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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.,
$\,3(2^4  1) = 45\,,$
$\,435 + 6 = 14\,$;
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 x^{n} and (x)^{n}
writing expressions in the form kx^{n}
writing more complicated expressions in the form kx^{n}
writing quite complicated expressions in the form kx^{n}
practice with exponents
practice with order of operations
basic exponent practice with fractions
practice with x^{m}x^{n} = x^{m+n}
practice with (x^{m})^{n} = x^{mn}
practice with x^{m}/x^{n} = x^{mn}
practice with x ^{p} = 1/x ^{p}
onestep exponent law practice
multistep 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 “pointslope” 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
pointslope 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.,
$a^2  b^2 = (a+b)(ab)\,,$
$x^2 + 10x + 21 = (x+3)(x+7)\,,$
$5x^4 + 10x^3  5x^2 = 5x^2(x^2 + 2x  1)\,$;
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 x^{2} + bx + c, c > 0
factoring x^{2} + bx + c, c < 0
factoring trinomials, all mixed up
identifying perfect squares
writing expressions in the form A^{2}
factoring a difference of squares
factoring ax^{2} + 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.,
$\,x2 > 5\,$) 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
onestep conversions
multistep 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 twocolumn proof
similarity, ratios, and proportions
introduction to GeoGebra
applying logical equivalences to algebraic and geometric statements
practice with twocolumn 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 “pointslope” form of the equation.

introduction to equations and inequalities in two variables
finding equations of lines
pointslope 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 vertexedge 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, stemandleaf plots, boxandwhisker 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
