Unit

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0:
Growth Mindset

How does improving student attitudes toward math affect their learning? 

1. Math is about learning not performing.
2. Math is about making sense.
3. Math is filled with conjectures, creativity, and uncertainty.
4. Mistakes are beautiful things.


Students will understand the importance of a growth mindset (e.g., that math is not about talent or natural ability but is about thoughtful practice) and what it means to talk and listen. Students will also understand that class is where students practice thinking and doing math.

Students will learn the value of taking time to think about math and listen to how others make sense of their work to arrive at a common understanding.

Students will build the habits of using precise language, practicing, and sharing their thoughts.

Unit 1:
Expressions, Equations and Inequalities
Timing
~4 weeks
Objectives
A1.A.3.2
A1.A.3.4
A1.A.3.3
A1.N.1.1
A1.N.1.2
A1.A.1.1
A1.A.1.2
A1.A.3.1
A1.A.2.2

How can we manipulate information to help us solve realworld problems?


How can we represent information symbolically?

How do we develop mathematical arguments/proofs for solving realworld situations?

How can we use related, but different representations to solve realworld problems?


Polynomial expressions can be simplified and evaluated.

Polynomial expressions can be written as factors.

Square and cube roots can be added, subtracted, multiplied, divided, and simplified

Equations and inequalities can be solved in both algebraic and realworld contexts

A1.A.3.2 Simplify polynomial expressions by adding, subtracting, or multiplying.
A1.A.3.4 Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y.
A1.A.3.3 Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.
A1.N.1.1 Write square roots and cube roots of constants and monomial algebraic expressions in simplest radical form.
A1.N.1.2 Add, subtract, multiply, divide, and simplify square roots of constants, rationalizing the denominator when necessary.
A1.A.1.1 Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, statistics) and interpret the solutions in the original context.
A1.A.1.2 Solve absolute value equations and interpret the solutions in the original context.
A1.A.3.1 Solve equations involving several variables for one variable in terms of the others.
A1.A.2.2 Represent relationships using mathematical models with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line.

Unit 2:
Data
Timing
12 weeks
Objectives
A1.D.1.1
A1.D.1.2
A1.D.1.3

How does data help us interpret realworld situations?


How do we use evidence to support arguments?

How do we interpret evidence in order to support arguments?

What can we learn from patterns within data sets?


A1.D.1.1 Display, describe, and compare data sets using summary statistics (central tendency and spread (range)). Utilize technology (e.g., spreadsheets, calculators) to display data and calculate summary statistics.
A1.D.1.2 Collect data and analyze scatter plots for patterns, linearity, and outliers.
A1.D.1.3 Make predictions based upon the linear regression, and use the correlation coefficient to assess the reliability of those predictions using graphing technology.

Unit 3:
Functions
Timing
46 weeks
Objectives
A1.F.1.1
A1.F.1.2
A1.F.1.3
A1.F.3.3
A1.F.1.4
A1.F.1.5
A1.F.3.2
A1.F.2.1
A1.F.2.2

How can we use data to determine patterns and relationships from realworld situations?


How do we measure change?

How do we quantify the relationships between quantities?

Howcan different representations show relationships?

What patterns exist among quantities?

 A function is a rule that describes a set of data for which each input has one and only one output

Functions are written and manipulated using function notation.

Functions can be evaluated and interpreted both algebraically and graphically.

Function families share similar graphs, behaviors, and properties.

A1.F.1.1 Distinguish between relations and functions.
A1.F.1.2 Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models.
A1.F.1.3 Write linear functions, using function notation, to represent mathematical models.
A1.F.3.3 Add, subtract, and multiply functions using function notation.
A1.F.1.4 Read and interpret the linear piecewise function, given a graph modeling a situation.
A1.F.1.5 Interpret graphs as being discrete or continuous.
A1.F.3.2 Recognize the parent functions f(x) = x and f(x) = x. Predict the effects of vertical and horizontal transformations f(x+c) and f(x) +c, algebraically and graphically.
A1.F.2.1 Distinguish between linear and nonlinear (including exponential) functions. Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric).
A1.F.2.2 Recognize the parent functions f(x) = x and f(x) = x. Predict the effects of vertical and horizontal transformations f(x+c) and f(x) +c, algebraically and graphically.

Unit 4:
Linear Functions
Timing
46 weeks
Objectives
A1.D.1.2
A1.A.4.4
A1.A.4.5
A1.A.4.1
A1.A.4.3
A1.F.1.3
A1.F.3.1
A1.A.4.2
A1.A.2.1

How can patterns that exist in data help us make predictions to solve realworld problems?


How do we measure change?

How do we quantify the relationships between quantities?

How can relationships between quantities be represented?


Linear functions describe data sets that have a direct correlation.

Linear functions can be represented in multiple equivalent ways.

Linear Functions can be used to to solve real world problems and make predictions.

Linear inequalities represent relationships with multiple solutions.

A1.D.1.2 Collect data and analyze scatter plots for patterns, linearity, and outliers.
A1.A.4.4 Express linear equations in slopeintercept, pointslope, and standard forms. Convert between these forms.
A1.A.4.5 Analyze and interpret associations between graphical representations and written scenarios.
A1.A.4.1 Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret slope and the x and yintercepts of a line.
A1.A.4.3 Write the equation of the line given its slope and yintercept, slope and one point, two points, x and yintercepts, or a set of data points.
A1.F.1.3 Write linear functions, using function notation, to represent mathematical models.
A1.F.3.1 Identify and generate equivalent representations of linear functions, graphs, tables, and realworld situations.
A1.A.4.2 Analyze and interpret mathematical models involving lines that are parallel, perpendicular, horizontal, and vertical.
A1.A.2.1 Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions.

Unit 5:
Systems
Timing
23 weeks
Objectives
A1.A.1.3

How can representing realworld problems in many ways help us understand them well?

1. How can we apply our knowledge to model realworld situations with more than one variable?
2. How can we represent and analyze our solutions to problems?
3. How can we represent the same thing in multiple different ways?


A1.A.1.3 Analyze, use and apply mathematical models to solve problems involving systems of linear equations with a maximum of two variables by graphing, substitution, and elimination. Graphing calculators or other appropriate technology may be utilized. Interpret the solutions in the original context.

Unit 6:
Probability
Timing
~2 weeks
Objectives
A1.D.2.1
A1.D.2.2
A1.D.2.4
A1.D.2.3

How can we use probability to make predictions about realworld problems?


How can data help us make decisions?

How do we use the data gathered from experimentation?


Probability is calculated with multiplication or additional principles.

Probability is used to predict possible outcomes.

Experiments can model realworld probability situations.

A1.D.2.1 Apply simple counting procedures (factorials, permutations, combinations, and tree diagrams) to determine sample size, sample space, and calculate probabilities.
A1.D.2.2 Given a Venn diagram, determine the probability of the union of events, the intersection of events, and the complement of an event. Understand the relationships between these concepts and the words “AND,” “OR,” and “NOT.”
A1.D.2.4 Apply probability concepts to realworld situations to make informed decisions.
A1.D.2.3 Use simulations and experiments to calculate experimental probabilities.

Culminating Unit
Timing
~2 weeks

How can students show evidence of understanding?


Algebra 1 Showcase 

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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