Grade 7 Honors Math

PA Core Mathematics Standards

• CC.2.1.7.D.1 Students acquire the knowledge and skills needed to: Analyze proportional relationships and use them to model and solve real-world and mathematical problems.
  • M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
  • M07.A-R.1.1.2 Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).
  • M07.A-R.1.1.3 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  • M07.A-R.1.1.4 Represent proportional relationships by equations.
  • M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.
  • M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems.
• CC.2.2.8.B.2 Students acquire the knowledge and skills needed to: Understand the connections between proportional relationships, lines, and linear equations.
  • M08.B-E.2.1.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
• CC.2.3.7.A.2 Students acquire the knowledge and skills needed to: Visualize and represent geometric figures and describe the relationships between them.
  • M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area.

• Unit pricing and speed are ratios of two quantities. 
• Tables of ratios, tape diagrams, double number line diagrams, and equations can be used to solve ratios.
• Real-world and mathematical problems can be solved using ratios and rate reasoning.
• Ratio language can be used to describe the ratio relationship between two quantities.
• A unit rate is a ratio of two quantities where the denominator is 1.
• Tables of equivalent ratios, tape diagrams, double number line diagrams, or equations can be used to find equivalent rates. 

• Recognize proportional relationships between quantities and identify the constant of proportionality in tables, diagrams, and verbal descriptions of proportional relationships.
• Decide whether two quantities are in a proportional relationship and represent proportional relationships by equations.
• Compute unit rates associated with ratios of fractions.
• When looking at a graph, determine if the graph is proportional and identify the constant of proportionality within the graph.
• Use proportional relationships to solve multi-step ratio problems.
• Solve problems involving scale drawings of geometric figures and compute unit rates associated with ratios of fractions.
• Proportional relationships are used to solve multi-step ratio and percent problems.

• Use patterns and unit rates to analyze and describe relationships.
• Determine if a relationship represented in a table is proportional, identify the constant of proportionality, and write an equation in the form of y = kx.
• Use unit rates involving fractions to solve real-world problems.
• Students will identify the characteristics of a proportional relationship when graphed.
• Use a proportional relationship to solve multi-step problems.
• Use scale drawings to solve problems.
• Use proportional reasoning to calculate an increase or decrease.
• Calculate markups, markdowns, retail prices, and discount prices, and represent them using equations of the form y=kx.
• By applying proportional reasoning, represent taxes, gratuities, and total cost using equations y=kx. Use the equations to solve problems and assess the reasonableness of answers.
• Use proportional reasoning to calculate the final total earnings for someone earning a base salary plus a commission. Use proportional reasoning to find fees (including fees as a percent and as a constant) and assess the reasonableness of answers.
• Calculate simple interest and the total value of an account earning simple interest using proportional reasoning and assess the reasonableness of the answers. 

• How can identifying patterns and unit rates help us understand and describe real-world proportional relationships?
• In what ways can we determine if a relationship represented in a table is proportional, and how does this understanding enable us to write equations in the form of y=kx?
• How do the characteristics of proportional relationships appear when graphed, and why are these characteristics important in solving multi-step problems?
• How can we apply our understanding of proportional relationships and scale drawings to solve real-world problems effectively?
• How can proportional reasoning help us understand the relationship between markup, markdown, and retail prices in real-world scenarios?
• How can the equation y=kx be applied to represent and solve problems involving taxes, gratuities, and total costs?
• How do commissions and base salaries interact mathematically, and how can we use proportional reasoning to calculate total earnings effectively?
• What strategies can we use to assess the reasonableness of our calculations when determining total interest earned on an account using simple interest?
   

• L1.1 In what ways can I determine if relationships shown in tables, diagrams, and verbal descriptions can be expressed using a constant unit rate?
• L1.2 What steps can I take to recognize proportional relationships in tables and equations, identify the constant of proportionality, and write the related equation?
• L1.3 How can I compute unit rates that are associated with ratios of fractions?
• L1.4 What criteria can I use to decide if a relationship depicted in a graph is proportional, and how does the constant of proportionality relate to the point (1, r) on that graph?
• L1.5 How can I recognize the constant of proportionality, create an equation for a proportional relationship in various formats, and utilize it to tackle multi-step ratio problems?
• L1.6 How do I make scale drawings and use them to find actual dimensions?
• L2.1 How can the percent change be used to solve multi-step real-world problems?
• L2.2 How can equations represent real-world problems involving markups, markdowns, and retail prices?
• L2.3 How do equations of the form y=kx facilitate the calculation of taxes, gratuities, and total costs, and how can the reasonableness of these results be assessed in practical situations?
• L2.4 In what ways can commissions and fees be calculated to determine total earnings, and what strategies are effective for assessing the reasonableness of those results?
• L2.5 What is the significance of the equation I=prt in calculating simple interest and the total value of an account over time, and how can this knowledge be applied in real-world financial situations?
   

• Into Math Modules 1-2
• Two Color Counters
• Fraction Strips
• Grid Paper
   

• Dimension
• Equation
• Ratio
• Reciprocal
• Unit Rate
• Constant of Proportionality
• Proportional Relationship
• Scale
• Scale Drawing
• Commission
• Fee
• Gratuity
• Markdown
• Markup
• Percent Change
• Percent Decrease
• Percent Increase
• Principal
• Retail Price
• Sales Tax
• Simple Interest
• Tip

• Module 1 Test
• Module 2 Test
• IXL Quizzes
   

PA Core Mathematics Standards

• CC.2.1.7.E.1 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of operations with fractions to operations with rational numbers.
  • M07.A-N.1.1.1 Apply properties of operations to add and subtract rational numbers, including real-world contexts.
  • M07.A-N.1.1.2 Represent addition and subtraction on a horizontal or vertical number line.
  • M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.
• CC.2.2.7.B.1 Students acquire the knowledge and skills needed to: Apply properties of operations to generate equivalent expressions.
  • M07.B-E.1.1.1 Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.
• CC.2.2.7.B.3 Students acquire the knowledge and skills needed to: Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
  • M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.
  • M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem.

