Standard 1 Number and Computation:
The student uses numerical and computational concepts and procedures in a variety of situations.
Benchmark 1
Number Sense - The student demonstrates number sense for real numbers and simple algebraic expressions in a variety of situations.
Indicator 1
(K) The student knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers, fractions, decimals, percents, and ratios; rational number bases with integer exponents; rational numbers written in scientific notation with integer exponents; time; and money (2.4.K1a) $.
Indicator 2
(K) The student compares and orders rational numbers, the irrational number pi, and algebraic expressions (2.4.K1c), e.g., Which expression is greater -3n or 3n? It depends on the value of n. If n is positive, 3n is greater. If n is negative, -3n is greater. If n is zero, they are equal.
Indicator 3
(K) The student explains the relative magnitude between rational numbers, the irrational number pi, and algebraic expressions (2.4.K1a).
Indicator 4
(K) (K)The student recognizes and describes irrational numbers, e.g., non-repeating,non-termination decimal; or (pi) is a non-terminating decimal.
Indicator 5
(K) (K)The student knows and explains what happens to the product or quotient when (2.4.K1a):
a. a positive number is multiplied or divided by a rational number greater than zero and less than one,
b. a positive number is multiplied or divided by a rational number greater than one,
c. a nonzero real number is multiplied or divided by zero.
Indicator 6
(K) (K)The student explains and determines the absolute value of real numbers (2.4.K1a).
Indicator 1
(A) The student generates and/or solves real-world problems using equivalent representations of rational numbers and simple algebraic expressions (2.4.A1a) $ e.g., ex. a paper reports a company's gross income as $1.2 billion and their total expenses were $30,450,000. What is the company's profit?
Indicator 2
(A) The student determines whether or not solutions to real-world problems using rational numbers, the irrational number pi, and simple algebraic expressions are reasonable. the city park is putting a picket fence around their circular rose garden. The garden has a diameter of 7.5 meters. The planner wants to buy 20 meters of fencing. Is this a reasonable length of fence?
Benchmark 2
Number Systems and Their Properties - The student demonstrates an understanding of the real number system, recognizes, applies, and explains its properties, and extends these properties to algebraic expressions.
Indicator 1
(K) The student explains and illustrates the relationship between the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] using mathematical models (2.4.K1a), e.g., number lines or Venn diagrams.
Indicator 2
(K) The student identifies all the subsets of the real number system [natural counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs. (For the purposes of assessment, irrational numbers will not be included).
Indicator 3
(K) The student names, uses, and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:
a. commutative, associative, distributive, and substitution properties [commutative: a + b = b + a and ab = ba; associative: a + (b + c) = (a + b) + c and a(bc) = (ab)c; distributive: a(b + c) = ab + ac; substitution: if a = 2, then 3a = 3 x 2 = 6];
b. identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity: a + 0 = a, multiplicative identity: a _ 1 = a, additive inverse: +5 + -5 = 0, multiplicative inverse: 8 x 1/8 = 1);
c. symmetric property of equality, e.g., 7 + 2 = 9 has the same meaning as 9 = 7 + 2;
d. addition and multiplication properties of equalities, e.g., if a = b, then a + c = b + c;
e. addition property of inequalities, e.g., if a > b, then a + c > b + c;
f. zero product property, e.g., if ab = 0, then a = 0 and/or b = 0.
Indicator 1
(A) The student generates and/or solves real-world problems with rational numbers using the concepts of these properties to explain reasoning (2.4.A1a):
a. commutative, associative, distributive, and substitution properties; e.g., ex;
b. identity and inverse properties of addition and multiplication; e.g., ex;
c. symmetric property of equality; e.g., ex;
d. addition and multiplication properties of equality; e.g., ex;
e. zero product property; e.g., ex.
Indicator 2
(A) The student analyzes and evaluates the advantages and disadvantages of using integers, whole numbers, fractions (including mixed numbers), or decimals in solving a given real-world problem (2.4.A1a) , e.g., ex.
Benchmark 3
Estimation - The student uses computational estimation with real numbers in a variety of situations.
