Download MCAS/Math Strategies Curriculum

HANOVER SCHOOLS
Hanover High School Benchmarks - Math Strategies
The Standards in this document are from the Massachusetts Department of Education:
Mathematics Curriculum Framework - Learning Standards for Data Analysis, Statistics, and Probability
Note: The parentheses at the end of a learning standard contain the codes for the corresponding standards in the two-year grade spans.
Document Key:
M = Mastery; These strands will be formally assessed each grading term using Common Assessment Opportunities.
D = Developing; The strands are introduced and explored.
R = Review; These topics were addressed in a prior course and will be reviewed.
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
Grading Term
1st 2nd 3rd 4th
Standard
10.D.1
Select, create, and interpret an appropriate graphical representation (e.g., scatter plot, 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.
10.D.1
10.D.1
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10.D.1
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10.D.1
Determine if a variable is quantitative or categorical
Choose an appropriate scale for a graph
Display categorical data in a bar graph
Display categorical data in a circle graph
Display categorical data in a table
Display quantitative data in a table
Display quantitative data in a stem - and - leaf plot
Display quantitative data in a box-plot
Display quantitative data in a dot plot
Display quantitative data in a box plot
Display two variable quantitative data in a scatter plot
Display two variable quantitative data in a line graph
Define: mean, median, mode, range, quartile, IQR
Calculate all measures of center (mean, median, mode)
Determine the most appropriate measure of center to represent information about the data
Calculate quartiles
Calculate all measures of spread (quartiles, range, IQR)
Compare sets of data using graphs and statistics
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10.D.1
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Choose most appropriate type of display for a given set of data
Read/interpret al types of displays to gain information about the data
Determine how the addition or removal of data will change specific statistics
10.D.2
Approximate a line of best fit (trend line) given a set of data (e.g., scatter plot). Use technology when appropriate.
10.D.2
10.D.2
10.D.2
10.D.2
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10.D.2
Create a scatter plot
Label axes appropriately
Describe the relationship between the two variables (positive, negative, no relationship)
Draw the line of best fit
Find the equation of the line of best fit by using two points on the line
Input data in calculator
Find the equation of the line of best fit through the use of technology
Use the equation of the line of best fit to make predictions about the data
10.G.1
Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of Symmetry.
10.G.1
Understand geometric symmetry
10.G.2
Draw congruent and similar figures using a compass, straightedge, protractor, or computer software. Make conjectures about methods of
construction. Justify the conjectures by logical arguments.
10.G.2
10.G.3
10.G.3
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10.G.3
10.G.3
10.G.3
10.G.3
10.G.3
10.G.3
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10.G.3
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Develop skills to make a variety of geometric constructions
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Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measures of central
and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, cords, and arcs within
or on the same circle.
Define: coplanar lines, parallel lines, transversal, central angle, inscribed angle, radii, major arc, minor arc, chord, alternate
interior angles (AIA), alternate exterior angles (AEA), corresponding angles, vertical angles, linear pairs
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Define: chord, alternate interior angles (AIA), alternate exterior angles (AEA), corresponding angles, vertical angles, linear
M
Define: vertical angles, linear pairs
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Given one angle measure of a linear pair, calculate the measure of the other angle
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Calculate angle measures when two coplanar lines intersect using the Vertical Angle Theorem
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Calculate angle measures when two parallel lines are cut by a transversal ( AIA, AEA and corresponding angles)
M
Determine if two lines are parallel given angle measures of angles created by a transversal
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Given angle measures (inscribed, central) calculate the length of an arc
M
Given the length of an arc, calculate a variety of angle measures (inscribed, central)
M
Calculate the length of radii within the same circle
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10.G.3
10.G.4
Calculate the length of chords within the same circle
M
Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and properties of the figures to find missing parts of geometric
figures, and provide logical justification.
10.G.4
10.G.5
10.G.5
10.G.5
10.G.5
Determine values using proportions and similarity concepts
Solve simple triangle problems using the triangle angle sum property, and/or the Pythagorean theorem.