• Understanding of positive and negative numbers.
• Plotting of numbers on the number line.
• Use of a number line for adding and subtracting integers.
• Fluency in adding and subtracting integers.
• Fluency in adding, subtracting, multiplying, and dividing multi-digit decimals using the standard algorithm for each operation.
• Interpretation and computation of the quotient of fractions.
• Division of multi-digit numbers using the standard algorithm.
• Evaluation of numerical expressions using parentheses, brackets, or braces.
• Writing of simple expressions.
• Interpretation of numerical expressions.
• Comparison and ordering of rational numbers.
• Division of fractions and mixed numbers.
• Application of operations with multi-digit decimals.

• Understanding how to use a number line to add and subtract integers lays the groundwork for more complex mathematical concepts, including algebra and rational numbers.
• Learning to assess the reasonableness of results when adding or subtracting negative integers fosters critical thinking and problem-solving skills, helping students verify their answers.
• Developing rules for products and quotients of rational numbers helps students understand the mathematical properties that govern these operations, aiding in more complex computations.
• Expressing rational numbers as decimals is crucial for understanding percentages, ratios, and real-world applications, such as shopping or budgeting.
• Learning to use properties to solve multi-step problems involving positive and negative rational numbers encourages persistence and deeper understanding of mathematical relationships.
• Adding, subtracting, factoring, and expanding linear expressions with rational coefficients builds essential algebraic skills necessary for success in high school mathematics.

• Use a number line to add and subtract positive integers.
• Use a number line to add and subtract a negative integer and then assess the results for reasonableness.
• Use a number line to add and subtract rational numbers.
• Calculate the sum of rational numbers.
• Calculate the difference of rational numbers.
• Develop rules to find products and quotients of rational numbers.
• Express rational numbers as decimals.
• Use products and quotients of rational numbers to solve problems.
• Use properties to solve multi-step problems involving positive and negative rational numbers.
• Solve multi-step problems involving a combination of rational-number operations.
• Add, subtract, factor, and expand linear expressions with rational coefficients.

• How does understanding positive and negative numbers enhance the ability to perform operations on integers and rational numbers?
• In what ways does plotting numbers on a number line facilitate the addition and subtraction of integers, and how can this visual representation aid in problem-solving?
• What strategies can be employed to achieve fluency in adding, subtracting, multiplying, and dividing multi-digit decimals, and how does this fluency impact the accuracy of calculations in real-world scenarios?
• How can the evaluation and interpretation of numerical expressions using various symbols, such as parentheses and brackets, influence the outcomes of mathematical problems, and why is it essential to compare and order rational numbers effectively?
   

• L3.1 How does utilizing a number line to add and subtract positive integers enhance understanding of numerical relationships and improve accuracy in mathematical calculations?
• L3.2 How can a number line help visualize and make sense of adding and subtracting negative numbers to determine if the answers are reasonable?
• L3.3  In what ways does a number line facilitate the addition and subtraction of rational numbers, and how does this visual representation help in understanding their relationships and operations?
• L4.1 What methods can be used to calculate the sum of rational numbers, and how does understanding their properties enhance the ability to solve related mathematical problems?
• L4.2 What strategies can be employed to effectively calculate the difference of rational numbers, and how does this understanding apply to real-world situations involving subtraction?
• L4.3 How can the development of rules for finding products and quotients of rational numbers enhance mathematical reasoning, and in what ways do these rules apply to solving real-world problems?
• L4.4 What processes are involved in expressing rational numbers as decimals, and how does this conversion facilitate comparisons and calculations in various mathematical contexts?
• L4.5  In what ways can the application of products and quotients of rational numbers be utilized to effectively solve real-world problems, and what strategies enhance problem-solving skills in this context?
• L5.1 How do mathematical properties assist in solving multi-step problems involving positive and negative rational numbers, and how can these strategies improve overall problem-solving effectiveness?
• L5.2 What strategies can be employed to effectively tackle multi-step problems that involve a combination of rational-number operations, and how does this process enhance critical thinking and problem-solving skills?
• L5.3 How can the properties of operations be used to rewrite and simplify linear expressions with rational coefficients in different forms?

• Into Math Modules 3-5
• iXL
• Number lines
• Two-colored counters
• Base 10 blocks
• Base 10 mats
• Fraction strips
• Decimal models
   

• Degree
• Opposite
• Additional Property of Opposites
• Additive Inverse

• Module 3 Test
• Module 4 Test
• Module 5 Test
• IXL Quizzes
   

PA Core Mathematics Standards

• CC.2.2.7.B.3 Students acquire the knowledge and skills needed to: Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
  • M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.
  • M07.B-E.2.2.1 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.
  • M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality.
  • M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem.
• CC.2.2.8.B.3 Students acquire the knowledge and skills needed to: Analyze and solve linear equations and pairs of simultaneous linear equations.
  • M08.B-E.3.1.1 Write and identify linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
  • M08.B-E.3.1.2 Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
• CC.2.3.7.A.1 Students acquire the knowledge and skills needed to: Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.
  • M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
     

• Application of the properties of operations to generate equivalent expressions.
• Solution of real-world problems involves the writing and solving of equations in the form x + p = q and px = q, with p, q, and x as non-negative rational numbers.
• Writing inequalities in the form x > c or x < c to represent constraints or conditions in real-world or mathematical problems.
• Determination of solutions to an inequality using given numbers.

• Knowing how to represent a real-world situation with an equation allows translation of everyday problems into mathematical expressions that can be analyzed and solved.
• When solving real-world problems with an equation or inequality, it helps find unknown quantities and make informed decisions based on mathematical reasoning.
• Using algebraic properties to solve one-variable linear equations and inequalities helps systematically isolate variables and solve equations and inequalities accurately and efficiently.
• Recognizing and interpreting linear equations that have no solution or infinitely many solutions aids in understanding different types of equations and their implications in various contexts.
• Solving equations to find unknown angle measurements connects algebra with geometry and enhances understanding and analysis of spatial relationships.