Indicator 1
(K) The student estimates real number quantities using various computational methods including mental math, paper and pencil, concrete objects, and/or appropriate technology (2.4.K1a) $.
Indicator 2
(K) The student knows and explains why a decimal representation of the irrational number pi is an approximate value (2.4.K1c).
Indicator 3
(K) The student knows and explains why a decimal representation of the irrational number pi is an approximate value (2.4.K1c).
Indicator 4
(K) The student knows and explains between which two consecutive integers an irrational number lies.
Indicator 1
(A) The student adjusts original rational number estimate of a real-world problem based on additional information (a frame of reference) (2.4.A1a) $, e.g., estimate the height of a building from a picture; in the next picture, a person is standing next to the building, and then adjust your original estimate.
Indicator 2
(A) The student estimates to check whether or not the result of a real world problem using rational numbers and/or simple algebraic expressions is reasonable and makes predictions based on the information $, e.g., ex.
Indicator 3
(A) The student determines a reasonable range for the estimation of a quantity given a real-world problem and explains the reasonableness of the range (2.4 A1c), e.g., estimate the weight of a book.
Indicator 4
(A) The student determines if a real-world problem calls for an exact or approximate answer and performs the appropriate computation using various computational methods including mental mathematics, paper and pencil, concrete objects, and/or appropriate technology $, e.g., ex.
Indicator 5
(A) (A)The student explains the impact of estimation on the result of a real-world problem (underestimate, overestimate, range of estimates) $, e.g., You are estimating the total of three large purchases ($489, $553, and $92). If you rounded each to the nearest $10, would your estimate be slightly lower or higher than the actual amount spent? What if you rounded each to the nearest $100, would your estimate be slightly lower or higher than the actual amount spent?
Benchmark 4
Computation - The student models, performs, and explains computation with rational numbers, the irrational number pi, and algebraic expressions in a variety of situations.
Indicator 1
(K) The student computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1a) $.
Indicator 2
(K) The student performs and explains these computational procedures with rational numbers (2.4.K1a):
a. addition, subtraction, multiplication, and division of integers $, N;
b. order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right) ,N;
c. approximation of roots of numbers using calculators;
d. multiplication or division to find $:
i. a percent of a number, e.g., What is 0.5% of 10?;
ii. percent of increase and decrease, e.g, ex;
iii percent one number is of another number, e.g., What percent of 80 is 120?;
iv a number when a percent of the number is given, e.g., 15% of what number is 30?;
e. addition of polynomials, e.g., ex;
f. simplifies algebraic expressions in one variable by combining like terms or using the distributive property (2.4.K1a),
Indicator 3
(K) The student finds factors and common factors of simple monomial expressions (2.4.K1d), e.g., given the monomials 10m^2n^3 and 15a^2mn^2 ; some common factors would be 5, m, and n^2.
Indicator 1
(A) The student generates and/or solves one- and two-step real-world problems using computational procedures and mathematical concepts (2.4.A1a) with:
a. rational numbers, e.g., find the height of a triangular garden given that the area to be covered is 400 square feet with a base of 12 1/2 feet;
b. the irrational number pi as an approximation, e.g., find the radius to the nearest tenth of a foot of a sprinkler system given the area in square feet;
c. applications of percents $, e.g., sales tax or discounts. (For the purposes of assessment, percents will not be between 0 and 1.)
The student uses algebraic concepts and procedures in a variety of situations.
Benchmark 1
Patterns - The student recognizes, describes, extends, develops, and explains the general rule of a pattern from a variety of situations.
Indicator 1
(K) The student identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes:
a. counting numbers including perfect squares, cubes, and factors and multiples with positive rational numbers (number theory).
b. rational numbers including arithmetic and geometric sequences (arithmetic: sequence of numbers in which the difference of two consecutive numbers is the same, geometric: a sequence of numbers in which each succeeding term is obtained by multiplying the preceding term by the same number) (2.4.K1a), e.g., 1/4, 1/2, 3/4,...;
c. geometric figures;
d. measurements $;
e. things related to daily life $;
f. variables and simple expressions, e.g.,_1 - x, 2 - x, 3 - x, 4 - x, ...; or x, x^2, x^3, ...
