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Map of MCAS Objectives to Fisher Web Site, Grades 9–10

Grades 5–6 MCAS Objectives
Grades 7–8 MCAS Objectives
Mathematics Curriculum Framework (Massachusetts Department of Elementary & Secondary Education)
released MCAS test items

MCAS stands for Massachusetts Comprehensive Assessment System.

As required by the Massachusetts Education Reform Act of 1993,
students must pass the grade 10 MCAS tests in English Language Arts and Mathematics
as one condition of eligibility for a high school diploma (in addition to fulfilling local requirements).

In addition, the MCAS program is used to hold Massachusetts schools and districts accountable, on a yearly basis,
for the progress they have made toward the objective of the No Child Left Behind Act
that all students be proficient in Reading and Mathematics by 2014.

MCAS tests measure how well students have learned the academic standards outlined in the Massachusetts Curriculum Frameworks.
All Massachusetts public school students take MCAS tests: each year in grades 3 through 8, and at least once in high school (usually grade 10).

This page lists the Learning Standards that form the basis for MCAS, and then provides links to my web exercises covering the material.
Of course, concepts are often covered in many different exercises; I have tried to provide the most relevant links.

Five strands organize the MCAS mathematics content:

Number Sense and Operations
Patterns, Relations, and Algebra
Geometry
Measurement
Data Analysis, Statistics, and Probability

Each learning standard has a unique identifier (like 10.N.2) that consists of:

the grade level (10.N.2)
the strand (10.N.2)
the standard number (10.N.2)

For example, 10.N.2 is a 10^th grade standard in the "Number Sense and Operations" strand, and it is the 2^nd standard in this strand.

The learning standards specify what students should know at the end of each grade span.
Students are held responsible for learning standards listed at earlier grade spans as well as their current grade span.

All of the MCAS sample problems (links in the second column below) are incorporated,
in appropriate places, in my online Algebra I and Geometry courses.
Therefore, if you use these online courses in their entirety, you will automatically hit all the MCAS sample problems.

MCAS LEARNING STANDARDS		LINKS TO FISHER SITE
GRADES 9–10 LEARNING STANDARDS
NUMBER SENSE AND OPERATIONS
10.N.1	Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of n^th roots of positive real numbers for any positive integer n; and the inverse relationship between taking the n^th root of and the n^th power of a positive real number.	addition multiplication basic properties of zero and one practice with the distributive law practice with radicals
10.N.2	Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(2 4-1) =45 , 4\|3- 5\|+6=14 ; apply such simplifications in the solution of problems. Practice with 10.N.2 problems	practice with exponents practice with order of operations basic exponent practice with fractions practice with x^mxⁿ = x^m+n practice with (x^m)ⁿ = x^mn practice with x^m/xⁿ = x^m-n practice with x ^-p = 1/x ^p one-step exponent law practice ♥ multi-step exponent law practice simplifying basic absolute value expressions determining the sign (plus or minus) of absolute value expressions
10.N.3	Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g., 3 2-1≈ 2.8 . Practice with 10.N.3 problems	♥ approximating radicals
10.N.4	Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
PATTERNS, RELATIONS, and ALGEBRA
10.P.1	Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships.
10.P.2	Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.	introduction to the slope of a line practice with slope graphing lines finding equations of lines ♥ point-slope form
10.P.3	Add, subtract, and multiply polynomials. Divide polynomials by monomials.	identifying variable parts and coefficients of terms combining like terms simplifying expressions like -a(3b - 2c - d) basic FOIL more complicated FOIL simplifying (a + b)² and (a - b)² simplifying expressions like (a - b)(c + d - e)
10.P.4	Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms; factoring (e.g., a2 -b2 =(a+b )(a-b) , x2 +10x+21 =(x+3) (x+7) , 5x 4+10x 3-5 x2= 5x2 (x2 +2x-1 ) ; identifying and canceling common factors in rational expressions; and applying the properties of positive integer exponents.	recognizing products and sums; identifying factors and terms identifying common factors factoring simple expressions listing all the factors of a whole number finding the greatest common factor of 2 or 3 numbers finding the greatest common factor of variable expressions factoring out the greatest common factor basic concepts involved in factoring trinomials factoring x² + bx + c, c > 0 factoring x² + bx + c, c < 0 factoring trinomials, all mixed up identifying perfect squares writing expressions in the form A² factoring a difference of squares factoring ax² + bx + c ♥ multiplying and dividing fractions with variables ♥ adding and subtracting fractions with variables
10.P.5	Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods.	identifying quadratic equations writing quadratic equations in standard form solving simple quadratic equations by factoring solving more complicated quadratic equations by factoring ♥ quadratic functions and the completing the square technique ♥ algebraic definition of absolute value ♥ the quadratic formula
10.P.6	Solve equations and inequalities including those involving absolute value of linear expressions (e.g., \|x-2\|>5 ) and apply to the solution of problems.	solving sentences like 2x - 1 = ±5 solving absolute value equations solving absolute value inequalities involving "less than" solving absolute value inequalities involving "greater than" solving absolute value sentences (all types)
10.P.7	Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate.	♥ Getting bigger? Getting smaller? ♥ the compound interest formula
10.P.8	Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems.	♥ simple word problems resulting in linear equations
GEOMETRY
10.G.1	Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry.
10.G.2	Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments.	♥ Constructions
10.G.3	Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle.	♥ Angles: Complementary, Supplementary, Vertical and Linear Pairs ♥ Parallel Lines
10.G.4	Apply congruence and similarity correspondences (e.g., ΔABC≅ ΔXYZ ) and properties of the figures to find missing parts of geometric figures, and provide logical justification.	♥ Triangle Congruence ♥ Similarity, Ratios, and Proportions
10.G.5	Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem.	♥ The Pythagorean Theorem
10.G.6	Use the properties of special triangles (e.g., isosceles, equilateral, 30�-60�-90�, 45�-45�-90�) to solve problems.	♥ Two Special Triangles
10.G.7	Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems.	locating points in quadrants and on axes practice with points ♥ the distance formula ♥ the midpoint formula
10.G.8	Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation.	♥ horizontal and vertical lines ♥ parallel and perpendicular lines
10.G.9	Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems.
10.G.10	Demonstrate the ability to visualize solid objects and recognize their projections and cross sections.
10.G.11	Use vertex-edge graphs to model and solve problems.
MEASUREMENT
10.M.1	Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.	♥ Introduction to Area and Perimeter ♥ Area Formulas: Triangle, Parallelogram, Trapezoid
10.M.2	Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.
10.M.3	Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume.
10.M.4	Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements.
DATA ANALYSIS, STATISTICS, and PROBABILITY
10.D.1	Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.	♥ mean, median, and mode
10.D.2	Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.
10.D.3	Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.

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