• Represent a real-world situation with an equation.
• Solve real-world problems using an equation.
• Use algebraic properties to solve one-variable linear equations.
• Recognize and interpret linear equations that have no solution or infinitely many solutions.
• Solve and apply linear equations in one variable.
• Solve equations to find unknown angle measurements.
• Apply properties to solve one-step inequalities.
• Write two-step inequalities to represent situations.
• Write, solve, and graph one-step and two-step inequalities to solve problems in context.

• How can equations and inequalities be used to represent and solve real-world problems?
• What strategies and properties help us solve linear equations and inequalities accurately and efficiently?
• What do different types of solutions to linear equations tell us about the problem being solved?
• How can equations be used to find unknown angle measures and describe relationships between geometric figures?
   

• L6.1-2 How can two-step equations be used to represent and solve real-world situations involving unknown values?
• L6.3  How can understanding integer and rational number operations help solve linear equations accurately and efficiently?
• L6.4 How can the structure of a linear equation help determine the number of possible solutions it has?
• L6.5  How does solving an equation help make sense of real-world situations, and what does the solution show about the problem?
• L7.1 How can one-step inequalities be used to represent and solve real-world situations with a range of possible solutions?
• L7.2-3 How can two-step inequalities help represent and solve problems that involve limits or ranges in real-world situations?

• Into Math Modules 6-7
• iXl
• Algebra Tiles
• Equation Mat
• Number Line

• Coefficient
• Common Denominator
• Distributive Property
• Isolate the Variable
• Like Terms
• Multiple
• Solution of an Equation
• Adjacent Angles
• Complementary Angles
• Infinitely Many Solutions
• No Solutions
• Supplementary Angles
• Vertical Angles
• Inequality
• Number Line
• Solution of an Inequality
• Rate of Change

• Module 6 Test
• Module 7 Test
• IXL Quizzes
   

PA Core Mathematics Standards

• CC.2.3.8.A.2 Students acquire the knowledge and skills needed to: Understand and apply congruence, similarity, and geometric transformations using various tools.
  • M08.C-G.1.1.1 Identify and apply properties of rotations, reflections, and translations.
  • M08.C-G.1.1.2 Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.
  • M08.C-G.1.1.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  • M08.C-G.1.1.4 Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.
• CC.2.3.7.A.2 Students acquire the knowledge and skills needed to: Visualize and represent geometric figures and describe the relationships between them.
  • M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures.
  • M07.C-G.1.1.3 Use and apply the triangle inequality theorem.

• Geometric shapes are identified and drawn using the given coordinates.
• Length is measured accurately using a ruler.
• Angles are measured precisely using a protractor.
• Figures are drawn and positioned correctly in the coordinate plane.
• Lines of symmetry are identified and drawn in two-dimensional figures.
• Areas of complex figures are found by decomposing them into triangles and other shapes.
• Volumes of rectangular prisms are calculated using length, width, and height.
• The concept of a ratio is understood and applied to compare quantities
• Ratio and rate reasoning are used to solve real-world and mathematical problems.
• Angle relationships are applied to find unknown angle measures and solve geometric problems.
• Polygons are drawn in the coordinate plane using given vertices.
• Geometric shapes are constructed based on specific conditions.
• Problems involving scale drawings are solved by applying proportional reasoning.
• The length of a vertical or horizontal segment is found using coordinates.

• Exploring and observing the effects of rigid motions on a figure helps students understand how shapes move without changing their size or shape, thereby building a foundation for concepts of congruence and symmetry.
• Describing transformations and their effects on a figure allows students to communicate how a figure moves, flips, and turns across a plane and recognizes patterns in coordinate changes.
• Dilations show how figures change size proportionally while maintaining shape, distinguish between similarity and congruence, accurately apply scale factors and centers of transformation in various contexts, and solve real-world problems involving proportional reasoning and geometric modeling.

• Explore and observe the effects of rigid motions on a figure.
• Describe translations and their effects on a figure.
• Describe reflections and their effects on a figure.
• Recognize and perform rotations.
• Describe rotations algebraically. 
• Understand that rotating a figure produces an image that is congruent to the preimage. 
• Draw and construct figures using technology and freehand with given conditions.
• Determine how many triangles or quadrilaterals can be made given the side lengths: none, one, or many.
• Determine how many triangles can be made given the angle measures: none, one, or many.
• Draw, construct, and analyze two-dimensional figures to solve real-world problems.
• Perform enlargements and reductions.
• Understand that the result of enlarging or reducing a preimage is not congruent to the preimage.
• Describe and apply the properties of dilations.
• Understand and find the scale factor and center of dilation, both on and off the coordinate plane. 
• Recognize and use similar figures using transformations.

• How do different rigid motions, such as translations, reflections, and rotations, affect the position and orientation of a figure while preserving its size and shape?
• In what ways can translations be described and performed to accurately move a figure on the coordinate plane without altering its congruence?
• How can reflections and rotations be recognized, performed, and described both visually and algebraically to understand their impact on figures?
• Why does rotating a figure always produce an image congruent to the original, and how does this property support understanding of geometric transformations and congruence?
• How can side lengths and angle measures determine the number of possible triangles or quadrilaterals, and what reasoning helps identify when none, one, or many figures can be formed?
• In what ways can drawing, constructing, and analyzing two-dimensional figures assist in solving real-world problems, especially when considering the uniqueness or multiplicity of shapes based on given measurements?
• How do enlargements and reductions transform a figure, and why do these transformations produce images that are similar but not congruent to the original?
• What properties define dilations, and how can these properties be applied to understand changes in size and position of geometric figures?
• How can the scale factor and center of dilation be identified and used both on and off the coordinate plane to perform size transformations accurately?
• In what ways can recognizing and using similar figures through transformations deepen understanding of proportional relationships and support solving real-world problems?
   