Indicator 2
(K) The student generates and explains a pattern.
Indicator 3
(K) The student generates a pattern limited to two operations (addition, subtraction, multiplication, division, exponents) when given the rule for the nth term, e.g., the nth term is n^2+1, find the first 4 terms beginning with n = 1; the terms are 2, 5, 10, and 17.
Indicator 4
(K) The student states the rule to find the nth term of a pattern using explicit symbolic notation, e.g., given 2, 5, 8, 11, .; find the rule for the nth term, the rule is 3^n -1.
Indicator 5
(K) The student describes the pattern when given a table of linear values and plots the ordered pairs on a coordinate plane (2.4.K1g-h), e.g., the x-coordinates are increasing by three, while the y-coordinates are increasing by 6 or if the x is doubled, add one to find the y realizing that the written descriptions may vary.
Indicator 1
(A) The student recognizes the same general pattern presented in different representations [numeric (list or table), visual (picture, table, or graph), and written] (2.4.A1f-g).
Indicator 2
(A) The student between the equation, graph, and table of values resulting from the generalization (2.4.A1f-g) $, e.g., Water is billed at $.01 per gallon, plus a basic fee of $10 per month for being connected to the water district.
Benchmark 2
Variable, Equations, and Inequalities - The student uses variables, symbols, real numbers, and algebraic expressions to solve equations and inequalities in a variety of situations.
Indicator 1
(K) The student identifies independent and dependent variables within a given situation.
Indicator 2
(K) The student simplifies algebraic expressions in one variable by combining like terms or using the distributive property (2.4.K1a), e.g., -3(x - 4) is the same as -3x + 12.
Indicator 3
(K) The student solves:
a. one- and two-step linear equations in one variable with rational number coefficients and constants intuitively and/or analytically (2.4.K1a,c) $;
b. one-step linear inequalities in one variable with rational number coefficients and constants intuitively, analytically, and graphically (2.4.K1a,c), e.g., -2x > 10;
c. systems of given linear equations with whole number coefficients and constants graphically (2.4.K1a).
Indicator 4
(K) The student knows and describes the relationship between ratios, proportions, and percents and how to solve for a missing term in a proportion (2 4.K1c), e.g., 2/5=1/x+2.
Indicator 5
(K) The student represents and solves algebraically $:
a. the number when a percent and a number are given,
b. what percent one number is of another number,
c. percent of increase or decrease, e.g., finding the percent when given the original and current amount.
Indicator 6
(K) The student evaluates formulas using substitution $.
Indicator 1
(A) The student represents real-world problems using (2.4.A1a-b):
a. variables, symbols, expressions, one- or two-step equations with rational number coefficients and constants $, e.g., Today John is 3.25 inches more than half his sister's height. If J = John's height, and S= his sister's height, then J=0 5S+3.25.
b. one-step inequalities with rational number coefficients and constants, e.g., ex;
c. systems of linear equations with whole number coefficients and constants, e.g, Two students collected the same amount of money for a walk-a-thon. One student received $5 per mile and a donation of $10, while the other student received $2 per mile and a donation of $20. How many miles did they walk?
d. solves real-world problems with two-step linear equations in one variable with rational number coefficients and constants and rational solutions intuitively, analytically, and graphically.
Indicator 2
(A) The student generates real-world problems that represent:
a. one- or two-step linear equations, (2.4.A1d-e) $, e.g., Given the equation 2x + 10 = 30, the problem could be I bought two shirts and a pair of $10 pants. How much was a shirt, if the total bill was $30?;
b. one-step linear inequalities, e.g., Write a real-world situation that represents the inequality x + 10 > 30. The problem could be If you give me $10, I will have more than $30.
Indicator 3
(A) The student explains the mathematical reasoning that was used to solve a real-world problem using one- or two-step linear equations and inequalities and discusses the advantages and disadvantages to various strategies that may have been used to solve the problem, e.g., ex.
Benchmark 3
Functions - The student recognizes, describes, and analyzes, constant, linear, and nonlinear relationships in a variety of situations.
Indicator 1
(K) The student recognizes and examines constant, linear, and nonlinear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology (2.4.K1a,e-f,h) $.
Indicator 2
(K) The student knows and describes the difference between constant, linear, and nonlinear relationships (2.4.K1h).
Indicator 3
(K) The student explains the concepts of slope and x- and y-intercepts of a line 2.4.K1h).
Indicator 4
(K) The student recognizes and identifies the graphs of constant and linear functions (2.4.K1h).
Indicator 5
(K) The student identifies ordered pairs from a graph, and/or plots ordered pairs using a variety of scales for the x- and y-axis(2.4.K1g-h).
Indicator 1
(A) The student represents a variety of constant and linear relationships using written or oral descriptions of the rule, tables, graphs, and symbolic notation (2.4 A1f).
Indicator 2
(A) The student interprets, describes, and analyzes the mathematical relationships of numerical, tabular, and graphical representations (2.4.A1f) $.
Indicator 3
(A) The student translates between the numerical, tabular, graphical, and symbolic representations of linear relationships with integer coefficients and constants, e.g., y = 2x + 5 (symbolic) can be represented in a table (tabular) (2.4 A1f),
Benchmark 4
Models - The student generates and uses mathematical models to represent and justify mathematical relationships found in a variety of situations.
Indicator 1
(K) The student knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships.
Mathematical models include:
a. process models (concrete objects, pictures, diagrams, number lines, coordinate grids, hundred charts, measurement tools, multiplication arrays, or division sets) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations (1.1.K1-3, 1.1.K5-6, 1.2.K1, 1 3.K1, 1.3.K4, 1.4.K1, 1.4K2a, 1.4.K3, 2.2.K2, 2.2.K3a-c, 2.2.K6, 2.3.K1) $;
b. factor trees to model least common multiple, greatest common factor, and prime factorization; (1.4.K2a)
c. equations and inequalities to model numerical relationships (2.2.K3a b, 2.2.K4 2.2.K6, 2.3.K1);
d. function tables to model numerical and algebraic relationships (2.1.K5, 2.3.K1, 3.4.K2);
e. coordinate planes to model relationships between ordered pairs and linear equations and inequalities (2.1.K5, 2.2.K6, 2.2.K8, 2.3.K1-5, 3.4.K1-2);
f. two- and three-dimensional geometric models (geoboards, dot paper, nets, or solids) and real-world objects to model perimeter, area, volume, and surface area (3.2.K1-2, 3.2.K4, 3.3.K4-5);
g. scale drawings to model large and small real-world objects (3.3.K4 5);
h. geometric models (spinners, targets, or number cubes), process models coins, pictures, or diagrams), and tree diagrams to model probability (4.1.K1, 4.1 K3-4);
i. frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts tables, single and double stem-and-leaf plots, scatter plots, box and-whisker plots, and histograms to organize and display data (4.2.K1, 4.2.K6) $.
j. Venn diagrams to sort data and to show relationships.
Indicator 1
(A) The student recognizes that various mathematical models can be used to represent the same problem situation.
Mathematical models include:
a. process models (concrete objects, pictures, diagrams, flowcharts, number lines, coordinate grids, hundred charts, measurement tools, multiplication arrays, or division sets) to model computational procedures, algebraic relationships, mathematical relationships, and problem situations and to solve equations (1.4 A1, 2.2.A1a-c, 2.2.A2, 3.2.A2, 3.4.A2) $;
b. equations and inequalities to model numerical relationships (2.2.A1a-c, 2.2 A2, 3.4.A2);
c. function tables to model numerical and algebraic relationships (2.1.A1 2, 2.2 A1, 2.3.A1-3, 3.4.A2) $;
d. coordinate planes to model relationships between ordered pairs and linear equations and inequalities; (2.1.A1-2, 2.2.A3, 2.3.A1-3, 3.4.A1 3)
e. two- and three-dimensional geometric models (geoboards, dot paper, nets, or solids) and real-world objects to model perimeter, area, volume, and surface area (3.2.A1-3, 3.3.A1, 3.3.A4);
f. scale drawings to model large and small real-world objects (3.1.A1-2, 3.3.A4);
g. geometric models (spinners, targets, or number cubes), process models coins, pictures, or diagrams), and tree diagrams to model probability (4.1.A1, 4 1.A3-4);
h. frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, and histograms to describe, interpret, and analyze data (4.2.A1).
