Curriculum Standards

1.1.1: knows, explains, and uses equivalent representations for real numbers and algebraic expressions including integers, fractions, decimals, percents, ratios; rational number bases with integer exponents; rational numbers written in scientific notation; absolute value; time; and money, e.g., -4/2 = (-2); a to the -2 power x b cubed = b cubed/a squared.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

Part-to-part and Part-to-whole Ratios

Rational Numbers, Opposites, and Absolute Values

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

1.1.2: compares and orders real numbers and/or algebraic expressions and explains the relative magnitude between them, e.g., e.g., will (5n) squared always, sometimes, or never be larger than 5n? The student might respond with (5n)2 is greater than 5n if n > 1 and (5n) squared is smaller than 5 if o < n < 1.

Comparing and Ordering Decimals

Rational Numbers, Opposites, and Absolute Values

1.2.3: names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects:

1.2.3.a: 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], and substitution properties (if a = 2, then 3a = 3 x 2 = 6);

Equivalent Algebraic Expressions I

1.2.3.b: identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity: a + 0 = a, multiplicative identity: a x 1 = a, additive inverse: +5 + -5 = 0, multiplicative inverse: 8 x 1/8 = 1);

Rational Numbers, Opposites, and Absolute Values

Simplifying Algebraic Expressions I

1.4.2: performs and explains these computational procedures:

1.4.2.a: addition, subtraction, multiplication, and division using the order of operations;

Solving Algebraic Equations II

1.4.2.d: simplification of radical expressions (without rationalizing denominators) including square roots of perfect square monomials and cube roots of perfect cubic monomials;

Operations with Radical Expressions

Simplifying Radical Expressions

1.4.2.e: simplification or evaluation of real numbers and algebraic monomial expressions raised to a whole number power and algebraic binomial expressions squared or cubed;

Simplifying Algebraic Expressions II

1.4.2.f: simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents;

Dividing Exponential Expressions

Multiplying Exponential Expressions

Simplifying Algebraic Expressions II

2.1.1: identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written:

2.1.1.b: patterns using geometric figures;

Arithmetic and Geometric Sequences

Finding Patterns

2.1.1.c: algebraic patterns including consecutive number patterns or equations of functions, e.g., n, n + 1, n + 2,... or f(n) = 2n – 1;

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

2.1.1.d: special patterns, e.g., Pascal’s triangle and the Fibonacci sequence.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

2.1.2: generates and explains a pattern.

Arithmetic Sequences

Geometric Sequences

2.1.3: classify sequences as arithmetic, geometric, or neither.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

2.1.4: defines:

2.1.4.a: a recursive or explicit formula for arithmetic sequences and finds any particular term,

Arithmetic Sequences

Arithmetic and Geometric Sequences

2.1.4.b: a recursive or explicit formula for geometric sequences and finds any particular term.

Arithmetic and Geometric Sequences

Geometric Sequences

2.2.1: knows and explains the use of variables as parameters for a specific variable situation, e.g., the m and b in y = mx + b or the h, k, and r in (x – h) squared + (y – k) squared = r squared.

Solving Equations on the Number Line

Using Algebraic Equations

2.2.3: solves:

2.2.3.a: linear equations and inequalities both analytically and graphically;

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Systems of Linear Inequalities (Slope-intercept form)

2.2.3.b: quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring);

Modeling the Factorization of *x*^{2}+*bx*+*c*

2.2.3.d: radical equations with no more than one inverse operation around the radical expression;

Operations with Radical Expressions

Radical Functions

2.2.3.g: exponential equations with the same base without the aid of a calculator or computer, e.g., 3 to the power (x + 2) = 3 to the fifth power.

2.3.1: evaluates and analyzes functions using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Radical Functions

2.3.2: matches equations and graphs of constant and linear functions and quadratic functions limited to y = ax squared + c.

Addition and Subtraction of Functions

Exponential Functions

Point-Slope Form of a Line

Quadratics in Factored Form

Quadratics in Polynomial Form

Roots of a Quadratic

Slope-Intercept Form of a Line

Standard Form of a Line

Translating and Scaling Functions

Zap It! Game

2.3.3: determines whether a graph, list of ordered pairs, table of values, or rule represents a function.

Exponential Functions

Introduction to Exponential Functions

Introduction to Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Radical Functions

2.3.5.: a. relationships given the graph or table,

2.3.6: recognizes how changes in the constant and/or slope within a linear function changes the appearance of a graph.

Slope-Intercept Form of a Line

2.3.8: evaluates function(s) given a specific domain.

2.4.1: knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include:

2.4.1.a: process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations;

2.4.1.d: equations and inequalities to model numerical and geometric relationships;

Comparing and Ordering Decimals

2.4.1.f: coordinate planes to model relationships between ordered pairs and equations and inequalities and linear and quadratic functions

2.4.1.g: constructions to model geometric theorems and properties;

2.4.1.h: two- and three-dimensional geometric models (geoboards, dot paper, coordinate plane, nets, or solids) and real-world objects to model perimeter, area, volume, and surface area and isometric views of three-dimensional figures.

Classifying Quadrilaterals

Pyramids and Cones

2.4.1.j: Pascal’s Triangle to model binomial expansion and probability;

2.4.1.l: 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, histograms, and matrices to organize and display data;

Box-and-Whisker Plots

Compound Inequalities

Correlation

Describing Data Using Statistics

Distance-Time Graphs

Histograms

Least-Squares Best Fit Lines

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Solving Using Trend Lines

Stem-and-Leaf Plots

Trends in Scatter Plots

3.1.1: recognizes and compares properties of two-and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.

Classifying Quadrilaterals

Classifying Triangles

Parallelogram Conditions

Similar Figures

Special Parallelograms

3.1.2: discusses properties of regular polygons related to:

3.1.2.b: diagonals.

3.1.4: recognizes that similar figures have congruent angles, and their corresponding sides are proportional.

3.1.5: uses the Pythagorean Theorem to:

3.1.5.b: find a missing side of a right triangle.

Cosine Function

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Tangent Function

3.1.6: recognizes and describes:

3.1.6.b: the ratios of the sides in special right triangles: 30°-60°-90° and 45°-45°-90°.

Cosine Function

Sine Function

Tangent Function

3.1.7: recognizes, describes, and compares the relationships of the angles formed when parallel lines are cut by a transversal.

Constructing Congruent Segments and Angles

Triangle Angle Sum

3.1.8: recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines, central and inscribed angles.

Chords and Arcs

Circumference and Area of Circles

Inscribed Angles

3.2.4: states, recognizes, and applies formulas for:

3.2.4.a: perimeter and area of squares, rectangle, and triangles;

Area of Parallelograms

Area of Triangles

Perimeter and Area of Rectangles

3.2.4.b: circumference and area of circles;

Circumference and Area of Circles

3.2.4.c: volume of rectangular solids.

Prisms and Cylinders

Pyramids and Cones

3.2.5: uses given measurement formulas to find perimeter, area, volume, and surface area of two- and three-dimensional figures (regular and irregular).

Area of Parallelograms

Area of Triangles

Circumference and Area of Circles

Perimeter and Area of Rectangles

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

3.2.6: recognizes and applies properties of corresponding parts of similar and congruent figures to find measurements of missing sides.

Beam to Moon (Ratios and Proportions)

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures

Similarity in Right Triangles

3.2.7: knows, explains, and uses ratios and proportions to describe rates of change $, e.g., miles per gallon, meters per second, calories per ounce, or rise over run.

3.3.1: describes and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on two- and three-dimensional figures.

Circles

Dilations

Holiday Snowflake Designer

Reflections

Rotations, Reflections, and Translations

Similar Figures

Translations

3.3.3: generates a two-dimensional representation of a three-dimensional figure.

Surface and Lateral Areas of Prisms and Cylinders

3.4.2: determines if a given point lies on the graph of a given line or parabola without graphing and justifies the answer.

3.4.3: calculates the slope of a line from a list of ordered pairs on the line and explains how the graph of the line is related to its slope.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Slope

Slope-Intercept Form of a Line

3.4.4: finds and explains the relationship between the slopes of parallel and perpendicular lines, e.g., the equation of a line 2x + 3y = 12. The slope of this line is 2/3. What is the slope of a line perpendicular to this line? Write an equation for a line perpendicular to 2x + 3y = 12 (or for multiple choice: Which is an equation of a line perpendicular to 2x + 3y = 12?

Cat and Mouse (Modeling with Linear Systems)

3.4.6: recognizes the equation of a line and transforms the equation into slope-intercept form in order to identify the slope and y-intercept and uses this information to graph the line.

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

3.4.7: recognizes the equation y = ax squared + c as a parabola; represents and identifies characteristics of the parabola including opens upward or opens downward, steepness (wide/narrow), the vertex, maximum and minimum values, and line of symmetry; and sketches the graph of the parabola.

Addition and Subtraction of Functions

Parabolas

Translating and Scaling Functions

Zap It! Game

3.4.8: explains the relationship between the solution(s) to systems of equations and systems of inequalities in two unknowns and their corresponding graphs, e.g., for equations, the lines intersect in either one point, no points, or infinite points; and for inequalities, all points in double-shaded areas are solutions for both inequalities.

Cat and Mouse (Modeling with Linear Systems)

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

4.1.1: finds the probability of two independent events in an experiment, simulation, or situation.

Binomial Probabilities

Independent and Dependent Events

Theoretical and Experimental Probability

4.1.2: finds the conditional probability of two dependent events in an experiment, simulation, or situation.

Independent and Dependent Events

4.2.1: organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays.

4.2.1.a: frequency tables;

4.2.1.b: bar, line, and circle graphs;

Reaction Time 1 (Graphs and Statistics)

4.2.1.c: Venn diagrams or other pictorial displays;

4.2.1.d: charts and tables;

Describing Data Using Statistics

Stem-and-Leaf Plots

4.2.1.h: histograms.

4.2.2: explains how the reader’s bias, measurement errors, and display distortions can affect the interpretation of data.

Polling: City

Polling: Neighborhood

Populations and Samples

4.2.3: calculates and explains the meaning of range, quartiles and interquartile range for a real number data set.

Reaction Time 1 (Graphs and Statistics)

4.2.5: approximates a line of best fit given a scatter plot and makes predictions using the equation of that line.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

4.2.6: compares and contrasts the dispersion of two given sets of data in terms of range and the shape of the distribution including

4.2.6.b: skew (left or right),

4.2.6.c: bimodal,

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Correlation last revised: 3/1/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.