• L8.1 How do transformations affect the side lengths and angle measures of geometric figures?
• L8.2 How can a translation be described and represented using words, coordinates, and algebraic rules on the coordinate plane?
• L8.3 How does reflecting a figure over an axis affect its coordinates, and how can the reflection be described using algebraic rules?
• L8.4 How can a rotation be identified, performed, and described using coordinates and algebraic rules on the coordinate plane?
• L8.5 How can a sequence of transformations show that two figures are congruent?
• L9.1 How can geometric figures be constructed to meet specific conditions, such as inscribing a triangle in a circle?
• L9.2 How can the relationships between side lengths be used to determine whether a triangle can be formed and what the possible length of the third side could be?
• L9.3 How can given angle measures and construction tools be used to determine whether one, none, or many triangles can be created?
• L9.4 How can shapes like circles and triangles be drawn and analyzed to solve real-world problems?
• L10.1 How can enlargements and reductions be identified and performed to change the size of a figure while maintaining its shape?
• L10.2 How can dilations be identified and performed using a scale factor and center of dilation, and how can their effects be described algebraically on the coordinate plane?
• L10.3 How can a sequence of transformations be used to show that two figures are similar?

• Into Math Modules 8-10
• iXL
• Ruler
• Protractor
• Grid Paper
• Coordinate Plane

• Center of Rotation
• Congruent
• Image
• Line of Reflection
• Preimage
• Prime Notation
• Reflection
• Rotation
• Transformation
• Translation
• Enlargement
• Center of Dilation
• Dilation
• Reduction
• Scale Factor
• Similar

• Module 8 Test
• Module 9 Test
• Module 10 Test
• IXL Quizzes
   

PA Core Mathematics Standards

• CC.2.3.7.A.1 Students acquire the knowledge and skills needed to:  Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.
  • M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).
• CC.2.2.8.B.2 Students acquire the knowledge and skills needed to: Understand the connections between proportional relationships, lines, and linear equations.
  • M08.B-E.2.1.2 Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.
  • M08.B-E.2.1.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
• CC.2.2.7.B.3 Students acquire the knowledge and skills needed to: Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
  • M08.B-E.2.1.3 Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
• CC.2.2.8.C.2 Students acquire the knowledge and skills needed to: Use concepts of functions to model relationships between quantities.
  • M08.B-F.2.1.2 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch or determine a graph that exhibits the qualitative features of a function that has been described verbally.

• Identification and use of supplementary, complementary, vertical, and adjacent angles in multi-step problems.
• Understanding and description of similar figures.
• Problem solving with scale drawings.
• Recognition and representation of proportional relationships.
• Knowledge of unit rate concepts.
• Analysis of relationships using graphs.
   

• Recognizing when two triangles are similar based on their angle measures enables the identification of proportional relationships that are meaningful for scaling and modeling real-world situations.
• Determining unknown angles in similar triangles reinforces the connection between similarity and proportionality, deepening comprehension of geometric concepts.
• Calculating angles formed when a transversal intersects parallel lines provides insight into the analysis of complex figures and supports an understanding of parallelism and corresponding angle properties.
• These skills, when combined, enhance spatial reasoning and the ability to visualize and manipulate shapes, laying a strong foundation for exploring transformations such as rotations, reflections, dilations, and translations in coordinate geometry.
• Understanding the relationship between right triangles and lines through the origin provides a foundational visual and conceptual basis for comprehending the persistent nature of slope as a ratio of "rise over run," a fundamental concept in algebra and geometry with broad applications in modeling proportional relationships and analyzing rates of change in real-world phenomena.
• Learning how to write the equation of a proportional relationship is crucial because it allows them to mathematically model and solve a vast array of real-world problems involving constant ratios, such as calculating earnings based on hours worked, adjusting recipes, determining sales tax, or understanding scientific principles like density and speed.
• Writing the equation of a line provides a powerful algebraic tool for modeling and representing constant rates of change and linear relationships observed in various real-world scenarios, enabling predictions, analysis, and problem-solving across disciplines such as science, economics, and engineering.

• Use angle relationships in triangles.
• Identify whether two triangles are similar, given angle measures in the triangles. 
• Find unknown angle measures in triangles known to be similar.
• Find unknown angle measures when a transversal cuts parallel lines.
• Relate right triangles to the coordinates of a line going through the origin, and compare persistent features of the triangles to persistent features of a line.
• Write the equation of a proportional relationship.
• Write the equation of a line.
• Sketch and analyze a graph that exhibits qualitative features.

• How do angle relationships within triangles help in determining unknown angle measures and understanding the properties of geometric figures?
• What criteria can be used to identify similarity between two triangles based on their angle measures, and how does this knowledge support solving real-world problems involving proportional relationships?
• In what ways can finding unknown angles in similar triangles deepen understanding of the connection between similarity, proportionality, and geometric transformations?
• How does analyzing angles formed by a transversal intersecting parallel lines enhance the ability to solve complex geometric problems and apply concepts of parallelism and congruence?
• How can the relationship between right triangles and the coordinates of a line through the origin help in understanding the concept of slope and proportional relationships in geometry and algebra?
• What steps are involved in writing the equation of a proportional relationship, and how does this equation represent connections between geometric figures and algebraic expressions?
• In what ways does writing the equation of a line link geometric concepts like similarity and slope to coordinate systems, and how does this support solving real-world problems involving linear relationships?
   

• L11.1 How can understanding the relationships between angles within a triangle help us solve for unknown angle measures?
• L11.2 How can angle-angle similarity be used to determine whether two triangles are similar, and how does this understanding help in finding unknown angle measures while connecting geometric reasoning to proportional relationships and real-world problem solving?
• L11.3 How do the positions and measurements of two angles determine whether they are supplementary or congruent, and what does this reveal about their geometric relationship?
• L12.1 How does understanding the slope of a line, as a measure of its steepness and proportional relationship between coordinates, help in determining additional points on the line?
• L12.2 How can analyzing a graph or table of values help in writing the equation of a line, and how does this process connect geometric concepts like slope, proportional relationships, and similarity to algebraic expressions?
• L12.3 How can the given slope of a line and a single point on that line be used to determine its algebraic equation in the form y=mx+b uniquely?
• L12.4 How does understanding the key features of a graph allow one to translate a relationship into a verbal description accurately, and conversely, how does a verbal description guide the accurate representation of a relationship on a graph?
   

