Integrated Math 1
Integrated Math 1
Quarter 4
Math Champions & Chapters 11-12
Quarter 4
Math Champions & Chapters 11-12
Embedded Files
Math Champions & Chapters 11-12
The Mathematics Department has organized the topics of Integrated Math 1 Quarter 4 begin with a thorough review of Chapters 1 through 10 to have students assessment-ready. We conclude the year with specialized chapters on data set analysis and rigid motions.
Math Champions is a 4-week program designed to provide practice opportunities for test-style items. Many of the concepts and skills review what was taught from Chapters 1 through 10.
Chapter 11 - Multi-variable Data Sets provides a complete analysis of a multi-variable data set. The chapter begins with categorical data analysis and ends with quantitative data analysis.
Chapter 12 - Rigid Motions and Triangle Congruence covers the basics of translations, reflections, and rotations. This transitions into determining whether triangles are congruent using these rigid motions and side-angle theorems.
Quarter 4 - Focus Objectives and Priority Standards
Quarter 4 - Focus Objectives and Priority Standards
Math Champions (click on arrows to expand section)
Math Champions (click on arrows to expand section)
Day 1.1 Ordered Pairs & Day 1.2 Exponent Rule
Day 1.1 Ordered Pairs & Day 1.2 Exponent Rule
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Seeing Structure in Expressions A.SSE.1b 🔗 Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
Algebra » Reasoning with Equations & Inequalities A.REI.10 🔗 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Day 2.1 Combine Polynomials & Day 2.2 Multiply Polynomials
Day 2.1 Combine Polynomials & Day 2.2 Multiply Polynomials
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Seeing Structure in Expressions A.SSE.1b 🔗 Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
Day 3.1 Difference of Squares & Day 3.2 Squaring Binomials
Day 3.1 Difference of Squares & Day 3.2 Squaring Binomials
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Seeing Structure in Expressions A.SSE.1b 🔗 Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
Day 4.1 Sum of Cubes & Day 4.2 Quadratic Function - Binomial Factor Form
Day 4.1 Sum of Cubes & Day 4.2 Quadratic Function - Binomial Factor Form
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Seeing Structure in Expressions A.SSE.1b 🔗 Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
Day 5 Linear Inequality Graphs
Day 5 Linear Inequality Graphs
Algebra » Reasoning with Equations & Inequalities A.REI.12 🔗 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Day 6.1 Quadratic Function - Standard Form & Day 6.2 Quadratic Function - Vertex Form
Day 6.1 Quadratic Function - Standard Form & Day 6.2 Quadratic Function - Vertex Form
Functions » Interpreting Functions F.IF.1 🔗 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Functions » Interpreting Functions F.IF.2 🔗 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Day 7.1 Additive Inverse Equations & Day 7.2 Create Equation from Formula
Day 7.1 Additive Inverse Equations & Day 7.2 Create Equation from Formula
Algebra » Reasoning with Equations & Inequalities A.REI.1 🔗 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Day 8.1 Multiplicative Inverse Equations & Day 8.2 Equation Solution Types (One, None, Infinite)
Day 8.1 Multiplicative Inverse Equations & Day 8.2 Equation Solution Types (One, None, Infinite)
Algebra » Reasoning with Equations & Inequalities A.REI.1 🔗 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Day 9.1 Multiplicative Inverse Equations - Variable in the Denominator & Day 9.2 Simplify Polynomial Expressions
Day 9.1 Multiplicative Inverse Equations - Variable in the Denominator & Day 9.2 Simplify Polynomial Expressions
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Seeing Structure in Expressions A.SSE.1b 🔗 Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
Algebra » Reasoning with Equations & Inequalities A.REI.1 🔗 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Day 10 Linear Function Graphs
Day 10 Linear Function Graphs
Functions » Interpreting Functions F.IF.7a 🔗 Graph linear and quadratic functions and show intercepts, maxima, and minima.
