Grade 7 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.
• 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 and 2
• iXL
• 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

• Performance Task
• Module 1 & 2 Tests
• 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.
• 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.
• 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-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.
  • M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems.

• Understand positive and negative integers.
• Add and subtract positive numbers with a positive result.
• Plot numbers on a number line.
• Add and subtract multi-digit decimals fluently.
• Use positive and negative numbers to represent quantities in real-world contexts.
• Understand ordering and absolute value of rational numbers.
• Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• Perform operations with positive rational numbers.
• Interpret positive and negative numbers as opposites on a number line.
• Use ordering and absolute value of rational numbers.
• Add, subtract, multiply, and divide integers and signed rational numbers.

• Conceptual understanding of addition/subtraction helps them see addition as movement on a number line, reinforcing that adding or subtracting can be represented visually.
• Foundation for algebra assists in grasping the distance and direction on a number line is critical for later work in algebra and coordinate geometry.
• Connecting math to real life makes the math meaningful and helps students see how math applies in everyday situations (e.g. finances, temperature changes, elevation).
• Critical thinking encourages them to think about whether a given situation should be modeled by addition or subtraction and to check whether their answer makes sense.
• Understanding the concept of zero as a balance point reinforces that adding a number and its opposite returns you to zero, showing balance or cancellation.
• Connecting math to real-life situations (like temperatures, finances, distances) helps students see relevance and practical use.
• Critical thinking helps them decide when addition or subtraction is appropriate and what the sign of the answer means in context.
• Understanding that the distributive property still works with negatives ensures that math remains logical and coherent, connecting their earlier work with fractions to new topics with negative numbers.
• Many real-world situations (like debts, temperature changes, and directional changes) involve multiplying signed numbers, so understanding these rules helps students apply math outside the classroom.
• Fractions and decimals are everywhere in real life—money, cooking, measurements, data, sports statistics, etc. Understanding operations helps students apply math to practical situations.
• Operations on fractions and decimals are prerequisites for algebra, geometry, probability, and beyond. Without mastering these, students struggle with more advanced math concepts.

• Use a number line to add and subtract positive integers.
• Use a number line to add or subtract a negative.
• Use a number line to add and subtract rational numbers.
• Calculate the sum of two integers.
• Calculate the difference of two integers without using a number line.
• Fluently add and subtract rational numbers without a number line.
• Use properties to solve multi-step problems involving sums and differences of positive and negative rational numbers.
• Develop rules to find the product or quotient of two integers.
• Find the product of three or more signed rational numbers.
• Express quotients in different forms.
• Use products and quotients of rational numbers to solve problems.
• Apply properties and strategies to operate with rational numbers.
• Use estimation to check the reasonableness of answers when solving multi-step real-world problems.
• Solve multi-step problems involving a combination of rational number operations.

• How can I use a number line to visualize and understand addition and subtraction, and how does this help me apply these concepts to real-life situations?
• How does understanding zero as a balance point help me interpret positive and negative numbers in real-world contexts and decide when to add or subtract?
• How does understanding the distributive property with negatives help me make sense of multiplying signed numbers, and how can I apply this knowledge to real-world situations?
• How can I apply operations with fractions and decimals to solve real-world problems and prepare for more advanced math?
   

• L3.1 How can I use a number line to model and explain the addition and subtraction of positive integers?
• L3.2 How can I use a number line to understand and explain the addition and subtraction of negative integers?
• L3.3 How can I use a number line to add or subtract rational numbers?
• L4.1 How can I identify, write, and evaluate integer addition expressions to solve real-world problems confidently?
• L4.2 How can I identify integer subtraction problems and feel confident that I can write and evaluate expressions to solve real-world integer subtraction problems?
• L4.3 In what ways can I identify and write expressions to represent rational number problems?
• L4.4 How can I identify and write expressions to represent multi-step addition and subtraction problems?
• L5.1 How can I evaluate expressions and solve real-world problems involving rational number multiplication and division?
• L5.2 How can I compute the products of signed numbers using the properties of numbers to simplify calculations?
• L5.3 How can I express quotients in different forms?
• L5.4 How do I multiply and divide rational numbers in context?
• L6.1 How can I write and evaluate expressions involving rational numbers and name the properties used?
• L6.2 How can I underestimate and overestimate to check the reasonableness of answers?
• L6.3 How can I solve multi-step problems that involve rational numbers in different forms and multiple operations?
   