• Into Math Modules 11-12
• iXL
• Ruler
• Protractor
• Grid paper
• Coordinate grids
   

• Alternate Interior Angles
• Angle-Angle Similarity Postulate
• Corresponding Angles
• Exterior Angles
• Exterior Angle Theorem
• Remote Interior Angle
• Same-Side Exterior Angles
• Transversals
• Triangle Sum Theorem
• Unit Rate
• Hypotenuse
• Legs
• Linear Equation
• Linear Relationship
• Rise
• Run
• Slope-Intercept Form
• y=mx
• y-intercept

• Module 11 Test
• Module 12 Test
• IXL Quizzes

PA Core Mathematics Standards

• CC.2.1.8.E.1 Students acquire the knowledge and skills needed to: Distinguish between rational and irrational numbers using their properties.
  • M08.A-N.1.1.1 Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).
  • M08.A-N.1.1.2 Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).
• CC.2.2.8.B.1 Students acquire the knowledge and skills needed to: Apply concepts of radicals and integer exponents to generate equivalent expressions.
  • M08.B-E.1.1.1 Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided.
  • M08.B-E.1.1.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of perfect squares (up to and including 122) and cube roots of perfect cubes (up to and including 53) without a calculator.
  • M08.B-E.1.1.3 Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another.
  • M08.B-E.1.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g., interpret 4.7EE9 displayed on a calculator as 4.7 × 109).
• CC.2.1.8.E.4 Students acquire the knowledge and skills needed to: Estimate irrational numbers by comparing them to rational numbers.
  • M08.A-N.1.1.3 Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144).
  • M08.A-N.1.1.4 Use rational approximations of irrational numbers to compare and order irrational numbers.
  • M08.A-N.1.1.5 Locate/identify rational and irrational numbers at their approximate locations on a number line.
• CC.2.3.8.A.3 Students acquire the knowledge and skills needed to: Understand and apply the Pythagorean Theorem to solve problems.
  • M08.C-G.2.1.1 Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
  • M08.C-G.2.1.2 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  • M08.C-G.2.1.3 Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

• Understanding of rational numbers as points on the number line.
• Conversion of rational numbers to decimals.
• Classification of fractions and decimals as rational numbers.
• Graphing of rational numbers on a number line.
• Writing and evaluation of numerical expressions involving whole-number exponents.
• Understanding of irrational numbers and roots.
• Drawing of geometric shapes with given coordinates.
• Writing and evaluation of numerical expressions involving whole-number exponents.
• Application of the properties of operations to generate equivalent expressions.
• Solution of problems posed with positive and negative rational numbers in any form.

• Square roots and cube roots appear in fields like engineering (e.g., calculating forces, stresses), physics (e.g., formulas for motion, energy), and even finance (e.g., compound interest).
• Proving the theorem helps students understand the concept of mathematical proof, logical deduction, and the structure of mathematical arguments.
• This theorem has numerous real-world applications in construction and architecture, ensuring that structures are square and stable. Navigation: calculating distances and bearings. Engineering: designing and analyzing structures and machines. Sports: calculating distances in various athletic scenarios. Art and Design: creating perspectives and accurate representations.
• These concepts are not isolated facts, but rather interconnected ideas that build upon one another. They develop critical thinking, problem-solving skills, and a deeper understanding of the world around us, preparing students for success in STEM fields and everyday life.
• Understanding how to develop and use the properties of integer exponents allows individuals to simplify complex expressions and solve real-world problems involving exponential relationships efficiently.
• Expressing and computing numbers using scientific notation helps to concisely represent extremely large or small values frequently encountered in fields such as science, engineering, and astronomy, where traditional decimal notation becomes cumbersome.

• Determine if a number is rational.
• Evaluate square and cube roots.
• Order a list of real numbers consisting of both rational and irrational numbers.
• Prove and use the Pythagorean Theorem and its converse.
• Use the Pythagorean Theorem to solve real-world problems involving right triangles.
• Use the Pythagorean Theorem to find the distance between any two points in the coordinate plane.
• Develop and use the properties of integer exponents.
• Express numbers using scientific notation.
• Compute with numbers written in scientific notation.

• How can identifying rational and irrational numbers, along with ordering real numbers, deepen understanding of number systems and support accurate mathematical reasoning?
• In what ways do evaluating square and cube roots and applying the properties of integer exponents strengthen connections between geometry and algebra, particularly in solving problems involving powers and roots?
• How does proving and using the Pythagorean Theorem, including finding distances between points on the coordinate plane, help solve real-world problems and link geometric concepts with algebraic representations?
• What strategies can be used to express and compute numbers in scientific notation, and how does this skill support working with very large or small quantities in mathematical and real-world contexts?

• L13.1 What defines a rational number, and how does its fractional form reveal its fundamental nature as a point on the number line?
• L13.2 How do inverse operations, specifically square roots and cube roots, help us to understand and quantify relationships involving squares and cubes in mathematics and real-world contexts?
• L13.3 How can we effectively compare and arrange diverse forms of real numbers (fractions, decimals, irrationals) to make sense of their relative magnitudes and positions on the number line?
• L14.1 What is the fundamental relationship between the sides of a right triangle, and how can understanding this relationship allow us to prove it and solve for unknown lengths, including identifying special sets of side lengths?
• L14.2 How does the Pythagorean Theorem provide a powerful tool for solving practical problems involving distances and dimensions in real-world scenarios, both in two and three dimensions?
• L14.3 How can the Pythagorean Theorem bridge the gap between algebraic coordinates and geometric distances, allowing us to precisely measure lengths of segments and figures on the coordinate plane?
• L15.1 How can the properties of integer exponents be applied to simplify mathematical expressions?
• L15.2 How does scientific notation help describe and compare quantities that are extremely large or small?
• L15.3 How can numbers in scientific notation be accurately computed, and how can appropriate units be selected for extremely large or small quantities?
   