Indicator 2
(A) The student determines if a given graphical, algebraic, or geometric model is an accurate representation of a given real-world situation $.
Indicator 3
(A) The student uses the mathematical modeling process to analyze and make inferences about real-world situations $.
The student uses geometric concepts and procedures in a variety of situations.
Benchmark 1
Geometric Figures and Their Properties - The student recognizes geometric figures and compares properties and concepts of geometric figures in a variety of situations.
Indicator 1
(K) The student recognizes and compares properties of two- and three dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.
Indicator 2
(K) The student discusses properties of triangles and quadrilaterals related to:
a. sum of the interior angles of any triangle is 180°;
b. sum of the interior angles of any quadrilateral is 360°;
c. parallelograms have opposite sides that are parallel and congruent, opposite angles are congruent;
d. rectangles have angles of 90°, sides may or may not be equal;
e. rhombi have all sides equal in length, angles may or may not be equal;
f. squares have angles of 90°, all sides congruent;
g. trapezoids have one pair of opposite sides parallel and the other pair of opposites sides are not parallel;
h. kites have two distinct pairs of adjacent congruent sides.
Indicator 3
(K) The student recognizes and describes the rotational symmetries and line symmetries that exist in two-dimensional figures.
Indicator 4
(K) The student recognizes and uses properties of corresponding parts of similar and congruent triangles and quadrilaterals to find side or angle measures using standard notation for similarity and congruence.
Indicator 5
(K) The student knows and describes Triangle Inequality Theorem to determine if a triangle exists.
Indicator 6
(K) The student uses the Pythagorean theorem to:
a. determine if a triangle is a right triangle,
b. find a missing side of a right triangle where the lengths of all three sides are whole numbers.
Indicator 7
(K) The student recognizes and compares the properties of a point, line, and plane.
Indicator 8
(K) The student describes the intersection of plane figures, e.g., two circles could intersect at no point, one point, two points, or all points.
Indicator 9
(K) The student describes and explains angle relationships:
a. when two lines intersect including vertical and supplementary angles;
b. when formed by parallel lines cut by a transversal including corresponding, alternate interior, and alternate exterior angles.
Indicator 10
(K) The student recognizes and describes arcs and semicircles as parts of a circle and uses the standard notation for arc and circle.
Indicator 1
(A) The student solves real-world problems by (2.4.A1a,e):
a. using the properties of corresponding parts of similar and congruent figures, e.g., scale drawings, map reading, proportions, or indirect measurements.
b. applying the Pythagorean Theorem, e.g., indirect measurements, map reading/distance, or diagonals.
Benchmark 2
Measurement and Estimation - The student estimates, measures, and uses geometric formulas in a variety of situations.
Indicator 1
(K) The student determines and uses rational number approximations estimations) for length, width, weight, volume, temperature, time, perimeter, area and surface area using standard and nonstandard units of measure (2.4.K1a) $.
Indicator 2
(K) The student selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate real number representations for length, weight, volume, temperature, time, perimeter, area, surface area, and angle measurements (2.4.K1a) $.
Indicator 3
(K) The student converts within the customary system and within the metric system.
Indicator 4
(K) The student estimates the measure of a concrete object in one system given the measure of that object in another system and the approximate conversion factor, e.g., a mile is about 2.2 kilometers; how far is 2 miles?
Indicator 5
(K) The student uses given measurement formulas to find (2.4.K1h):
a. area of parallelograms and trapezoids;
b. surface area of rectangular prisms, triangular prisms, and cylinders;
c. volume of rectangular prisms, triangular prisms, and cylinders;
Indicator 6
(K) The student recognizes how ratios and proportions can be used to measure inaccessible objects, e.g., using shadows to measure the height of a flagpole.
Indicator 7
(K) The student calculates rates of change, e.g., speed or population growth.
Indicator 8
(K) The student describes the intersection of plane figures, e.g., two circles could intersect at no point, one point, two points, or all points.
