Integrated Math 1
Integrated Math 1
Quarter 2
Chapters 4-7
Quarter 2
Chapters 4-7
Embedded Files
Chapters 4-7
The Mathematics Department has organized the topics of Integrated Math 1 Quarter 2 to provide techniques for solving various one-variable equations. In Quarter 2, students transition from one-variable equations and expressions into two-variable equations and expressions. Functions are introduced as a result of analyzing variable relationships.
Chapter 4 - Equations with Negative Numbers reviews all the equation-solving techniques of Chapter 3, but now with the inclusion of negative numbers.
Chapter 5 - Equation Solving Techniques covers various equation solving techniques for different equation types, such as equal ratios (cross-multiplication) and literal equations. Chapter 5 provides early exposure to many equation-solving techniques they will use in later Chapters.
Chapter 6 - Two-Variable Equations & Introduction to Functions builds on Chapter 2 skills of substitution and understanding a solution as values that make an equation true. Graphs of linear and non-linear equations are created by plot solutions to the equation. At the end of Chapter 6, functions are introduced with specific analysis on domain and range.
Chapter 7 - Linear Functions builds on top of the general function introduction of Chapter 6 into linear functions specifically. Linear functions and linear equations are compared to solidify the understanding that y=f(x). After thorough work with one linear equation, systems of two linear equations are introduced at the end of Chapter 7
Quarter 2- Focus Objectives and Priority Standards
Quarter 2- Focus Objectives and Priority Standards
Chapter 4 - Equations with Negative Numbers (click on arrows to expand section)
Chapter 4 - Equations with Negative Numbers (click on arrows to expand section)
Lesson 4.1 We will combine with positive and negative terms.
Lesson 4.1 We will combine with positive and negative terms.
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.
Lesson 4.2 We will multiply and divide with positive and negative terms.
Lesson 4.2 We will multiply and divide with positive and negative terms.
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.
Lesson 4.3 We will check solutions. (Negative numbers)
Lesson 4.3 We will check solutions. (Negative numbers)
Number and Quantity » Quantities N.Q.1 🔗Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
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.
Lesson 4.4 We will solve equations using inverse operations. (Negative numbers)
Lesson 4.4 We will solve equations using inverse operations. (Negative numbers)
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.
Lesson 4.5 We will solve equations with the variable on both sides.
Lesson 4.5 We will solve equations with the 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.
Chapter 5 - Equation Solving Techniques (click on arrows to expand section)
Chapter 5 - Equation Solving Techniques (click on arrows to expand section)
Lesson 5.1 We will solve equations by cross multiplying.
Lesson 5.1 We will solve equations by cross multiplying.
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 » Creating Equations A.CED.4 🔗 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
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.
Lesson 5.2 We will solve equations by squaring both sides.
Lesson 5.2 We will solve equations by squaring 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.
Lesson 5.3 We will solve equations using the square root operation.
Lesson 5.3 We will solve equations using the square root operation.
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.
Lesson 5.4 We will solve equations with fractions.
Lesson 5.4 We will solve equations with fractions.
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.
Lesson 5.5 We will solve equations with more than one variable.
Lesson 5.5 We will solve equations with more than one variable.
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.
Lesson 5.6 We will solve equations with no solutions or infinite solutions.
Lesson 5.6 We will solve equations with no solutions or infinite solutions.
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.
Chapter 6 - Two-Variable Equations & Introduction to Functions (click on arrows to expand section)
Chapter 6 - Two-Variable Equations & Introduction to Functions (click on arrows to expand section)
Lesson 6.1 We will use the order of operations to evaluate expressions.
Lesson 6.1 We will use the order of operations to evaluate 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.
Lesson 6.2 We will graph solutions of equations (straight lines).
Lesson 6.2 We will graph solutions of equations (straight lines).
Algebra » Creating Equations A.CED.1 🔗 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
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.
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.7a 🔗 Graph linear and quadratic functions and show intercepts, maxima, and minima.
Lesson 6.3 We will graph solutions of equations (curves).
Lesson 6.3 We will graph solutions of equations (curves).
Algebra » Creating Equations A.CED.1 🔗 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
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.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.7a 🔗 Graph linear and quadratic functions and show intercepts, maxima, and minima.
Lesson 6.4 We will evaluate and graph functions.
Lesson 6.4 We will evaluate and graph functions.
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.
Functions » Interpreting Functions F.IF.7a 🔗 Graph linear and quadratic functions and show intercepts, maxima, and minima.
