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Unit 1 : Variable Statistics
Unit 1 : Variable Statistics
1: Statistical Data Representations and Questioning
Timeline: 1 week
CCSS: S-ID.A 1
Topics:
Represent data with plots on the real number line
Histograms
Box plots
Dot plots
Measures of Center
Resources:
2: Distribution Shapes/Center and Variability
Timeline: 1 week
CCSS: S-ID.A 2
Topics:
Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
Spread
Interquartile range (IQR)
Mean Absolute Deviation (MAD)
Standard deviation
Interpret differences in spread, shape and center
Resources:
3: Manipulating Data
Timeline: 2 weeks
CCSS: S-ID.A 3
Topics:
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.
Observe effects of outliers
Modified Box Plots* (optional)
Use mean and standard deviation to fit to a normal distribution
Resources:
Evidence Pieces
Haircuts Task [Task | Digital Task | Digital Task (ES) | Rubric]
Emergency Rooms [ Task | Digital Task (please make a copy) | Digital Task (ES) (please make a copy) | Rubric ]
Common Activities/Lessons
Unit 2: Linear Equations, Inequalities, and Systems
Unit 2: Linear Equations, Inequalities, and Systems
1: Reasoning through Equations
Timeline: 2 week
CCSS:
Topics:
Students explain how to solve simple linear equations/inequalities.
Use algebraic properties to show that two equations and/or inequalities are equivalent.
Solve linear equations/inequalities in one variable including literal equations.
Resources:
Illustrative Math - Delivery Truck (A-SSE.A.1)
Illustrative Math - Same Solutions? (A-REI.A)
Illustrative Math - Paying the Rent (A-CED.A)
Illustrative Math - Harvesting the Field (A-CED.A.1) (challenging problem)
2: Systems of Linear Equations
Timeline: 2 weeks
CCSS: A-REI.C.5,6; A-CED.A.2
Topics:
Prove that given a system, replacing one equation with the sum of that equation and a multiple of the other produces a system with the same solution.
Interpret the terms of the equations of a linear system in the context of the problem.
Write a system of linear equations based on the context of a problem.
Solve linear systems using substitution, elimination/linear combinations, and graphing. (pairs only)
Resources:
Review
Graphing
Substitution
Elimination/Linear Combinations
Summary
3: Linear Inequalities
Timeline: 1.5 week
Topics:
Interpret the terms and units of a linear inequality in the context of the problem.
Write linear inequalities in one and two variables based on the context of the problem.
Solve, graph, and reason through the solution to linear inequalities in one variable.
Graph and interpret the solution of linear inequalities in two variables.
Resources:
4: Systems of Linear Inequalities
Timeline: 2 weeks
Topics:
Interpret the terms of the inequalities in a system of linear inequalities based on the context of the problem.
Write a system of linear inequalities based on the context of a problem.
Graph and interpret the solution to a system of linear inequalities.
EXTENSION: Linear Programming
Resources:
Evidence Pieces:
Common Activities/Lessons:
Unit 3: Functions
Unit 3: Functions
1: What is a Function?
Timeline: 1.5 weeks
CCSS: F.IF.A.1-3
Topics:
Represent relationships and functions using tables, operations, and graphs
Identify relationships that are functions
Describe the domain and range of a function
Find input and output pairs of a function
Use and interpret function notation
Evaluate a function for specific values of the domain
Resources:
2: Key Features of a Function
Timeline: 2 weeks
CCSS: F-IF.B.4-5
Topics:
Identify and interpret key features from graphs and tables including: intercepts; intervals where a function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity
Relate the domain and range of a function to its graph
Sketch graphs given key features in a verbal description of the relationship
Resources:
Desmos - Graphing Stories(careful using this one, it reinforces some misconceptions regarding graph outputs always relating to height in real life)
Evidence Pieces
Common Activities/Lessons
Unit 4: Linear and Exponential Functions
Unit 4: Linear and Exponential Functions
1: Arithmetic & Geometric Sequences
Timeline: 1 week
CCSS: F-BF.A.2
Topics:
Explore basic patterns and the common difference
Visualize both arithmetic sequences and geometric sequences
Focus on the change of the pattern or the next number in the pattern
Resources:
2: Modeling Linear and Exponential Data
Timeline: 2 - 3 weeks
Topics:
Choose between linear or exponential models
Prove that linear models grow by equal differences and exponential grow by different factors
Construct linear and exponential functions given a description, tables, and graphs
Use different forms- point-slope, slope-intercept and standard form
Observe from graphs and tables that exponential grows the fastest of any polynomial
Interpret parameters for linear and exponential in context
Resources:
Linear
Exponential
Desmos – What Comes Next (Exponential Patterns and Prediction)
Desmos – Marbleslides: Exponentials (Equations and their graphs)
Discovering Algebra: M&M’s Activity (can be used as an intro to exponential)
NCTM: Pay It Forward (can be used as an intro to exponential)
Achieve the Core – Xbox Xponentials (can be used as an intro to exponential)
3. Comparing Linear and Exponential Patterns
Timeline: 3 - 4 weeks
CCSS: S-ID.B.6a,c, S-ID.C.7
Topics:
Interpret slope and y-intercept in context
Line of fit linear and exponential to interpret exponential functions
Use properties of exponents to interpret functions
Line of fit linear and exponential and use to solve problems
Interpret parameters for exponential in context
Resources:
Evidence Pieces:
Sequences Quiz ( Task | Digital Task | Rubric )
Exponential & Linear Assessment ( Task | Digital Task | Rubric )
Comparing Linear & Exponential ( Task | Digital Task | Rubric )
Common Lessons/Activities:
Unit 5: Quadratic Functions
Unit 5: Quadratic Functions
1: Polynomials
Timeline: 2 weeks
CCSS: A-APR.A.1
Topics:
Identify and interpret key features of polynomials
Add, subtract, and multiply polynomials
Special products of binomials
Factor trinomials, including those when the leading coefficient does not equal 1
Resources:
2: Quadratic Functions
Timeline: 3-5 Weeks
Topics:
Quadratic terminology
Key features of quadratic functions
Identify patterns in tables and graphs
Find vertex algebraically and graphically
Find roots by factoring
Choose and convert between equivalent forms to highlight key features (zeros, vertex, etc.)
Solve quadratic equations in one variable by using square roots, factoring, completing the square, and quadratic formula.
Derive the quadratic formula by completing the square
Write complex solutions
Create, model, and solve real-world problems involving quadratic functions and interpret the results
Resources:
Intro
Parabolas
Factoring Quadratics
Forms of a Quadratic
Solving Quadratics
Applications
Possible Evidence Pieces
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