Indicator A: Develops and applies number sense to solve a variety of real-life problems and to determine if the results are reasonable

Resources

Date Completed

1. Develops concepts, number sense, and number relationships relating to integers and rational numbers (e.g., whole numbers, decimals, fractions)

a.Explains the meaning of absolute value, e.g., |-8| = 8

Boxer Intermediate Algebra 2,sec 2
Skillstutor Algebra Factoring

b.Uses positive and negative exponents

Boxer Introductory Algebra 7,sec 1-4
Skillstutor Algebra Factoring

2. Selects and uses appropriate techniques while solving problems and determining the reasonableness of results

Boxer Intermediate Algebra 2,sec 5
Top 50 Math Skills 42,44,45,46,47,48,49,50

3. Compares and contrasts the real number system and its various subsystems with regard to their structural characteristics

a.Classifies numbers as members of the sets (natural, whole, integers, rationals, and irrationals)

Boxer Introductory Algebra 5,sec 10

b.Compares subsets of the real number system with regard to their properties (commutative, associative, distributive, identity, inverse and closure properties)

Boxer Introductory Algebra 2,sec 6

Date Completed

1. Constructs, reads, analyzes, and interprets tables, charts, and graphs

a. Evaluates the reasonableness of conclusions drawn from interpretation of data in a graphic format

Supplemental: Country of origin

Smoking Statistics

2. Constructs and draws inferences including measures of central tendency, from charts, tables, graphs and data plots that summarize data from real-world situations

a.Organizes collections of data into frequency charts, stem-and-leaf plots, scatter plots and matrices and determines outliers

b.Constructs histograms, line graphs, circle graphs and box-and-whisker plots

c. Uses mode, quartiles and range as a means for effective decision making in analyzing the data

Supplemental Bar Graphs and Histograms

Stem and Leaf Charts

Box Plots

3. Applies curve fitting to make predictions from data

a. Draws a line or a curve which closely fits a scatter plot

Dave’s Trig Course
Top 50 math Skills 32

4. Explains the effects of sampling on statistical claims and recognizes misuses of statistics

a. Differentiates between a biased and an unbiased sample

b. Recognizes the impact of interpreting data from a biased sample

Supplemental: Bell Curve

Statistical Bias

5. Determines probabilities through experiments and/or simulations and compares the results with prediction

a. Uses simulations to estimate probabilities of real-life situations

b. Designs a statistical experiment based on a given hypothesis

Suppplemental: Probability Game

Lots of probability games
Top 50 math skills #40
Supplemental: Try one of these Ask Dr. Math

6.Describes, in general terms, the normal curve and uses its properties to answer questions about its of data that are assumed to be normally distributed

a. Determines if data gathered from a real-world situation fit a normal curve

b Describes the central tendency characteristics of the normal curve

c.Makes simple predictions from data represented on the graph

Boxer Intermediate Algebra 9,sec all
Functions and Verticle Line Test
Supplemetal: Bell Curve

7. Explains the concept of a random variable

a Distinguishes situations where a random variable is needed or used

b.Uses a random number table or technology to generate random numbers in modeling real-life situations (e.g., select randomly who belongs in what group)

Boxer Introductory Algebra 3,sec 2-12

Skillstutor Algebra Functions

8. Applies measures of central tendency, variability, and correlation

a. Draws conclusions about the "spread" of data given the variance and standard deviation (e.g., compare sets of data with the same central tendency but with different variance)

b.Determines, from a given plot of data, whether it has strong or weak, positive or negative correlation

Boxer Intermediate Algebra 9,sec all

Indicator C: Applies algebraic concepts and methods to explore, analyze or solve real life problems

Resources

Date Completed

1.Models real-world phenomena using functions and relations

a. Identifies the independent and dependent variables from a real-life situation

b. Expresses the relationship between two variables using a table, equation, graph, and matrix

c. Describes the relationship suggested by two or more graphs of related real-world situations

Boxer Intermediate Algebra 9,sec all

Graph Lesson

Top 50 Math Skills #48

Skillstutor Algebra Functions

2. Interprets algebraic equations and inequalities geometrically and describes geometric relationships algebraically

a.Graphs a linear equation in two variables

b.Graphs a linear inequality in two variables

c.Determines slope and intercepts of a linear equation

d.Writes an equation of the line that passes through two given points

e.Determines from two linear equations whether the lines are parallel, are perpendicular or coincide

Boxer Introductory Algebra 10,sec all

Boxer Intermediate Algebra 4,sec all

Top 50 Math Skills #48,49

Skillstutor Algebra Functions

3. Applies trigonometry to real-life problem situations (e.g., investigates how to find the distance across the river using similar triangles and trigonometric ratios; compares the sine and cosine curves to the curves of sound waves and tide variations)

a. Uses the definitions of trigonometric functions to find the sine, cosine and tangent of the acute angles of a right triangle

b. Solves simple right-triangle trigonometric equations involving sine, cosine and tangent

c. Uses an appropriate right-triangle trigonometric model to solve a real-life problem