Indicator 9
(K) The student describes and explains angle relationships:
a. when tow lines intersect including vertical and supplimentary angles;
b. when formed by parallel lines cut by a transversal including corresponding, alternate interior, and alternate exterior angles.
Indicator 10
(K) The student recognizes and describes arcs and semicircles as parts of a circle and uses the standard notation for arc and circle.
Indicator 1
(A) The student solves real-world problems (2.4.A1h) by:
a. converting within the customary and the metric systems, e.g., ex;
b. finding perimeter and area of circles, squares, rectangles, triangles, parallelograms, and trapezoids; e.g., ex;
c. finding the volume and surface area of rectangular prisms, e.g., ex.
Indicator 2
(A) The student estimates to check whether or not measurements or calculations for length, weight, volume, temperature, time, perimeter, area, and surface area in real world problems are reasonable and adjusts original measurement or estimation based on additional information (a frame of reference) (2.4.A1a,h) $, e.g., to check your calculation in finding the area of the floor in the kitchen; you count how many foot square tiles there are on the floor.
Indicator 3
(A) The student uses ratio and proportion to measure inaccessible objects (2.4 A1h), e.g., using shadows to measure the height of a flagpole.
Benchmark 3
Transformational Geometry - The student recognizes and applies transformations on geometric figures in a variety of situations.
Indicator 1
(K) The student identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two dimensional figure.
Indicator 2
(K) The student describes a reflection of a given two-dimensional figure that moves it from its initial placement (preimage) to its final placement (image) in the coordinate plane over the x- and y-axis.
Indicator 3
(K) The student draws (2.4.K1i):
a. three-dimensional figures from a variety of perspectives (top, bottom, sides, corners);
b. a scale drawing of a two-dimensional figure;
c. a two-dimensional drawing of a three-dimensional figure.
Indicator 4
(K) The student determines where and how an object or a shape can be tessellated using single or multiple transformations.
Indicator 1
(A) The student generalizes the impact of transformations on the area and perimeter of any two-dimensional geometric figure (2.4.A1h), e.g., enlarging by a factor of three triples the perimeter (circumference) and multiplies the area by a factor of nine.
Indicator 2
(A) The student describes and draws a two-dimensional figure after undergoing two specified transformations without using a concrete object.
Indicator 3
(A) The student investigates congruency, similarity, and symmetry of geometric figures using transformations.
Indicator 4
(A) The student uses a scale drawing to determine the actual dimensions and/or measurements of a two-dimensional figure represented in a drawing (2.4.A1h,I).
Benchmark 4
Geometry from an Algebraic Perspective - The student uses an algebraic perspective to examine the geometry of two-dimensional figures in a variety of situations.
Indicator 1
(K) The student uses the coordinate plane to (2.4.K1h):
a. list several ordered pairs on the graph of a line and finds the slope of the line;
b. recognize that ordered pairs that lie on the graph of an equation are solutions to that equation;
c. recognize that points that do not lie on the graph of an equation are not solutions to that equation;
d. determine the length of a side of a figure drawn on a coordinate plane with vertices having the same x-or y-coordinates;
e. solve simple systems of linear equations.
Indicator 2
(K) The student uses a given linear equation with integer coefficients and constants and an integer solution to find the ordered pairs, organizes the ordered pairs using a T-table, and plots the ordered pairs on a coordinate plane (2.4.K1g-h).
Indicator 3
(K) The student examines characteristics of two-dimensional figures on a coordinate plane using various methods including mental math, paper and pencil concrete objects, and graphing utilities or other appropriate technology (2.4.A1g).
Indicator 1
(A) The student represents, generates, and/or solves distance problems including the use of the Pythagorean theorem, but not necessarily the distance formula) (2.4.A1g), e.g., A student lives five miles west and three miles north of school and another student lives 4 miles south and 7 miles east of school. What is the shortest distance between the students' homes (as the crow flies)?
Indicator 2
(A) The student translates between the written, numeric, algebraic, and geometric representations of a real-world problem (2.4.A1d-g), e.g., given a situation (ex), make a T-table, define the algebraic relationship, and graph the ordered pairs.