• Into Math Modules 13-15
• iXL
• Ruler
• Protractor
• Grid Paper
• Dot Paper
• Tape Measure
   

• Rational Number
• Repeating Decimal
• Terminating Decimal
• Cube Root
• Irrational Number
• Perfect Cube
• Perfect Square
• Principal Square Root
• Radical Symbol
• Real Number
• Square Root
• Cone
• Pythagorean Theorem
• Pythagorean Triples
• Base
• Exponent
• Power
• Properties of Exponents
• Scientific Notation
• Standard form of a number

• Module 13 Test
• Module 14 Test
• Module 15 Test
• IXL Quizzes
   

PA Core Mathematics Standards

• CC.2.2.7.B.3 Students acquire the knowledge and skills needed to: Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
  • M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.
  • M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem.
• CC.2.3.7.A.1 Students acquire the knowledge and skills needed to: Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.
  • M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided.
  • CC.2.3.7.A.2 Students acquire the knowledge and skills needed to: Visualize and represent geometric figures and describe the relationships between them.
  • M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures.
  • M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided.
• CC.2.3.8.A.1 Students acquire the knowledge and skills needed to: Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.
  • M08.C-G.3.1.1 Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.

• Determination of areas of triangles, quadrilaterals, and other figures.
• Application of proportional relationships in multi-step ratio problems.
• Drawing of geometric shapes with given conditions, including circles with radius and diameter.
• Understanding of proportional reasoning.
• Understanding the diameter and radius of a circle.
• Calculation of circumference and area of circles.
• Determination of surface area and volume of solids.
• Determination of areas of triangles and special quadrilaterals.
• Identification of diameter and radius of circles.
• Drawing and analysis of shapes to solve problems.
• Description and drawing of two-dimensional figures created by horizontal or vertical slicing of three-dimensional circular solids.
• Use of nets to determine surface area of three-dimensional figures.
• Application of surface area in real-world and mathematical problems.
• Representation of three-dimensional figures using nets of rectangles and triangles, and use of the nets to determine surface area.
• Calculation of volume of right rectangular prisms.
• Representation of three-dimensional figures with nets and use of the nets to determine surface area.
• Calculation of volume of right rectangular prisms.
• Problem solving involving two-dimensional composite figures.
• Recognition of volume as an attribute of solid figures and understanding of volume measurement concepts.
• Volume calculation for a right cylinder.
• Measurement of volume by unit cube counting.
• Solution of volume problems.

• Applying geometric concepts like angles, shapes, and measurements helps students think critically, make logical decisions, and solve real-world problems.
• Measuring angles, calculating area and volume, and using scale drawings are essential in fields like construction, design, engineering, and everyday situations.
• Drawing shapes, analyzing nets, and visualizing cross-sections strengthen students’ ability to think about space and dimensions, which is key for STEM and art careers.
• Understanding geometry concepts prepares students for higher-level topics like trigonometry, algebra, and calculus, supporting academic success.
• Using variables and constructing equations and inequalities connects geometry to algebra, helping students interpret and model real-life situations.
• Working with 3D shapes helps students develop strong spatial reasoning skills, which are vital not only in mathematics but also in art, design, navigation, and many scientific disciplines. They learn to visualize objects in three dimensions and understand how different dimensions affect the overall volume.
• Knowing how to apply volume concepts and formulas for cylinders, cones, and spheres equips students with practical skills for everyday life, develops crucial spatial reasoning, and lays essential groundwork for future studies in science, technology, engineering, and mathematics.

• Derive and apply formulas for circumference.
• Derive and apply formulas for the area of a circle.
• Describe and analyze cross sections of circular solids that result in circles, rectangles, and triangles.
• Use known formulas to calculate the areas of composite figures.
• Identify and describe the two-dimensional figures resulting from horizontal and vertical cross sections of pyramids and prisms.
• Learn to calculate the surface area of a right prism using the surface area formula.
• Calculate the volume of a right prism using the volume formula.
• Develop and use the formula for the volume of a cylinder. 
• Develop and use the formula for the volume of a cone. 
• Develop and use the formula for the volume of a sphere. 
• Use the formulas to solve problems involving cylinders, cones and spheres.  
• Solve multi-step problems involving three-dimensional figures using formulas for surface area and volume.

• How can I use properties of two- and three-dimensional shapes, including nets, surface area, and volume, to model and solve real-world and mathematical problems?
• How do I connect geometry and algebra to understand relationships among angles, lines of symmetry, and composite figures in problem-solving contexts?
• How does understanding the underlying principles behind the volume formulas for cylinders, cones, and spheres empower us to precisely quantify the capacity of three-dimensional objects and solve real-world problems involving space?

• L16.1 How can I use the circumference formulas C = πd and C = 2πr to solve for C, r, or d when the value of the other variable is given?
• L16.2 How can I use the area formulas for a circle to find the area of a circle if I know its radius or circumference or to find the radius or circumference if I know the area?
• L16.3 How can I break a composite figure into simple shapes and use area formulas to find its area?
• L17.1 How can I identify the shapes of cross sections of circular solids and solve problems involving the areas of cross sections?
• L17.1 How can I describe and analyze the cross sections of pyramids and prisms of all types, with or without a diagram?
• L17.2 How can I derive and apply the formulas for surface area of any right prism?
• L17.3 How can I accurately apply the formula to find the volume of right prisms?
• L17.4 How can I find the volume of a cylinder or the dimensions of a cylinder when given the volume?
• L17.5 How can I find the volume of cones and spheres or the dimensions of a cone or sphere when given the volume?
• L17.6 How can I solve multi-step surface area and volume problems?
   

• Into Math Modules 16-17
• iXL
• Compass 
• Ruler
• Grid Paper
• Centimeter Cubes
• Base-ten Blocks

• Composite Figure
• Cross Section
• Sphere
• Pi
• Surface Area
• Pyramid
• Cylinder
• Rectangular Prism
• Right Cone

• Module 16 Test
• Module 17 Test
• IXL Quizzes
• Unit 7 Performance Task
   

PA Core Mathematics Standards

• CC.2.4.7.B.1 Students acquire the knowledge and skills needed to: Draw inferences about populations based on random sampling concepts.
  • M07.D-S.1.1.1 Determine whether a sample is a random sample given a real-world situation.
  • M07.D-S.1.1.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
• CC.2.4.7.B.2 Students acquire the knowledge and skills needed to: Draw informal comparative inferences about two populations.
  • M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability.

• Exploration of statistical data collection.
• Recognition of a statistical question as one that anticipates variability in data.
• Display of data in dot plots.
• Summarization and analysis of data sets.
• Description of distributions of data.
• Calculation of five key values: minimum, lower quartile, median, upper quartile, and maximum.
• Construction of box plots using five key values.
• Summary and analysis of sets of data.
• Use of measures of center and measures of variability for data analysis.
• Description of the overall pattern and deviations from the overall pattern in a data set.

• Understand how data is collected and recognize statistical questions to assess the trustworthiness of information critically.
• Use dot plots and box plots, along with key summaries, to quickly see and condense data patterns.
• Describe data distributions and use measures of center and variability to understand data's typical values and spread comprehensively.
• Learn to summarize and analyze data sets to make meaningful conclusions and support them with evidence.
• Recognize overall patterns and investigate deviations to uncover unusual findings or errors.

• Understand what a population and a sample are.
• Understand how to select a representative sample.
• Understand that a random sample will usually be representative.
• Understand the different ways that a sample could be biased.
• Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
• Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
• Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
• Identify the median, mean, and spread of a set of data displayed in a dot plot.
• Compare the shapes, centers, and spreads of data displayed in dot plots.
• Conclude populations based on sample data displayed in dot plots.
• Compare characteristics of data sets displayed in box plots.
• Draw inferences about two populations based on data displayed in box plots.
• Calculate the ratio of the difference of means to the MAD (when two distributions have similar MADs) and use the ratio to assess whether there are meaningful differences in the two populations.
• Use measures of center and variability for data from random samples to draw informal comparisons about the populations.

• Why is understanding data collection and distinguishing a statistical question essential for trusting and approaching any problem with data?
• How do dot plots and box plots help you quickly grasp a data set's overall pattern and key features, making visual insights crucial?
• How do summaries like the five-number summary, combined with measures of center and variability, provide a complete picture when comparing data sets?
• Why is describing data distribution necessary, and what can deviations from the overall pattern reveal about a data set's story or potential issues?
   

• L18.1 How can the population and sample be identified in a survey scenario, and what determines whether the sample is random?
• L18.2 How can proportional reasoning be applied to conclude a population from the results of a random sample?
• L18.3 How can multiple random samples of the same size be used to make reliable inferences about a population based on survey results?
• L19.1-2 How can comparing two data sets in dot plots lead to meaningful inferences about the populations they represent?
• L19.3 How can the means and mean absolute deviations (MADs) be used to evaluate the degree of overlap between two numerical data distributions?
   

• Into Math Modules 18-19
• iXL
• Fraction Circles
• Number Lines
   

• Bias
• Population
• Sample
• Random Sample
• Representative Sample
• Box Plot
• Interquartile Range
• Lower Quartile
• Mean
• Mean Absolute Deviation
• Median
• Range
• Upper Quartile

• Module 18 Test
• Module 19 Test
• IXL Quizzes
   

PA Core Mathematics Standards

• CC.2.4.7.B.3 Students acquire the knowledge and skills needed to: Investigate chance processes and develop, use, and evaluate probability models.
  • M07.D-S.3.1.1 Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event).
• CC.2.1.7.D.1 Students acquire the knowledge and skills needed to: Analyze proportional relationships and use them to model and solve real-world and mathematical problems.
  • M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems.
  • M07.D-S.3.2.1 Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability.
  • M07.D-S.3.2.2 Find the probability of a simple event, including the probability of a simple event not occurring.
  • M07.D-S.3.2.3 Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation.
• CC.2.2.7.B.1 Students acquire the knowledge and skills needed to: Apply properties of operations to generate equivalent expressions.
• CC.2.2.7.B.3 Students acquire the knowledge and skills needed to: Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
  • M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.
  • M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem.

• Summarization of numerical data sets in relation to their context.
• Identification and representation of proportional relationships.
• Understanding of event probability.
• Knowledge that the probability of a chance event is a number between 0 and 1, expressing the likelihood of the event's occurrence.
• Approximation of chance event probability through data collection on the process.
• Development and utilization of a probability model for event probabilities.
• Development of statistical variability understanding.
• Representation of sample spaces for compound events.
• Design and utilization of a simulation to generate frequencies for compound events.
• Prediction of approximate relative frequency given an experimental probability.
• Development of a uniform probability model and its use to determine event probabilities.

• Students learn to effectively condense, understand, and communicate insights from numerical data by summarizing it within its context and recognizing statistical variability.
• Students grasp the fundamental idea of probability as a measure of likelihood between 0 and 1, providing a framework for understanding chance events in everyday life.
• Students develop the ability to create and use probability models (including uniform models and sample spaces for compound events) and run simulations to approximate and predict the likelihood of various events.
• By approximating probabilities through data collection and relating experimental frequencies to predictions, students learn to bridge the gap between theoretical chance and real-world observations.
• These skills empower students to identify proportional relationships, analyze uncertain situations, and make more informed decisions in a world driven by data and chance.

• Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
• Determine a sample space.
• Find the experimental probability of an event.
• Determine the probability of compound events.
• Use experimental probability and proportional reasoning to make predictions about real-world scenarios.
• Find the theoretical probability of simple events and compare the theoretical probability to experimental probability.
• Find and compare theoretical probabilities of compound events using a table, a tree diagram, and an organized list.
• Use proportional relationships to solve multi-step ratio and percent problems.
• Predict the approximate relative frequency, given a theoretical probability.
• Design and perform a simulation to test the probability of a simple event or a compound event.
   