• Into Math Modules 3-6
• iXL
• Number lines
• Two-color counters
• Fraction strips
• Decimal models
   

• Addition Property of Opposites
• Additive Inverse
• Absolute Value
• Addend
• Mixed Number
• Associative Property of Multiplication
• Dividend
• Divisor
• Factor
• Inverse operations
• Product
• Quotient
• Rational Number
• Compatible Numbers
• Distributive Property
• Identity Property of Multiplication
• Inverse Property of Multiplication
• Order of Operations

• Performance Task
• Module Tests
• iXL Quizzes

PA Core Mathematics Standards

• 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.2.2.1 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.2.3.7.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.
  • 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).

• How to solve real-world problems by writing and solving equations of the form x + p = q and px = q, where p, q, and x are all nonnegative rational numbers.
• The properties of operations to generate equivalent expressions. 
• Written inequalities of the form x > c or x < c to represent constraints or conditions in a real-world or mathematical problem.
• How to solve equations as a process of answering a question.
• How to use variables to represent quantities in a real-world or mathematical problem, and construct simple equations to solve problems by reasoning about the quantities.
   

• See how different parts of an expression are connected, revealing important relationships between quantities.
• Interpret and analyze what each part of an equation represents, fostering deeper understanding and decision-making skills.
• Understand equations and inequalities so they can interpret complex topics like systems of equations, functions, and real-world modeling.
• Writing and solving equations based on angle relationships to reinforce algebraic skills and show how geometry and algebra work together.
• Choose the correct inequality, solve it, and interpret its meaning to develop reasoning skills applicable in math and beyond.
• Construct inequalities so that students can reason about relationships between quantities—like understanding what it means for one quantity to be greater or less than another.

• Use linear expressions to represent a quantity in different ways.
• Add, subtract, factor and expand linear expressions with rational coefficients. 
• Represent a real-world situation with an equation.
• Solve real-world situations using an equation.
• Write and solve two-step equations involving unknown angle measurements.
• Apply properties to solve one-step inequalities.
• Write two-step inequalities to represent situations.
• Write and solve two-step inequalities to solve problems.

• How can I analyze and connect the parts of expressions and equations to interpret relationships between quantities and solve real-world problems?
• How can I use algebra and geometry together to write and solve equations and inequalities, and interpret their solutions in meaningful, real-world contexts?
   

• L7.1 How can I write different forms of linear expressions to represent the same real-world situation?
• L7.2 How can I identify problems that require me to add, subtract, factor, and expand linear expressions with rational coefficients?
• L7.3 How can I write two-step equations for various situations?
• L7.4 How can I use two-step equations to solve a variety of problems?
• L7.5 How can I identify angle relationships, and use them to write and solve equations?
• L8.1 How can I solve one-step inequalities by applying properties and graph the solution on a number line?
• L8.2 How can I write two-step inequalities for real-world scenarios and determine whether given values are solutions?
• L8.3 How can I write and solve two-step inequalities for real-world scenarios?

• Into Math Modules 7-8
• iXL
• Counters
• Algebra Tiles
• Number Lines
   

• Equilateral Triangle
• Greatest Common Factor
• Isosceles Triangle
• Like Terms
• Perimeter
• Right Angle
• Solution of an equation
• Terms
• Adjacent Angles
• Complementary Angles
• Supplementary Angles
• Vertical Angles
• Equivalent
• Inequality
• Solution of an Inequality

• Performance Task
• Module Tests
• iXL Quizzes
   

PA Core Mathematics Standards

• 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.
• 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.
• 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.
  • 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).
  • 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.2.3.7.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.
     

• Classification of triangles and quadrilaterals.
• Identification and drawing of lines of symmetry.
• Determination of areas of triangles, quadrilaterals, and other figures.
• Drawing of polygons in the coordinate plane.
• Use of a protractor for drawing and measuring angles.
• Application of proportional relationships in multi-step ratio problems.
• Problem solving involving scale drawings of geometric figures.
• 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.
   

