### MCAS Topics

 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 nth roots of positive real numbers for any positive integer n;and the inverse relationship between taking the nth root of and the nth power of a positive real number. additionmultiplicationbasic properties of zero and onerecognizing zero and onedeciding if a number is a whole number, integer, etc.finding reciprocalspractice with the distributive lawpractice with radicalsapproximating radicals 10.N.2 Simplify numerical expressions, including those involving positive integer exponents or the absolute value,e.g., 3(24−1)=45, 4|3−5|+6=14; apply such simplifications in the solution of problems.Practice with 10.N.2 problems expressions versus sentencesdivisibilityaddition of signed sumberssubtraction of signed numbersmixed addition and subtraction of signed numberswriting fractions with a denominator of 2 in decimal formaverage of two signed numbersaverage of three signed numbersidentifying place valuesmultiplying by powers of tenchanging decimals to fractionsmultiplying and dividing decimals by powers of tenchanging decimals to percentschanging percents to decimalsscientific notationrewriting fractions as a whole number plus a fractionlocating fractions on a number linefractions involving zerodetermining if a product is positive or negativemultiplying and dividing fractionspractice with the form a(b/c)more practice with the form a(b/c)renaming fractional expressionspractice with multiplesfinding least common multiplesrenaming fraction with a specified denominatorpractice with factorsadding and subtracting fractionsadding and subtracting simple fractions with variablesdivisibility equivalenceswriting fractions in simplest formdeciding if a fraction is a finite or infinite repeating decimalwriting radicals in rational exponent formwriting rational exponents as radicalspractice with rational exponentspractice with x and -xpractice with products of signed variablesequal or opposites?recognizing the patterns xn and (-x)nwriting expressions in the form kxnwriting more complicated expressions in the form kxnwriting quite complicated expressions in the form kxnpractice with exponentspractice with order of operationsbasic exponent practice with fractionspractice with  xmxn = xm+npractice with  (xm)n = xmnpractice with  xm/xn = xm-npractice with  x -p = 1/x pone-step exponent law practicemulti-step exponent law practicesimplifying basic absolute value expressionsdetermining the sign (plus or minus) of absolute value expressionsrounding 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., 32−1−−−−−√≈2.8.Practice with 10.N.3 problems approximating radicalsmental math: addition 10.N.4 Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers. approximating radicalsdeciding 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 sequencesarithmetic 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 linepractice with slopegraphing linesfinding equations of linespoint-slope formhorizontal and vertical lines 10.P.3 Add, subtract, and multiply polynomials.Divide polynomials by monomials. identifying variable parts and coefficients of termscombining like termssimplifying expressions like -a(3b - 2c - d)basic FOILmore complicated FOILsimplifying  (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.,a2−b2=(a+b)(a−b),x2+10x+21=(x+3)(x+7),5x4+10x3−5x2=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 termsidentifying common factorsfactoring simple expressionslisting all the factors of a whole numberfinding the greatest common factor of 2 or 3 numbersfinding the greatest common factor of variable expressionsfactoring out the greatest common factorfactoring simple expressionsbasic concepts involved in factoring trinomialsfactoring x2 + bx + c,   c > 0factoring x2 + bx + c,   c < 0factoring trinomials, all mixed upidentifying perfect squareswriting expressions in the form A2factoring a difference of squaresfactoring ax2 + bx + cmultiplying and dividing fractions with variablesadding 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 equationswriting quadratic equations in standard formsolving simple quadratic equations by factoringsolving more complicated quadratic equations by factoringquadratic functions and the completing the square techniquealgebraic definition of absolute valuethe quadratic formulasolving equations of the form xy = 0solving simple equations involving perfect squaressolving 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 inspectionidentifying inequalities as true or falseidentifying inequalities with variables as true or falseintroduction to variablesreading set notationgoing from a sequence of operations to an expressiongoing from an expression to a sequence of operationssolving simple sentences by inspectionusing mathematical conventions"undoing" a sequence of operationsthe Addition Property of Equalitythe Multiplication Property of Equalitysolving simple linear equations with integer coefficientssolving more complicated linear equations with integer coefficientssolving linear equations involving fractionssolving linear equations, all mixed upsolving simple linear inequalities with integer coefficientssolving linear inequalities with integer coefficientssolving linear inequalities involving fractionssolving simple absolute value sentencessolving sentences like 2x - 1 = ±5solving absolute value equationssolving absolute value inequalities involving "less than"solving absolute value inequalities involving "greater than"solving absolute value sentences (all types)solving for a particular variablebigger, smaller, greater, lesserpractice 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 formulaintroduction to exponential functionsgraphs of functionsbasic models you must knowgraphical interpretation of sentences like f(x)=0 and f(x)>0graphical interpretation of sentences like f(x)=g(x) and f(x)>g(x)parabolasequations of simple parabolasquadratic functions and the completing the square techniquetables of unit conversion informationclassifying units as length, time, volume, weight/masspractice with unit abbreviationspractice with unit namespractice with unit conversion informationone-step conversionsmulti-step conversionstranslating simple mathematical phraseswriting expressions involving percent increase and decreasecalculating percent increase and decreaseproblems involving percent increase and decreasemore problems involving percent increase and decreaseword problems involving perfect squaresintroduction to setsinterval and list notation introduction to functionsintroduction to function notationmore practice with function notationdomain 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 equationsintroduction to systems of equationssolving systems using substitutionsolving systems using eliminationrate problems GEOMETRY 10.G.1 Identify figures using properties of sides, angles, and diagonals.Identify the figures' type(s) of symmetry. introduction to polygonsinterior and exterior angles in polygonsquadrilateralsmore terminology for segments and anglesparallelograms 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. constructionsintroduction to geometry: points, lines and planessegments, rays, anglesif... then... sentencescontrapositive and converselogical equivalence and practice with truth tablesproof techniquesintroduction to the two-column proofsimilarity, ratios, and proportionsintroduction to GeoGebraapplying logical equivalences to algebraic and geometric statementspractice with two-column proofspractice 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 pairsparallel 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 congruencesimilarity, ratios, and proportionsrelationships between angles and sides in trianglesIs 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 theoreminterior 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 trianglesrelationships 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 axespractice with pointsthe distance formulathe midpoint formulaintroduction to the slope of a linepractice 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 variablesfinding equations of linespoint-slope formhorizontal and vertical linesparallel 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 perimeterarea 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
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