Algebra 1 Unit 1:  Expressions, Equations, and Inequalities

Unit Driving Question 

How can we manipulate information to help us solve real-world problems? 

Essential Questions 

1. How can we represent information symbolically?

2. How do we develop mathematical arguments/proofs for solving real-world situations?

3. How can we use related, but different representations to solve real-world problems?

Launch Task 

Big Ideas for Development Lessons --click on each for its activities

Closure & Assessment 

1 Lesson 

4 Weeks (approximately 1 week per big idea) 

1 Week 

Students will engage in various problem-solving strategies in this Mystery Letters Task.

Bootstrap Lesson: Order of Operations (Note, this is for Bootstrap Trained Teachers)

Click on the links below to see Big Idea Lesson Overviews (with links to teacher notes and lesson activities)

1. Polynomial expressions can be simplified and evaluated.
   
2. Polynomial expressions can be written as factors.
   
3. Square and cube roots can be added, subtracted, multiplied, divided, and simplified.
   
4. Equations and inequalities can be solved in both algebraic and real-world contexts.

1. Unit 1 Formative Assessment 1 (after Big Idea #2)
2. Unit 1 Formative Assessment 2 (after Big Idea #4) 
3. Re-engagement Activity (not provided, to be based on formative assessment results)
4. Unit 1 Assessment

Big Idea 1: Polynomial expressions can be simplified and evaluated.

Lessons and Additional Activities

Big Idea 1 Lessons 1-4 Overview (includes links to teacher notes and student activities)

• Lesson 1
• Lesson 2 (updated 8-2020)
• Lesson 2B
• Lesson 3
• Lesson 4

Evidence of Understanding 

Generate equivalent expressions using operations on whole numbers and exponents

• Add and subtract like terms within a polynomial expression

• Determine when an expression is completely simplified

• Multiply terms in a polynomial expression and use proper exponent rules

• Understand what happens to the power of a variable when multiplied

• Justify reasoning

Evaluate a polynomial expression

• Evaluate a variety of algebraic expressions including absolute value, radicals (square or cube roots), or rationals for given values of the variables.

• Understand how to reason and work with a non-standard operation.

• Example:

• Justify reasoning.

Big Idea 2: Polynomial expressions can be written as factors.

Lessons and Additional Activities

Big Idea 2 Lessons 1-3 Overview (Includes links to teacher notes and student activities)

Evidence of Understanding 

Factor out a GCF

• Identify when an expression has a common factor that can be factored out

• Determine the greatest common monomial factor

• Divide out that factor

Factor a quadratic expression

• Use knowledge of multiplication of polynomial expressions to factor a quadratic equation into two binomials if possible

• Understand how the signs of the binomials impact the quadratic expression

Big Idea 3: Square and cube roots can be added, subtracted, multiplied, divided, and simplified.

Lessons and Additional Activities

Big Idea 3 Lessons 1-4 Overview (includes links to teacher notes and student activities)

Additional Collaborative Activity:

Stations Activity: Radicals and Irrational Numbers- Students will work in collaborative groups to complete station activities providing opportunities to develop concepts and skills related to simplifying radicals, performing operations with radicals, and classifying and comparing rational versus irrational numbers.

Evidence of Understanding 

Simplify square roots and cube roots

• Use knowledge of factors to produce the simplest form of roots

• Apply absolute value bars when taking the square root of a variable that results in an odd exponent

Perform arithmetic operations on square roots

• Add and subtract square roots

• Combine like radicals by adding or subtracting the coefficients

• Understand that radical will not change when adding or subtracting

• Multiply a square root

• Multiplying  will change the radicand and might need to be simplified further

• Divide square roots

• Simplifying square roots may make it easier to rationalize

• Radicals may not be left in the denominator and must be rationalized

Big Idea 4: Equations and inequalities can be solved in both algebraic and real-world contexts.

Lessons and Additional Activities

• Big Idea 4 Lessons 1-5 Overview (includes links to teacher notes and student activities)

Additional Activities

Bootstrap Computer Science Integration Activity

• Problem Decomposition (Note: This lesson is for Bootstrap trained teachers.)

Additional Performance Assessment

• When I'm 64 (covers A1.A.1.1 and A1.A.3.1)- For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.   

Evidence of Understanding 

Solve equations and inequalities in real-world problems

• Use knowledge of solving equations to solve real world problems such as angle measure, geometric formulas, or science and statistics problems.

• Use formulas or other necessary equations to solve problems

• Interpret solutions in original context to check for reasonableness

Solve equations with several variables in terms of one specific variable

• Apply algebraic properties of equality in order to create equivalent equations in order to isolate the appropriate variable.

Solve absolute value equations

• Know that absolute value is a distance from zero and results in two solutions, one in each direction (positive and negative)

• Isolate absolute value before solving equation

• Recognize |x-a| =b is b units away from a since |x|=b is b units away from zero

• Solve absolute value equations and interpret the solutions in the original context

Solve and graph compound and absolute value inequalities

• Compound inequalities can have separate, or disjoint, solutions or overlapping, conjunction, solutions

• Make connections between algebraic and graphical solutions

• Graph solutions to inequalities on a number line.

• Identify two separate inequalities of absolute value and determine outcome of their graphs

• Write and graph compound inequalities given a  real world situation

• Use correct vocabulary of compound inequalities and determine number of solutions

• Know the difference between disjunction and conjunction solutions