M11.A: Numbers and Operations

M11.A.1: Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.

M11.A.1.1: Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, exponents and scientific notation).

M11.A.1.1.1: Find the square root of an integer to the nearest tenth using either a calculator or estimation.

Square Roots

M11.A.1.1.2: Express numbers and/or simplify expressions using scientific notation (including numbers less than 1).

Unit Conversions 2 - Scientific Notation and Significant Digits

M11.A.1.1.3: Simplify square roots. (e.g., square root of 24 = 2 times the square root of 6)

Operations with Radical Expressions
Simplifying Radical Expressions

M11.A.1.3: Estimate the value of an irrational number.

M11.A.1.3.2: Compare and/or order any real numbers (rational and irrational may be mixed).

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

M11.A.2: Understand the meanings of operations, use operations and understand how they relate to each other.

M11.A.2.1: Apply ratio and/or proportion in problem-solving situations.

M11.A.2.1.2: Solve problems using direct and inverse proportions.

Direct and Inverse Variation

M11.A.2.1.3: Identify and/or use proportional relationships in problem solving settings.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios

M11.A.2.2: Use exponents, roots and/or absolute value to solve problems.

M11.A.2.2.1: Simplify/evaluate expressions involving positive and negative exponents, roots and/or absolute value (may contain all types of real numbers - exponents should not exceed power of 10).

Absolute Value Equations and Inequalities
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

M11.A.3: Compute accurately and fluently and make reasonable estimates.

M11.A.3.1: Apply the order of operations in computation and in problem-solving situations.

M11.A.3.1.1: Simplify/evaluate expressions using the order of operations to solve problems (any rational numbers may be used).

Solving Equations on the Number Line

M11.A.3.2: Use estimation strategies in problem-solving situations.

M11.A.3.2.1: Use estimation to solve problems.

Estimating Population Size

M11.B: Measurement

M11.B.2: Apply appropriate techniques, tools and formulas to determine measurements.

M11.B.2.2: Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface area and/or volume. (May require conversions within the same system.)

M11.B.2.2.1: Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

M11.B.2.2.2: Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.

Prisms and Cylinders

M11.B.2.2.4: Find the measurement of a missing length given the perimeter, circumference, area or volume.

Perimeters and Areas of Similar Figures

M11.C: Geometry

M11.C.1: Analyze characteristics and properties of two- and three- dimensional geometric shapes and demonstrate understanding of geometric relationships.

M11.C.1.1: Identify and/or use parts of circles and segments associated with circles.

M11.C.1.1.2: Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central angles.

Chords and Arcs
Inscribed Angles

M11.C.1.2: Recognize and/or apply properties of angles, triangles and quadrilaterals.

M11.C.1.2.1: Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem).

Concurrent Lines, Medians, and Altitudes
Similarity in Right Triangles
Triangle Inequalities

M11.C.1.2.2: Identify and/or use properties of quadrilaterals (e.g., parallel sides, diagonals, bisectors, congruent sides/angles and supplementary angles).

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

M11.C.1.2.3: Identify and/or use properties of isosceles and equilateral triangles

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Triangle Inequalities

M11.C.1.3: Use properties of congruence, correspondence and similarity in problem-solving settings involving two- and three- dimensional figures.

M11.C.1.3.1: Identify and/or use properties of congruent and similar polygons or solids.

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

M11.C.1.4: Solve problems involving right triangles using the Pythagorean Theorem.

M11.C.1.4.1: Find the measure of a side of a right triangle using the Pythagorean Theorem (Pythagorean Theorem included on the reference sheet).

Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Tangent Function

M11.C.3: Locate points or describe relationships using the coordinate plane.

M11.C.3.1: Solve problems using analytic geometry.

M11.C.3.1.1: Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane (formula provided on the reference sheet).

Circles
Distance Formula
Parabolas

M11.D: Algebraic Concepts

M11.D.1: Demonstrate an understanding of patterns, relations and functions.

M11.D.1.1: Analyze and/or use patterns or relations.

M11.D.1.1.1: Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.

Arithmetic Sequences
Geometric Sequences

M11.D.1.1.2: Determine if a relation is a function given a set of points or a graph.