Supplemetal: Leslie

Dave’s Trig Lessons

4. Performs mathematical operations on expressions and matrices, and solves equations and inequalities

a. Simplifies numerical expressions using the order of operations including exponents

b. Evaluates algebraic expressions using substitution

c. Simplifies square roots and cube roots with monomial radicands that are perfect squares or perfect cubes

d .Evaluates numerical and algebraic absolute value expressions

e. Multiplies and divides monomial expressions with integer exponents

f. Solves linear equations and inequalities in one variable

g. Solves quadratic equations

h. Solves radical equations involving one radical

I Solves proportions which generate linear or quadratic equations

j Solves absolute value equations containing a single absolute value expression

k. Solves systems of linear equations in two variables

Boxer Introductory Algebra 8,9,10,sec all

Top 50 Math Skills #41,44,47,48,49,50

Skillstutor Algebra Equations, Factoring

5.Translates among tabular, symbolic and graphical representations of functions

a. Creates a linear equation from a table of values

b. Creates a graph from a table of values

c. Determines the solution to a system of inequalities in two variables, from a given graph (e.g., "Which of the shaded regions represents the solution to the system?")

d. Determines the solution to a system of equations in two variables, from a given graph

Boxer Intermediate Algebra 6,sec 8

Graph Lesson

Skillstutor Algebra Functions

Top 50 Math Skills #48

Indicator D: Uses geometric properties, relationships, and methods to identify, analyze and solve real-life problems

Resources

Date Completed

1. Interprets and draws three-dimensional objects

a .Sketches prisms, pyramids, cones, and spheres

b. Classifies prisms, pyramids, cones, cylinders and spheres by base shape, lateral surface shape, related surface area and volume formulas

Surface Area and Volume

2. Represents problem situations with geometric models and applies properties of figures

a. Calculates surface areas and volumes of three-dimensional geometric figures given the required formulas

Area Lesson

3. Deduces properties of figures using transformations in coordinate systems, identifying

congruency and similarity

a. Determines whether a figure is symmetric with respect to a line or a point

b. Gives the new coordinates of a transformed geometric figure

c. Determines the effects of a transformation on linear and area measurements of the original figure

d. Sketches the figure that is the result of a given transformation

Symmetry Lesson

4.Deduces properties of and relationships between figures from given assumptions

a. Finds similarities and differences among geometric shapes and designs using a given attribute (e.g., height, area, perimeter, diagonals, angle measurements)

b.Identifies arcs, chords, tangents and secants of a circle

c.States valid conclusions using informal deductive reasoning

Dave’s Trig Lessons

5. Translates between synthetic and coordinate representations (e.g., a straight line is represented by the algebraic equation Ax + By = C)

a.Verifies characteristics of a given geometric figure using coordinate formulas such as distance, mid-point, and slope to confirm parallelism, perpendicularity, and congruency

Graphs and Functions

6.Recognizes and analyzes Euclidean transformations (e.g., reflections, rotations, dilations and translations)

a.Classifies transformations based on whether they produce congruent or similar non- congruent figures

b.Determines whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation and/or dilation.

c.Applies transformational principles to practical situations (e.g., enlarge a photograph)

Geometry Tessellations

Translations, Reflections, Rotations

Four Symmetries in Plane

Indicator E: Uses both inductive and deductive reasoning in making conjectures and testing the validity of arguments

Resources

Date Completed

1. Uses inductive and deductive logic to construct simple valid arguments

a. Constructs a simple informal deductive proof (e.g., write a proof of the statement: "You can fly from Bombay to Mexico City, given an airline schedule")

b. Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations (e.g., if 10' = 10, 10'= 100, 10'= 1000, make a conjecture)

Unusual School

Lots of Proofs

2. Determines the validity of arguments

a. Determines if the converse of a given statement is true or false

b. Draws a simple valid conclusion from a given if ... then statement and a minor premise

c.Lists related if….then statements in logical order

d. Distinguishes valid arguments from invalid arguments

e. Analyzes assertions about everyday life by using principles of logic (e.g., examine the fallacies of advertising)

f. Uses Venn diagrams to determine the validity of an argument

g Recognizes the difference between a statement verified by mathematical proof(i.e., a theorem) and one verified by empirical data (e.g., women score higher than men on vocabulary tests)

Supplemetal: Deductions

Lots of Proofs

Misuse of Statistics

3.Formulates counterexamples and uses indirect proof

Lots of Proofs

a. Constructs a counterexample to show that a given invalid conjecture is false (e.g., Nina makes a conjecture that x' > x' for all values of x. Find a counterexample.)

b. Writes an algorithm that explains a particular mathematical process (e.g., tell a younger child how to find the average of two numbers)

c. Determines the purpose of a given algorithm

d. Determines whether given algorithms are equivalent

Supplemental: Ice Cream Stand Algorithm