Day 11.1 Multiplicative Inverse Inequalities & Day 11.2 Equation Solution Types (None, One, Two)
Day 11.1 Multiplicative Inverse Inequalities & Day 11.2 Equation Solution Types (None, One, Two)
Algebra » Reasoning with Equations & Inequalities A.REI.1 🔗 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Day 12.1 Equations - Variable on Both Sides & Day 12.2 Multiply Polynomials
Day 12.1 Equations - Variable on Both Sides & Day 12.2 Multiply Polynomials
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Seeing Structure in Expressions A.SSE.1b 🔗 Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
Algebra » Reasoning with Equations & Inequalities A.REI.1 🔗 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Day 13.1 Multiplicative Negative Inverse Inequalities & Day 13.2 Cross Multiplication - Variable on One Side
Day 13.1 Multiplicative Negative Inverse Inequalities & Day 13.2 Cross Multiplication - Variable on One Side
Algebra » Reasoning with Equations & Inequalities A.REI.1 🔗 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Day 14.1 Solve Equations - Substitution & Day 14.2 Cross Multiplication - Variable on Both Sides
Day 14.1 Solve Equations - Substitution & Day 14.2 Cross Multiplication - Variable on Both Sides
Algebra » Reasoning with Equations & Inequalities A.REI.1 🔗 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Day 15 Inequality System Solution Region
Day 15 Inequality System Solution Region
Algebra » Reasoning with Equations & Inequalities A.REI.12 🔗 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Day 16.1 System of Linear Equation Solution Types (None, One, Infinite) - Graphs & Day 16.2 Multiplicative Negative Inverse Inequalities - Two-Step
Day 16.1 System of Linear Equation Solution Types (None, One, Infinite) - Graphs & Day 16.2 Multiplicative Negative Inverse Inequalities - Two-Step
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Algebra » Reasoning with Equations & Inequalities A.REI.6 🔗 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Functions » Linear, Quadratic, & Exponential Models F.LE.5 🔗 Interpret the parameters in a linear or exponential function in terms of a context.
Day 17.1 Approximate Solutions - Quadratic Functions & Day 17.2 Solve Equations - Graphs/Tables
Day 17.1 Approximate Solutions - Quadratic Functions & Day 17.2 Solve Equations - Graphs/Tables
Algebra » Reasoning with Equations & Inequalities A.REI.3 🔗 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Algebra » Reasoning with Equations & Inequalities A.REI.10 🔗 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Functions » Interpreting Functions F.IF.2 🔗 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Day 18.1 Approximate Solutions - 3rd Degree Polynomials & Day 18.2 Non-Linear Equation Graph Types (Parabola, Circle)
Day 18.1 Approximate Solutions - 3rd Degree Polynomials & Day 18.2 Non-Linear Equation Graph Types (Parabola, Circle)
Algebra » Reasoning with Equations & Inequalities A.REI.10 🔗 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Functions » Interpreting Functions F.IF.1 🔗 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Functions » Interpreting Functions F.IF.2 🔗 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Day 19 Equation Graph Interpretation
Day 19 Equation Graph Interpretation
Algebra » Reasoning with Equations & Inequalities A.REI.10 🔗 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Functions » Interpreting Functions F.IF.1 🔗 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Functions » Interpreting Functions F.IF.2 🔗 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Chapter 11 - Multi-variable Data Sets (click on arrows to expand section)
Chapter 11 - Multi-variable Data Sets (click on arrows to expand section)
Lesson 11.1 We will analyze the types of data in a data set.
Lesson 11.1 We will analyze the types of data in a data set.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.5 🔗 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Lesson 11.2 We will analyze two-way frequency tables.
Lesson 11.2 We will analyze two-way frequency tables.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.5 🔗 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Lesson 11.3 We will analyze associations in two-way frequency tables.
Lesson 11.3 We will analyze associations in two-way frequency tables.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.5 🔗 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Lesson 11.4 We will analyze scatterplots.
Lesson 11.4 We will analyze scatterplots.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.6c 🔗 Fit a linear function for a scatter plot that suggests a linear association.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.7 🔗 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Lesson 11.5 We will interpret the correlation between two quantitative variables.
Lesson 11.5 We will interpret the correlation between two quantitative variables.
Lesson 11.6 We will create a regression line using Desmos.com.
Lesson 11.6 We will create a regression line using Desmos.com.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.6b 🔗 Informally assess the fit of a function by plotting and analyzing residuals.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.6c 🔗 Fit a linear function for a scatter plot that suggests a linear association.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.7 🔗 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.8 🔗 Compute (using technology) and interpret the correlation coefficient of a linear fit.
Statistics & Probability » Interpreting Categorical & Quantitative Data S.ID.9 🔗 Distinguish between correlation and causation.
Chapter 12 - Rigid Motions and Triangle Congruence (click on arrows to expand section)
Chapter 12 - Rigid Motions and Triangle Congruence (click on arrows to expand section)
Lesson 12.1 We will identify geometric notation.