Lesson 6.5 We will distinguish between functions and non-functions.
Lesson 6.5 We will distinguish between functions and non-functions.
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).
Lesson 6.6 We will interpret the domain and range of real-world function graphs.
Lesson 6.6 We will interpret the domain and range of real-world function graphs.
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.
Functions » Interpreting Functions F.IF.4 🔗 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Functions » Interpreting Functions F.IF.5 🔗 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Lesson 6.7 We will interpret the domain type of real-world functions.
Lesson 6.7 We will interpret the domain type of real-world functions.
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.5 🔗 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Chapter 7 - Linear Functions (click on arrows to expand section)
Chapter 7 - Linear Functions (click on arrows to expand section)
Lesson 7.1 We will identify linear function graphs using the coefficient of x and the constant.
Lesson 7.1 We will identify linear function graphs using the coefficient of x and the constant.
Functions » Interpreting Functions F.IF.7a 🔗 Graph linear and quadratic functions and show intercepts, maxima, and minima.
Lesson 7.2 We will determine if linear equations and linear functions are equal.
Lesson 7.2 We will determine if linear equations and linear functions are equal.
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.
Functions » Interpreting Functions F.IF.7a 🔗 Graph linear and quadratic functions and show intercepts, maxima, and minima.
Lesson 7.3 We will find the x-intercept and y-intercept of a linear equation.
Lesson 7.3 We will find the x-intercept and y-intercept of a linear equation.
Algebra » Creating Equations A.CED.1 🔗 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
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.
Functions » Interpreting Functions F.IF.7a 🔗 Graph linear and quadratic functions and show intercepts, maxima, and minima.
Lesson 7.4 We will write linear equations in slope-intercept form.
Lesson 7.4 We will write linear equations in slope-intercept form.
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Creating Equations A.CED.2 🔗 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Functions » Linear, Quadratic, & Exponential Models F.LE.2 🔗 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Lesson 7.5 We will convert linear equations in standard form to slope-intercept form.
Lesson 7.5 We will convert linear equations in standard form to slope-intercept form.
Algebra » Seeing Structure in Expressions A.SSE.1a 🔗Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Creating Equations A.CED.2 🔗 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Functions » Linear, Quadratic, & Exponential Models F.LE.2 🔗 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Lesson 7.6 We will find the solution type of a system of linear equations.
Lesson 7.6 We will find the solution type of a system of linear equations.
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.
Lesson 7.7 We will find the solution of a system of linear equations.
Lesson 7.7 We will find the solution of a system of linear equations.
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.
Lesson 7.8 We will analyze a system of linear equations using Desmos.com.
Lesson 7.8 We will analyze a system of linear equations using Desmos.com.
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.
Quarter 2 - Lesson At-A-Glance
Quarter 2 - Lesson At-A-Glance
Chapter 5
Equation Solving Techniques
· · · · ·
Lesson 5.1 Cross Multiplication
Lesson 5.2 Solve Equations by Squaring
Lesson 5.3 Solve Equations using Square Roots
Lesson 5.4 Solve Equations with Fractions
Lesson 5.5 Solve Equations with More Than One Variable
Lesson 5.6 Equations with No Solutions and Infinite Solutions
Chapter 6
Two-Variable Equations & Introduction to Functions
· · · · ·
Lesson 6.1 Order of Operations
Lesson 6.2 Graph Equation Solutions (Straight Lines)
Lesson 6.3 Graph Equation Solutions (Curves)
Lesson 6.4 Evaluate and Graph Linear and Quadratic Functions
Lesson 6.5 Distinguish Between Functions and Non-Functions
Lesson 6.6 Domain and Range of Real-World Function Graphs
Lesson 6.7 Domain Types Real World Functions
Chapter 7
Linear Functions
· · · · ·
Lesson 7.1 Identify Linear Function Graphs
Lesson 7.2 Determine if Linear Equations and Functions are Equal
Lesson 7.3 Find Intercepts of Linear Equations
Lesson 7.4 Linear Equations in Slope-Intercept Form
Lesson 7.5 Linear Equations Standard to Slope-Intercept Form
Lesson 7.6 Find the solution type of a system of equations
Lesson 7.7 Find the solution of a system of linear equations
Lesson 7.8 Analyze systems of linear equations using desmos.com
Quarter 2 - Weekly At-A-Glance
Quarter 2 - Weekly At-A-Glance
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Quarter 2 - Assessment At-A-Glance
Quarter 2 - Assessment At-A-Glance
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