The student uses concepts and procedures of data analysis in a variety of situations.
Benchmark 1
Probability - The student applies the concepts of probability to draw conclusions, generate convincing arguments, and make predictions and decisions including the use of concrete objects in a variety of situations.
Indicator 1
(K) The student knows and explains the difference between independent and dependent events in an experiment, simulation, or situation (2.4.K1l).
Indicator 2
(K) The student identifies situations with independent or dependent events in an experiment, simulation, or situation (2.4.K1k), e.g., There are three marbles in a bag. If you draw one marble and give it to your brother, and another marble and give it to your sister, are these independent events or dependent events?
Indicator 3
(K) The student finds the probability of a compound event composed of two independent events in an experiment, simulation, or situation, e.g., what is the probability of getting two heads, if you toss a dime and a quarter?
Indicator 4
(K) The student finds the probability of simple and/or compound events using geometric models (spinners or dartboards) (2.4.K1k).
Indicator 5
(K) The student finds the odds of a desired outcome in an experiment or simulation and expresses the answer as a ratio (2/3 or 2:3 or 2 to 3) (2.4.K1l).
Indicator 6
(K) The student describes the difference between probability and odds.
Indicator 1
(A) The student conducts an experiment or simulation with independent or dependent events including the use of concrete objects; records the results in a chart, table, or graph; and uses the results to draw conclusions and make predictions about future events (2.4.A1k).
Indicator 2
(A) The student analyzes the results of an experiment or simulation of two independent events to generate convincing arguments, draw conclusions, and make predictions and decisions in a variety of real-world situations, e.g., examine the precipitation totals for the last 20 years to estimate the probability that the rainfall for this year will be more than 17 inches.
Indicator 3
(A) The student compares theoretical probability (expected results) with empirical probability (experimental results) in an experiment or simulation with a compound event composed of two independent events and understands that the larger the sample size, the greater the likelihood that the experimental results will equal the theoretical probability (2.4.A1k).
Indicator 4
(A) The student makes predictions based on the theoretical probability of (2.4 A1k):
a. a simple event,
b. compound events composed of two independent events.
Benchmark 2
Statistics - The student collects, organizes, displays, explains, and interprets numerical (rational) and non-numerical data sets in a variety of situations.
Indicator 1
(K) The student qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays (2.4.K1i) $:
a. frequency tables;
b. bar, line, and circle graphs;
c. Venn diagrams or other pictorial displays;
d. charts and tables;
e. stem-and-leaf plots (single and double);
f. scatter plots;
g. box-and-whiskers plots;
h. histograms.
Indicator 2
(K) The student recognizes valid and invalid data collection and sampling techniques.
Indicator 3
(K) The student determines and explains the measures of central tendency mode, median, mean) for a rational number data set (2.4.K1i).
Indicator 4
(K) The student determines and explains the range, quartiles, and interquartile range for a rational number data set.
Indicator 5
(K) The student explains the effects of outliers on the median, mean, and range of a rational number data set.
Indicator 6
(K) The student makes a scatter plot and draws a line that approximately represents the data, determines whether a correlation exists, and if that correlation is positive, negative, or that no correlation exists (2.4.K1m).
Indicator 1
(A) The student uses data analysis (mean, median, mode, range) in real world problems with rational number data sets to compare and contrast two sets of data, to make accurate inferences and predictions, to analyze decisions, and to develop convincing arguments from these data displays (2.4.A1h) $:
a. frequency tables;
b. bar, line, and circle graphs;
c. Venn diagrams or other pictorial displays;
d. charts and tables;
e. stem-and-leaf plots (single and double);
f. scatter plots;
g. box-and-whiskers plots;
h. histograms.
Indicator 2
(A) The student explains advantages and disadvantages of various data collection techniques (observations, surveys, or interviews), and sampling techniques (random sampling, samples of convenience, biased sampling, or purposeful sampling) in a given situation.
Indicator 3
(A) The student recognizes and explains:
a. misleading representations of data;
b. the effects of scale or interval changes on graphs of data sets.
Indicator 4
(A) The student recognizes faulty arguments and common errors in data analysis.
USD
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