• How can numerical data be summarized effectively, and why is statistical variability key to understanding its context?
• What is probability, and how does a 0-to-1 scale help us express the likelihood of events?
• How do probability models, data collection, and simulations help predict the likelihood of events?
• How do proportional relationships and probability help analyze situations and make predictions in daily life?
   

• L20.1 How can the likelihood of an event be described and interpreted using probability?
• L20.2 How can experimental probability and its complement be determined and used to understand the chances of different outcomes?
• L20.3 How can the experimental probability of compound events be determined through observation and data collection?
• L20.4 How can proportional reasoning or percent expressions be used to make predictions based on experimental probability?
• L21.1 How can the theoretical probability of a simple event be calculated and interpreted?
• L21.2 How can the theoretical probability of a compound event be calculated by analyzing all possible outcomes?
• L21.3 How can theoretical probability be used to make accurate predictions in real-world situations?
   

• Into Math Modules 20-21
• iXL
• Number Cubes
• Coins
• Paper Cups
• Coins
• Number Cubes
• Blank Spinners
   

• Complement of an event
• Compound Event
• Event
• Experiment
• Experimental Probability
• Outcome
• Probability
• Probability of an Event
• Sample Space
• Simulation
• Trial
• Theoretical Probability
• Tree Diagram

• Module 20 Test
• Module 21 Test
• IXL Quizzes
   

PA Core Standards

• CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties.
• CC.2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers.
• CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems.
• CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials.
• CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
• ​​CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.
• CC.2.2.8.C.1 Define, evaluate, and compare functions.
• CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions.
• CC.2.1.7.D.1 Students acquire the knowledge and skills needed to: Analyze proportional relationships and use them to model and solve real-world and mathematical problems. 
  • M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. 
  • M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems.
     

• Identification of rational and irrational numbers.
• Recognition of an expression, term, like terms, variable, power, and coefficient.
• Development and simplification of algebraic expressions.
• Understanding of various inequalities.
• Graphical representations of one variable inequalities.
• Knowledge of slope-intercept form and rate of change.
• Understanding percentages and ratios.

• Concepts like "closed sets" introduce students to abstract mathematical thinking and the properties of mathematical operations within specific sets, fostering logical reasoning.
• Polynomials can describe curves, trajectories, growth patterns, and financial models, making them essential for fields such as physics, engineering, and data analysis.
• Solving inequalities requires students to think critically about mathematical operations and how they affect the direction of the inequality sign.
• Learning to represent functions through tables, graphs, and mapping diagrams enables students to interpret data both visually and numerically, a crucial skill in statistics and data science.
• These topics collectively build a robust mathematical foundation, sharpen analytical and problem-solving skills, and provide essential tools for understanding and navigating a data-rich, technologically advanced world.

• Use properties of adding and multiplying rational and irrational numbers.
• Write closed sets for rational and irrational numbers.
• Interpret and define parts of an expression as terms and coefficients.
• Understand polynomials and classify them by the number of terms.
• Identify the degree of a polynomial.
• Simplify polynomials by grouping like terms.
• Add polynomials by grouping like terms.
• Solve one-step, multi-step, and variable on both sides inequalities and graph all solutions on a number line.
• Solve an inequality that has no solution or has all real numbers as a solution.
• Write and solve real-world inequalities.
• Understand a function by looking at the domain and range in a table, coordinate plane, and a mapping diagram.
• Graph a function given an equation.
• Determine if an equation is a linear function.
• Investigate the effect on a graph of changing the y-intercept of a linear function.
• Investigate the effect on a graph of changing the slope of a linear function.
• Calculate the average rate of change of a function.
• Distinguish between constant change and constant percent change of a function.

• How do the fundamental properties of real numbers and set operations define the characteristics and classifications of numerical results?
• How do the foundational components and operations of polynomial expressions enable their classification and simplification?
• How can the principles and procedures for solving various types of one-variable inequalities be applied to model and interpret real-world scenarios, including those with special solution sets?
• How do the various representations and key characteristics of functions, particularly linear functions, enable us to understand their graphical behavior, rates of change, and the impact of their parameters?

• L1 In which subset of real numbers does the sum of a rational number and an irrational number belong?
• L2 In which subset of real numbers does the product of a nonzero rational number and an irrational number belong?
• L3 What is a closed set?
• L4 What are terms and coefficients?
• L5 What are polynomial expressions, and how are they classified?
• L6 What is the degree of a polynomial?
• L7 How do you simplify a polynomial?
• L8 How do you add polynomials?
• L9 How do you solve a one–step inequality in one variable?
• L10 How do you solve a multi-step inequality in one variable?
• L11 How do you solve an inequality with variables on both sides?
• L12 What happens when you solve an inequality with all real numbers as solutions or no solution?
• L13 How do you write inequalities to model real-world situations?
• L14 How can you represent functions?
• L15 How can you graph a linear function given an equation?
• L16 How can you determine if an equation is a linear function?
• L17 How is a change in b reflected in the graph of a linear function f(x) = mx + b?
• L18 How is a change in m reflected in the graph of a linear function f(x) = mx + b?
• L19 How do you find the rate of change for a function over a given domain?
• L20 How do constant change and constant percent change differ?
   

• Into Math Getting Ready for Algebra Module
• iXL
• Graphing Calculator or Desmos
• Graph paper
• Ruler
   

• Rational
• Irrational
• Binomial
• Exponent
• Function
• Linear Function
• Percent Increase
• Closed Set
• Open Set
• Trinomial
• Like Terms
• Range
• Slope
• Terms
• Coefficients
• Monomial
• Inequality
• Domain
• y-intercept
• Algebraic Expression
• Polynomial
• Degree of a Polynomial
• Real Numbers
• Nonlinear Function
• Rate of Change

• Checkpoint 1: Lessons 1–3
• Checkpoint 2: Lessons 4–8
• Checkpoint 3: Lessons 9–13
• Checkpoint 4: Lessons 14–20
• Summative Assessment: Lessons 1-20