Use the Triangle Sum Property to find missing angles in a triangle
Given two legs of a right triangle, calculate the length of the hypotenuse
Given one leg and the hypotenuse of a right triangle, calculate the length of the other leg
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10.G.6
Use the properties of special triangles (e.g., isosceles, equilateral, 30º–60º–90º, 45º–45º–90º) to solve problems.
10.G.6
Determine lengths of sides of special right 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.
10.G.7
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10.G.7
Calculate the slope of a line or line segment given 2 coordinates
Calculate the distance between two coordinates
Calculate the length of a line segment using the distance formula
Calculate the midpoint of a line segment given the coordinates of the endpoints
Apply the distance formula to solve a word problem
Apply the midpoint formula to solve a word problem
Apply the slope formula to solve a word problem
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.
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Define the relationship between the slopes of parallel lines
Write the equation of a line parallel to a given line through a given point
Determine if two lines are parallel given their slopes
Determine if two lines are parallel given their equations
Define the relationship between the slopes of perpendicular lines
Write the equation of a line perpendicular to a given line through a given point
Determine if two lines are perpendicular given their equations
Determine if two lines are perpendicular given their slopes
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 solution of problems.
10.G.9
Investigate transformations on figures in the coordinate plane
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10.G.10
Demonstrate the ability to visualize solid objects and recognize their projections and cross sections.
10.G.10
Use hands-on models to explore solid figures
10.G.11
Use vertex-edge graphs to model and solve problems.
10.G.11
Investigate problems involving networks, paths, vertex-edge graphs
10.M.1
Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles.
10.M.1
10.M.1
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10.M.1
Calculate the perimeter of any triangle
Calculate the perimeter of any quadrilateral
Calculate the perimeter of any regular polygon
Calculate the perimeter of a basic non-regular polygon (e.g.. pentagons, octagons, etc.)
Calculate the circumference of a circle
Given the perimeter of a figure, determine the length of missing sides
Given the circumference of a circle, calculate the length of the radius (or diameter)
Calculate the area of any triangle
Calculate the area of any trapezoid, parallelogram, rhombus, kite, rectangle or square
Calculate the area of a regular polygon by breaking it up
Calculate the area of any irregular polygon by breaking it up
Calculate the area of a circle
Given the area of a figure, calculate the length of a particular side
Given the area of a circle, calculate the length of the radius (or diameter)
Given the measurement of a 2-D object, calculate another measure
Solve a word problem by calculating perimeters, circumferences or areas
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.2
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Define: lateral area, surface area, volume, base, edge, face
Identify and label (i.e. base, edge, radius, etc.) prisms, pyramids, cylinders, cones and spheres
Identify the difference between lateral area and surface area or prisms, pyramids, cylinders and cones
Calculate the lateral area of prisms, pyramids, cylinders and cones
Calculate the surface area of prisms, pyramids, cylinders, cones and spheres
Calculate the volume of prisms, pyramids, cylinders, cones and spheres
Given the measurement of a 3-D object, calculate another measure
Solve word problems by calculating the lateral area of prisms, pyramids, cylinders and cones
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10.M.2
10.M.2
Solve word problems by calculating the surface area of prisms, pyramids, cylinders, cones and spheres
Solve word problems by calculating the volume of prisms, pyramids, cylinders, cones and spheres
10.M.3
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
10.M.3
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10.M.3
Determine how changing one attribute of an object affects its perimeter
Determine how changing one attribute of an object affects its area
Determine how changing one attribute of an object affects its lateral area
Determine how changing one attribute of an object affects its surface area
Determine how changing one attribute of an object affects its volume
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; the inverse relationship between taking the nth root of and the nth power of a positive real number.
