Unit

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0:
Growth Mindset

How does mindset affect learning mathematics?



Math is about learning not performing

Math is about making sense

Math is filled with conjectures, creativity, and uncertainty

Mistakes are beautiful things


Develop a deep and flexible conceptual understanding

Develop accurate and appropriate procedural fluency

Develop strategies for
problem solving

Develop mathematical reasoning

Develop a productive mathematical disposition

Develop the ability to make conjectures, model, and generalize

Develop the ability to communicate mathematically

Unit 1: Expressions, Equations, and Inequalities
Timing
56 weeks
Objectives
PA.A.3.1
PA.A.3.2
PA.A.4.1
PA.A.4.2
PA.A.4.3

How can you use expressions, equations, and inequalities within realworld situations?


In what realworld situations can substitution become a valuable tool?

How can you determine if two expressions are equivalent?

How can equivalent expressions be used in the realworld?

How do linear equations give information for realworld situations?

What are realworld situations that would yield one solution, no solution, or infinite solutions?

How can we identify various situations in the world around us?


Substitution is used to simplify and evaluate algebraic expressions.

Properties of operations can be used to justify equivalent expressions.

Real world problems that can be represented as linear equations will yield one, infinitely many, or no solution.

Independent and dependent variables can be identified in the world around us.

PA.A.3.1 Use substitution to simplify and evaluate algebraic expressions.
PA.A.3.2 Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive).
PA.A.4.1 Solve mathematical problems using linear equations with one variable where there could be one, infinitely many, or no solutions. Represent situations using linear equations and interpret solutions in the original context
PA.A.4.2 Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form px + q > r and px + q < r, where p, q, and r are rational numbers.
PA.A.4.3 Represent realworld situations using equations and inequalities involving one variable.

Unit 2:
Linear Equations and Functions
Timing
56 weeks
Objectives
PA.A.1.1
PA.A.1.2
PA.A.1.3
PA.A.2.1
PA.A.2.2
PA.A.2.3
PA.A.2.4
PA.A.2.5
PA.D.1.3

How can we use graphs and other representations to gain knowledge of realworld situations?


How can we identify relationships in the world around us?

What information can the rate of change give you about a linear equation or realworld data?

How can you represent linear relationships?

How can you identify an equation or graph as linear or nonlinear?

How can
scatterplots
be used to gain information about realworld events?


A function is a relationship between an independent and dependent variable.

The rate of change describes how one quantity changes in respect to another.

Multiple representations can be used to express and analyze linear relationships.

Functions can be identified as linear if they can be expressed in slope intercept or graphed in a straight line.

Data can be displayed and interpreted using scatterplots.

PA.A.1.1 Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable.
PA.A.1.2 Use linear functions to represent and model mathematical situations.
PA.A.1.3 Identify a function as linear if it can be expressed in the form y=mx + b or if its graph is a nonvertical straight line.
PA.A.2.1 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.
PA.A.2.2 Identify, describe, and analyze linear relationships between two variables.
PA.A.2.3 Identify graphical properties of linear functions, including slope and intercepts. Know that the slope equals the rate of change, and that the yintercept is zero when the function represents a proportional relationship.
PA.A.2.4 Predict the effect on the graph of a linear function when the slope or yintercept changes. Use appropriate tools to examine these effects.
PA.A.2.5 Solve problems involving linear functions and interpret results in the original context.
PA.D.1.3 Collect, display, and interpret data using scatter plots. Use the shape of the scatter plot to find the informal line of best fit, make statements about the average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units.

Unit 3:
Exponents and Numbers
Timing
34 weeks
Objectives
PA.N.1.1
PA.N.1.2
PA.N.1.3
PA.N.1.4

How can exponents and real numbers be used to solve realworld situations?


How can you apply strategies to simplify expressions?

How can very large or very small numbers be written and applied in a way that is useful and meaningful?

What strategies can you use to compare numbers not easily found on a number line?

What strategies can be used to estimate the value of a nonperfect square root?


Equivalent numerical and algebraic expressions can be generated by applying the properties of integer exponents.

Scientific notation creates a realistic way to utilize really small or really large numbers.

The estimation of a nonperfect square root is located between two whole numbers on a number line.

PA.N.1.1 Develop and apply the properties of integer exponents, including a^{0} = 1 (with a 0 ), to generate equivalent numerical and algebraic expressions.
PA.N.1.2 Express and compare approximations of very large and very small numbers using scientific notation.
PA.N.1.3 Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.
PA.N.1.4 Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

Unit 4: Pythagorean Theorem
Timing
23 weeks
Objectives PA.GM.1.1
PA.GM.1.2

How can the Pythagorean Theorem be used in realworld situations?


What is the special relationship between the sides of a right triangle?

How can the Pythagorean Theorem be used to solve realworld applications?


Pythagorean Theorem utilizes the special relationship between the three sides of a right triangle.

Pythagorean Theorem can be used to find the distance between two points on a coordinate plane.

PA.GM.1.1 Justify the Pythagorean theorem using measurements, diagrams, or dynamic software to solve problems in two dimensions involving right triangles.
PA.GM.1.2 Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.

Unit 5:
Surface Area and Volume
Timing
23 weeks
Objectives
PA.GM.2.1
PA.GM.2.2
PA.GM.2.3
PA.GM.2.4

How are two dimensional and threedimensional objects related to each other in realworld situations?


How can formulas be used to better understand measurements of 3D objects?

How can nets be used to analyze 3D figures and calculate surface area and volume?

How are two dimensional and threedimensional objects related to each other?


Surface area and volume can be calculated for a rectangular prism.

Surface area and volume can be calculated for a cylinder.

PA.GM.2.1 Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units (e.g., cm^{2} ).
PA.GM.2.2 Calculate the surface area of a cylinder, in terms of pi (π ) and using approximations for pi (π ), using decomposition or nets. Use appropriate units (e.g., cm^{2})
PA.GM.2.3 Justify why base area (B) and height (h) in the formula V=Bh are multiplied to find the volume of a rectangular prism. Use appropriate units (e.g., cm^{3} ).
PA.GM.2.4 Develop and use the formulas V = (𝜋 r)^{2}h and V = Bh to determine the volume of right cylinders, in terms of (𝜋) and using approximations for pi(𝜋). Justify why base area (B) and height (h) are multiplied to find the volume of a right cylinder. Use appropriate units (e.g., cm^{3} ).

Unit 6:
Measures of Central Tendency
Timing
23 weeks
Objectives
PA.D.1.1
PA.D.1.2

How do data points affect mean and median in realworld situations?


What effects can changing data points have?

How do individual data points affect the entire data set?


The mean and median of a data set is impacted by inserting or deleting data points.

Outliers can have an effect on measures of central tendency.

PA.D.1.1 Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using technology to examine this impact.
PA.D.1.2 Explain how outliers affect measures of center and spread.

Unit 7:
Probability
Timing
34 weeks
Objectives
PA.D.2.1
PA.D.2.2
PA.D.2.3

How can probability be used in realworld situations?


How can probabilities be determined when actual probabilities are not known?

How can predictions be made on unknown probabilities?

How can you determine if the representation of a data population is fair?

How are conclusions about a data set
drawn
using sampling?


Experimental probability can be calculated and the result can be expressed in multiple ways.

Experimental probability can be used to make predictions.

Samples are used to generalize a population.

PA.D.2.1 Calculate experimental probabilities and represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.
PA.D.2.2 Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.
PA.D.2.3 Compare and contrast dependent and independent events.

Culminating Unit
Timing
23 weeks
Objectives
PA.A.1.2
PA.A.2.1
PA.A.2.2
PA.A.2.3
PA.D.1.3

How can mathematical patterns be used to expand our understanding? 

What influences temperature?

Which polygons can be tessellated?

 Patterns can be used to make predictions about data.
 Patterns and polygons can be used to create tessellations.

PA.A.1.2 Use linear functions to represent and model mathematical situations.
PA.A.2.1 Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.
PA.A.2.2 Identify, describe, and analyze linear relationships between two variables.
PA.A.2.3 Identify graphical properties of linear functions, including slope and intercepts. Know that the slope equals the rate of change, and that the yintercept is zero when the function represents a proportional relationship.
PA.D.1.3 Collect, display, and interpret data using scatter plots. Use the shape of the scatter plot to find the informal line of best fit, make statements about the average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units.

Distance Learning Resources/ Supplemental Activities 
How can students develop and show evidence of understanding? 


Multiple objectives are covered in this material. These math tasks are designed to enhance current curriculum and support distance learning. 
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