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

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 strand (10.N.2)
• the standard number (10.N.2)

For example,   10.N.2   is a 10th grade standard in the “Number Sense and Operations” strand, and it is the 2nd 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 LINKS OPEN IN A NEW WINDOW MCAS LEARNING STANDARDS LINKS TO FISHER BURNS 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 $\,n^{\text{th}}\,$ roots of positive real numbers for any positive integer $\,n\,$; and the inverse relationship between taking the $\,n^{\text{th}}\,$ root of and the $\,n^{\text{th}}\,$ power of a positive real number. addition multiplication basic properties of zero and one recognizing zero and one deciding if a number is a whole number, integer, etc. finding reciprocals practice with the distributive law practice with radicals approximating 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 expressions versus sentences divisibility addition of signed sumbers subtraction of signed numbers mixed addition and subtraction of signed numbers writing fractions with a denominator of 2 in decimal form average of two signed numbers average of three signed numbers identifying place values multiplying by powers of ten changing decimals to fractions multiplying and dividing decimals by powers of ten changing decimals to percents changing percents to decimals scientific notation rewriting fractions as a whole number plus a fraction locating fractions on a number line fractions involving zero determining if a product is positive or negative multiplying and dividing fractions practice with the form a(b/c) more practice with the form a(b/c) renaming fractional expressions practice with multiples finding least common multiples renaming fraction with a specified denominator practice with factors adding and subtracting fractions adding and subtracting simple fractions with variables divisibility equivalences writing fractions in simplest form deciding if a fraction is a finite or infinite repeating decimal writing radicals in rational exponent form writing rational exponents as radicals practice with rational exponents practice with x and -x practice with products of signed variables equal or opposites? recognizing the patterns xn and (-x)n writing expressions in the form kxn writing more complicated expressions in the form kxn writing quite complicated expressions in the form kxn practice with exponents practice with order of operations basic exponent practice with fractions practice with  xmxn = xm+n practice with  (xm)n = xmn practice with  xm/xn = xm-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 rounding decimals to a specified number of places 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., $\,\sqrt{3^2 - 1} \approx 2.8\,$. Practice with 10.N.3 problems approximating radicals mental math: addition 10.N.4 Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers. approximating radicals deciding if numbers are equal or approximately equal 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. introduction to recursion and sequences arithmetic and geometric sequences 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 horizontal and vertical lines 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) introduction to polynomials 10.P.4 Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms; factoring (e.g., $a^2 - b^2 = (a+b)(a-b)\,$, $x^2 + 10x + 21 = (x+3)(x+7)\,$, $5x^4 + 10x^3 - 5x^2 = 5x^2(x^2 + 2x - 1)\,$; 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 factoring simple expressions 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 solving equations of the form xy = 0 solving simple equations involving perfect squares solving more complicated equations involving perfect squares 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 simple sentences by inspection identifying inequalities as true or false identifying inequalities with variables as true or false introduction to variables reading set notation going from a sequence of operations to an expression going from an expression to a sequence of operations solving simple sentences by inspection using mathematical conventions "undoing" a sequence of operations the Addition Property of Equality the Multiplication Property of Equality solving simple linear equations with integer coefficients solving more complicated linear equations with integer coefficients solving linear equations involving fractions solving linear equations, all mixed up solving simple linear inequalities with integer coefficients solving linear inequalities with integer coefficients solving linear inequalities involving fractions solving simple absolute value sentences 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) solving for a particular variable bigger, smaller, greater, lesser practice with the phrases "at least" and "at most" 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 introduction to exponential functions graphs of functions basic models you must know graphical interpretation of sentences like f(x)=0 and f(x)>0 graphical interpretation of sentences like f(x)=g(x) and f(x)>g(x) parabolas equations of simple parabolas quadratic functions and the completing the square technique tables of unit conversion information classifying units as length, time, volume, weight/mass practice with unit abbreviations practice with unit names practice with unit conversion information one-step conversions multi-step conversions translating simple mathematical phrases writing expressions involving percent increase and decrease calculating percent increase and decrease problems involving percent increase and decrease more problems involving percent increase and decrease word problems involving perfect squares introduction to sets interval and list notation introduction to functions introduction to function notation more practice with function notation domain and range of a function 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 introduction to systems of equations solving systems using substitution solving systems using elimination rate problems GEOMETRY 10.G.1 Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry. introduction to polygons interior and exterior angles in polygons quadrilaterals more terminology for segments and angles parallelograms and negating sentences 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 introduction to geometry: points, lines and planes segments, rays, angles if... then... sentences contrapositive and converse logical equivalence and practice with truth tables proof techniques introduction to the two-column proof similarity, ratios, and proportions introduction to GeoGebra applying logical equivalences to algebraic and geometric statements practice with two-column proofs practice with the mathematical words "and", "or", "is equivalent to" 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., $\,\Delta ABC \cong \Delta XYZ\,\,$) and properties of the figures to find missing parts of geometric figures, and provide logical justification. triangle congruence similarity, ratios, and proportions relationships between angles and sides in triangles Is there an "SSA" congruence theorem? No! 10.G.5 Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. the Pythagorean theorem interior and exterior angles in polygons 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 relationships between angles and sides in 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 introduction to the slope of a line practice with slope 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. introduction to equations and inequalities in two variables finding equations of lines point-slope form 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. getting bigger? getting smaller? perimeters and areas of similar polygons 10.M.4 Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements. significant figures and related concepts 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. summation notation    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. measures of spread