Lesson 12.1 We will identify geometric notation.
Geometry » Congruence G.CO.1 🔗 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Lesson 12.2 We will distinguish between rigid motions.
Lesson 12.2 We will distinguish between rigid motions.
Geometry » Congruence G.CO.4 🔗 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Lesson 12.3 We will translate a shape.
Lesson 12.3 We will translate a shape.
Geometry » Congruence G.CO.2 🔗 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Lesson 12.4 We will reflect a shape.
Lesson 12.4 We will reflect a shape.
Geometry » Congruence G.CO.2 🔗 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Lesson 12.5 We will rotate a shape.
Lesson 12.5 We will rotate a shape.
Geometry » Congruence G.CO.2 🔗 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Lesson 12.6 We will use rigid motions to determine if triangles are congruent.
Lesson 12.6 We will use rigid motions to determine if triangles are congruent.
Geometry » Congruence G.CO.7 🔗 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Lesson 12.7 We will use side-angle theorems to determine if triangles are congruent.
Lesson 12.7 We will use side-angle theorems to determine if triangles are congruent.
Geometry » Congruence G.CO.8 🔗 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Quarter 4 - Lesson At-A-Glance
Quarter 4 - Lesson At-A-Glance
Math Champions 🏆
Assessesment Readiness
· · · · ·
Day 1.1 Ordered Pairs
Day 1.2 Exponent Rule
Day 2.1 Combine Polynomials
Day 2.2 Multiply Polynomials
Day 3.1 Difference of Squares
Day 3.2 Squaring Binomials
Day 4.1 Sum of Cubes
Day 4.2 Quadratic Function - Binomial Factor Form
Day 5 Linear Inequality Graphs
Day 6.1 Quadratic Function - Standard Form
Day 6.2 Quadratic Function - Vertex Form
Day 7.1 Additive Inverse Equations
Day 7.2 Create Equation from Formula
· · · · ·
Day 8.1 Multiplicative Inverse Equations
Day 8.2 Equation Solution Types (One, None, Infinite)
Day 9.1 Multiplicative Inverse Equations - Variable in the Denominator
Day 9.2 Simplify Polynomial Expressions
Day 10 Linear Functions
Day 11.1 Multiplicative Inverse Inequalities
Day 11.2 Equation Solution Types (None, One, Two)
Day 12.1 Equations - Variable on Both Sides
Day 12.2 Multiply Polynomials
Day 13.1 Multiplicative Negative Inverse Inequalities
Day 13.2 Cross Multiplication - Variable on One Side
Day 14.1 Solve Equations - Substitution
· · · · ·
Day 14.2 Cross Multiplication - Variable on Both Sides
Day 15 Inequality System Solution Region
Day 16.1 System of Linear Equation Solution Types (None, One, Infinite) - Graphs
Day 16.2 Multiplicative Negative Inverse Inequalities - Two-Step
Day 17.1 Approximate Solutions - Quadratic Functions
Day 17.2 Solve Equations - Graphs/Tables
Day 18.1 Approximate Solutions - 3rd Degree Polynomials
Day 18.2 Non-Linear Equation Graph Types (Parabola, Circle)
Day 19 Equation Graph Interpretation
Chapter 11
Multi-variable Data Sets
· · · · ·
Lesson 11.1 Analyze the Types of Data in a Data Set
Lesson 11.2 Analyze Two-Way Frequency Tables
Lesson 11.3 Analyze Associations in Two-Way Frequency Tables
Lesson 11.4 Analyze Scatterplots
Lesson 11.5 Interpret the Correlation Between two Variables
Lesson 11.6 Create a Regression Line using Desmos.com
Chapter 12
Rigid Motions and Triangle Congruence
· · · · ·
Lesson 12.1 Identify Geometric Notation.
Lesson 12.2 Distinguish between Translations, Reflections, and Rotations.
Lesson 12.3 Translate a Shape
Lesson 12.4 Reflect a Shape
Lesson 12.5 Rotate a Shape
Lesson 12.6 Determine if Triangles are Congruent using Rigid Motions
Lesson 12.7 Determine if Triangles are Congruent using Side-Angle Theorems
Quarter 4 - Weekly At-A-Glance
Quarter 4 - Weekly At-A-Glance
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Quarter 4 - Assessment At-A-Glance
Quarter 4 - Assessment At-A-Glance
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