Linear Functions

M11.D.2: Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs.

M11.D.2.1: Write, solve and/or graph linear equations and inequalities using various methods.

M11.D.2.1.1: Solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).

Absolute Value Equations and Inequalities
Compound Inequalities
Solving Linear Inequalities in One Variable

M11.D.2.1.2: Identify or graph functions, linear equations or linear inequalities on a coordinate plane.

Absolute Value Equations and Inequalities
Linear Functions
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

M11.D.2.1.3: Write, solve and/or apply a linear equation (including problem situations).

Linear Functions
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations
Standard Form of a Line

M11.D.2.1.4: Write and/or solve systems of equations using graphing, substitution and/or elimination (limit systems to 2 equations).

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

M11.D.2.1.5: Solve quadratic equations using factoring (integers only - not including completing the square or the Quadratic Formula).

Modeling the Factorization of x²+bx+c

M11.D.2.2: Simplify expressions involving polynomials.

M11.D.2.2.1: Add, subtract and/or multiply polynomial expressions (express answers in simplest form - nothing larger than a binomial multiplied by a trinomial).

Addition and Subtraction of Functions
Modeling the Factorization of x²+bx+c

M11.D.2.2.2: Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax²+bx+c where a is not equal to 0).

Dividing Polynomials Using Synthetic Division
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

M11.D.3: Analyze change in various contexts.

M11.D.3.1: Describe and/or determine change.

M11.D.3.1.1: Identify, describe and/or use constant or varying rates of change.

Compound Interest
Dilations
Direct and Inverse Variation
Distance-Time and Velocity-Time Graphs

M11.D.3.2: Compute and/or use the slope of a line.

M11.D.3.2.1: Apply the formula for the slope of a line to solve problems (formula given on reference sheet).

Slope

M11.D.3.2.2: Given the graph of the line, 2 points on the line, or the slope and a point on a line, write or identify the linear equation in point-slope, standard and/or slope-intercept form.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

M11.D.3.2.3: Compute the slope and/or y-intercept represented by a linear equation or graph.

Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

M11.D.4: Describe or use models to represent quantitative relationships.

M11.D.4.1: Interpret and/or use linear, quadratic and/or exponential functions and their equations, graphs or tables.

M11.D.4.1.1: Match the graph of a given function to its table or equation.

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions

M11.E: Data Analysis and Probability

M11.E.1: Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data.

M11.E.1.1: Appropriately display and/or use data in problem-solving settings.

M11.E.1.1.1: Create and/or use appropriate graphical representations of data, including box-and-whisker plots, stem-and-leaf plots or scatter plots.

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

M11.E.1.1.2: Analyze data and/or answer questions based on displayed data (box-and-whisker plots, stem-and-leaf plots or scatter plots).

Box-and-Whisker Plots
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

M11.E.2: Select and/or use appropriate statistical methods to analyze data.

M11.E.2.1: Use measures of central tendency to describe a set of data.

M11.E.2.1.1: Calculate or select the appropriate measure of central tendency (mean, mode or median) of a set of data given or represented on a table, line plot or stem-and-leaf plot.

Describing Data Using Statistics
Mean, Median, and Mode
Stem-and-Leaf Plots

M11.E.2.1.2: Calculate and/or interpret the range, quartiles and interquartile range of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Stem-and-Leaf Plots

M11.E.2.1.3: Describe how outliers affect measures of central tendency.

Describing Data Using Statistics
Mean, Median, and Mode

M11.E.3: Understand and/or apply basic concepts of probability or outcomes.

M11.E.3.1: Apply probability and/or odds to practical situations.

M11.E.3.1.2: Find, convert and/or compare the probability and/or odds of a simple event.

Independent and Dependent Events
Theoretical and Experimental Probability

M11.E.4: Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays.

M11.E.4.1: Make predictions using data displays and probability.

M11.E.4.1.2: Use probability to predict outcomes.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

M11.E.4.2: Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.

M11.E.4.2.1: Draw, find and/or write an equation for a line of best fit for a scatter plot.

Correlation
Determining a Spring Constant
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

M11.E.4.2.2: Make predictions using the equations or graphs of best-fit lines of scatter plots.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots