1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.
1.A: apply mathematics to problems arising in everyday life, society, and the workplace;
Estimating Population Size
1.B: use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
Estimating Population Size
1.C: select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
Estimating Sums and Differences
1.D: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Biconditional Statements
Using Algebraic Expressions
1.E: create and use representations to organize, record, and communicate mathematical ideas;
Describing Data Using Statistics
Stem-and-Leaf Plots
Using Algebraic Expressions
1.G: display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Using Algebraic Expressions
2: The student applies mathematical process standards to represent and use real numbers in a variety of forms.
2.B: approximate the value of an irrational number, including ? and square roots of numbers less than 225, and locate that rational number approximation on a number line;
Circumference and Area of Circles
Square Roots
2.C: convert between standard decimal notation and scientific notation; and
Number Systems
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits
2.D: order a set of real numbers arising from mathematical and real-world contexts.
Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
3: The student applies mathematical process standards to use proportional relationships to describe dilations.
3.A: generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation;
Dilations
Similar Figures
3.B: compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and
Dilations
3.C: use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.
Dilations
4: The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope.
4.B: graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and
Direct and Inverse Variation
4.C: use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.
Cat and Mouse (Modeling with Linear Systems)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Slope
Slope-Intercept Form of a Line
5: The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.
5.A: represent linear proportional situations with tables, graphs, and equations in the form of y = kx;
Direct and Inverse Variation
Proportions and Common Multipliers
5.B: represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ? 0;
Function Machines 1 (Functions and Tables)
5.C: contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation;
Correlation
Trends in Scatter Plots
5.D: use a trend line that approximates the linear relationship between bivariate sets of data to make predictions;
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
5.E: solve problems involving direct variation;
Direct and Inverse Variation
5.G: identify functions using sets of ordered pairs, tables, mappings, and graphs;
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
5.H: identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and
Direct and Inverse Variation
5.I: write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.
Slope-Intercept Form of a Line
6: The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas.
6.A: describe the volume formula V = Bh of a cylinder in terms of its base area and its height;
Prisms and Cylinders
Pyramids and Cones
6.B: model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; and
Pyramids and Cones
6.C: use models and diagrams to explain the Pythagorean theorem.
Circles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones
7: The student applies mathematical process standards to use geometry to solve problems.
7.A: solve problems involving the volume of cylinders, cones, and spheres;
Prisms and Cylinders
Pyramids and Cones
7.B: use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders;
Surface and Lateral Areas of Prisms and Cylinders
7.C: use the Pythagorean Theorem and its converse to solve problems; and
Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones
7.D: determine the distance between two points on a coordinate plane using the Pythagorean Theorem.
Circles
Distance Formula
8: The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.
8.A: write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants;
Absolute Value Equations and Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
8.B: write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants;
Solving Equations on the Number Line
8.C: model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; and
Absolute Value Equations and Inequalities
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations
8.D: use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
Constructing Congruent Segments and Angles
Isosceles and Equilateral Triangles
Polygon Angle Sum
Similar Figures
Triangle Angle Sum
10: The student applies mathematical process standards to develop transformational geometry concepts.
10.A: generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane;
Dilations
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations
10.B: differentiate between transformations that preserve congruence and those that do not;
Dilations
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations
10.C: explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; and
Dilations
Rock Art (Transformations)
Translations
10.D: model the effect on linear and area measurements of dilated two-dimensional shapes.
Dilations
11: The student applies mathematical process standards to use statistical procedures to describe data.
11.A: construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data;
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
11.C: simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected
Polling: City
Populations and Samples
12: The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor.
12.A: solve real-world problems comparing how interest rate and loan length affect the cost of credit;
Compound Interest
12.B: calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator;
Compound Interest
12.D: calculate and compare simple interest and compound interest earnings;
Compound Interest
12.E: identify and explain the advantages and disadvantages of different payment methods;
Household Energy Usage
Percent of Change
12.F: analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility; and
Household Energy Usage
Percent of Change
Correlation last revised: 9/16/2020