• 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.
• 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.

• Draw and construct circles and other 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.
• 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.
• Solve multi-step problems involving three-dimensional figures using formulas for surface area and volume.
• Find unknown angle measures when a transversal cuts parallel lines.

• How can I use geometric tools, such as a protractor and coordinate grid, to measure, classify, and draw geometric figures accurately?
• How can I apply proportional reasoning and scale to analyze, draw, and solve real-world geometric problems?
• 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?

• L9.1 How can I inscribe triangles in circles and draw geometric figures meeting given conditions?
• L9.2 How can I determine whether three lengths could be side lengths of a triangle, and, given two side lengths, I can find the range of possible lengths for the third side?
• L9.3 How can I determine whether it is possible to draw a triangle with three given angle measures?
• L9.4 How can I use tools to draw or construct figures that meet given criteria?
• L10.1 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?
• L10.2 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?
• L10.3 How can I identify the shapes of cross sections of circular solids and solve problems involving the areas of cross sections?
• L10.4 How can I break a composite figure into simple shapes and use area formulas to find its area?
• L11.1 How can I describe and analyze the cross sections of pyramids and prisms of all types, with or without a diagram?
• L11.2 How can I derive and apply the formulas for surface area of any right prism?
• L11.3 How can I accurately apply the formula to find the volume of right prisms?
• L11.4 How can I solve multi-step surface area and volume problems?
   

• Into Math Modules 9-11
• iXL
• Ruler
• Compass
• Protractor
• Grid Paper
• Geometry Software
• Circular Objects
• String
• Square Pyramid Net
• Rectangular Prism Net
• Centimeter Cubes
• Base-Ten Blocks

• Parallel
• Perpendicular
• Diameter
• Radius
• Base
• Height
• Circumference
• Cross Section
• Pi
• Plane
• Cross Section
• Net
• Pyramid
• Rectangular Prism
• Surface Area
• Vertex
• Volume

• Performance Task
• Module Tests
• iXL Quizzes

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 critically assess information's trustworthiness.
• 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 comprehensively understand data's typical values and spread.
• 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 sample is.
• 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.
• Draw conclusions about 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 important, and what can deviations from the overall pattern reveal about a data set's story or potential issues?
   

• L12.1 How can I identify the population and sample of given survey scenarios, and determine whether the sample is random and/or representative of the population?
• L12.2 How can I use proportional reasoning to make inferences about populations based on the results of a random sample?
• L12.3 How can I calculate sample ratios, and I can make inferences about the populations from the samples?
• L13.1 How can I compare important characteristics of data sets displayed in dot plots to draw conclusions based on data?
• L13.2 How can I make box plots and draw inferences about populations based on displayed data, make box plots and draw inferences about populations based on displayed data?
• L13.3 How can I use the means and MADs to assess the amount of visual overlap of two numerical data distributions?
   

• Into Math Modules 11-12
• iXL
• Pieces of red, blue, and green paper
   

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

• Performance Task
• Module Tests
• 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).
  • 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.2.1.7.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.
• 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 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 do we summarize numerical data 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 us predict the likelihood of events?
• How do proportional relationships and probability help us analyze situations and make predictions in daily life?
   

• L14.1 How can I describe the likelihood of an event?
• L14.2 How can I find an experimental probability and its complement?
• L14.3 How can I find the experimental probability of a compound event?
• L14.4 How can I use proportional reasoning or percent expressions to make a prediction based on an experimental probability?
• L15.1 How can I find the theoretical probability of a simple event?
• L15.2 How can I find the theoretical probability of a compound event?
• L15.3 How can I use theoretical probability to make predictions about real-world situations?
• L15.4 How can I use a simulation to test the probability of simple and compound events?
   

• Into Math Modules 14-15
• iXL
• Number Cubes
• Coins
• Paper Cups
• Number Cards 0-9
• Slips of Paper
   

• Complement
• Compound Event
• Event
• Experiment
• Experimental Probability
• Outcome
• Probability
• Proportion
• Sample Space
• Simulation
• Trial
• Theoretical Probability
• Tree Diagram

• Performance Task
• Module Tests
• iXL Quizzes