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Add, subtract, multiply, divide all real numbers
Correctly use the order of operations
Use the associative property
Use the commutative property
Use the distributive property (including signed numbers)
Determine and use the identity in an addition problem
Determine and use the identity in a multiplication problem
Determine and use the inverse in an addition problem
Determine and use the inverse in a multiplication problem
Given an example and identify the property used (eg. distibutive)
Recognize the appropriate use of the associative, commutative and distributive properties
Find the nth power of a positive real number
Find the nth root of a positive real number
Alternately find the nth powers and nth roots of numbers to recognize the inverse relationship
10.N.2
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; the inverse relationship between taking the nth root of and the nth power of a positive real number.
10.N.2
10.N.2
10.N.2
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10.N.2
Add, subtract, multiply, divide all integers
Add, subtract, multiply, divide rational numbers
Correctly use the order of operations
Define: base, exponent, power
Evaluate positive and negative numbers raised to positive integer exponents
Find the absolute value of positive and negative numbers
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10.N.2
Find the absolute value of a numerical expression
Evaluate multi-step expressions (e.g.. 4|3 – 5| + 6)
Translate word problems into numerical expressions, then simplify
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.
10.P.2
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10.P.2
Define: x-axis, y-axis, intercept, line, horizontal, vertical, oblique, slope, rate of change
Plot a point on the coordinate plane
Identify a line as horizontal, vertical or oblique (increasing or decreasing) from its graph
Identify a line as horizontal, vertical or oblique (increasing or decreasing) from its equation
Calculate the slope of a line from two points using The Slope Formula
Determine the slope of a line from an equation (in Slope-Intercept Form or Standard Form)
Determine the slope of a line from its graph
Identify the x and y - intercepts from a graph
Identify the x and y - intercepts from an equation (in Slope-Intercept Form or Standard Form)
Given a graph, write the equation of a line in Slope-Intercept Form and Standard Form
Write the equation of a line given one point on the line and the slope, using Point-Slope Form
Write the equation of a line given two points, using Point-Slope form
Translate between all forms of equations
Define: positive slope, negative slope, zero slope and undefined (no) slope
Classify the slope of a line as positive, negative, zero or undefined given a graph of the line
Classify the slope of a line as positive, negative, zero or undefined given the equation of the line
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.
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Define: term
Collect like terms using the appropriate operation (addition or subtraction)
Multiply monomials
Factor the GCF from a polynomial (include GCF of an integer, GCF of a variable and a combination of both)
Factor trinomials with leading coefficient of 1
Factor trinomials with leading coefficient which is not 1
Factor perfect square trinomials
Factor the difference of two squares
Complete multi-step factoring problems (ex. Factor out the GCF, then factor the resulting trinomial)
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10.P.4
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10.P.4
Cancel common factors in a rational expression
Apply the Product of Powers Property
Apply the Quotient of Powers Property
Apply the Power of a Power Property
Apply the Power of a Product Property
Apply the Power of a Quotient Property
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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.
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Identify a quadratic equation
Identify the coefficients representing a, b and c in a quadratic equation
Factor any non-prime trinomial
Complete the square to create a perfect square trinomial
Solve a quadratic equation through factoring
Solve a quadratic equation by completing the square
Solve a quadratic by using The Quadratic Formula
Manipulate a quadratic to set it equal to zero
Show the equivalence of all methods through examples
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.
10.P.7
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Create a T-chart
Use a T-chart to graph a function
Choose an appropriate scale for a graph
Solve a problem involving a linear function by using tables
Solve a problem involving a linear function by using graphs
Solve a problem involving a linear function symbolically
Solve an exponential growth or decay problem by using tables
Solve an exponential growth or decay problem by using graphs
Solve a basic compound interest problem
Solve a direct variation problem by using tables
Solve a direct variation problem by using graphs
Solve an inverse variation problem by using tables
Solve an inverse variation problem by using graphs
Determine if a given situation is direct or inverse variation
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10.P.7
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Choose the appropriate type of function (linear, reciprocal, quadratic, etc) to represent a graph
Choose the appropriate type of function (linear, reciprocal, quadratic, etc) to represent a table
Use the given information to determine which type of a function the situation should be modeled with
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