percent problems with interest, taxes, shopping sales, etc.
•	Represent real life ration and percent problems as equations
•	Model proportions on a graph
•	Estimate irrational numbers 
•	Compare the size of irrational numbers
•	Explain and apply zero property of exponents
•	Explain why a number raised to a negative exponent is the reciprocal
•	Multiply exponents with the same base
•	Divide exponents with the same base
•	Raise an exponent to an exponent
•	Evaluate square roots
•	Convert values to scientific notation
•	Perform operations with scientific notation values
•	Compare quantities in scientific notation

Algebraic and Non Algebraic Equations and Expressions
•       Simplify expressions and equations with decimals, fractions, and integers
•	Rewrite and identify equivalent expressions and equations
•	Learn how to use expressions and equations to solve real world problems
•	Graph proportional relationships
•	Compare at least two different proportional relationships
•	Interpret the unit rate of a proportional relationship as the slope of a line
•	Determine the slope between two distinct points
•	Recognize slope as rate of change
•	Describe and connect the initial value and rate of change of real life scenarios to slope intercept form
•	Graph slope intercept form
•	Identify the Y-Intercept
•	Determine if a given ordered pair is a solution to a linear equation
•	Write linear equations to model real life scenarios
•	Use similar triangles to determine the slope of a line
•	Understand the components of slope intercept form
•	Determine the quantity of solutions to an equation
•	Solve linear equations with rational number coefficients
•	Solve multistep linear equations that require the distributive property and combining like terms on both sides of an equation with one variable

Systems of Equations
•	Determine if an equation is a function
•	Identify a function using, graphs, tables, or equations
•	Compare and analyze functions
•	Identify and define linear functions on a graph, table, or by equation
•	Draw conclusions and make inferences from real life linear equations
•	Identify the solution to a system of two linear equations with two variables
•	Solve systems of linear equations with two unknowns algebraically
•	Determine and describe when two equations have no solution
•	Determine and describe when two equations have infinite solutions
•	Represent real world and mathematical problems leading to two linear equations
Geometry
•	Use scale drawings to solve problems with the actual length and size to scale
•	Use area, surface area, volume formula to solve for missing values of geometric figures
•	Use algebraic expressions to solve for supplementary, complementary, vertical, and adjacent angles.
•	Define and identify rotations, reflections and translations
•	Identify a line of reflection
•	Use models, and geometric software to confirm properties of rotations, reflections, and translations
•	Describe a sequence of rotations, reflections, and translations that exhibit congruence of -D figures with coordinates
•	Define and identify similar triangles
•	Identify angles created by a pair of parallel lines cut by a transversal
•	Use formulas to calculate the volume of cones, cylinders, and spheres and compare similar sizes of the same shape.

Statistics and Probability
•	Infer valid comparable conclusions about multiple populations using mean, median, and other measures of variability
•	Investigate chance using probability models
•	Describe scatter plot patterns like clustering, outliers, positive/negative associations and non linear associations
•	Construct, and interpret scatter plots with two different variables to investigate patterns of association between two quantities
•	Fit a straight line within plotted data
•	Informally assess the model fit 
•	Recognize patterns shown in comparison of two sets of data