This is the fourth course in year two of a series of middle school mathematics courses. These courses are taught in small-groups to provide individual instruction and social-learning opportunities aligned with a social constructionist or situated cognition view of learning. This series is based on an accelerated math curriculum that covers three years of content, aligned to Common Core Math Standards, over the course of two school years. It is perfect for students preparing to begin Algebra ahead of time, or those who need review and remedial support. The curriculum is problem-based this means instead of lectures or videos students work together as a small group to solve problems to discover principles and strategies with teacher guidance, as necessary. Therefore, we will spend approximately 90% of each class period working on problems and discussing them as a group. The use of discussion and problem-solving leads to generalized mathematics or proofs. This process prepares students well who may seek advanced mathematics in high-school or beyond. Students will complete a math notebook In the style of a main lesson book to help with recall and long-term retention.
In this unit, students expand on their previous work writing and solving equations with coefficients and an addend (unit 3). They will solve linear inequalities with one variable and learn to represent these solutions on the number line understanding that there may be none, one, or infinite solutions. They will generate equivalent expressions to numerical or linear equations and solve them. They will learn how to explain their solution using mathematical properties. 
Week 1
Day 1: We will begin with a readiness check to understand students existing conception of geometry and algebra ideas that may need to be addressed and inform instruction throughout the unit. 
Day 2: Students will revisit inequality statements from their work with rational numbers and extend them to real-world situations with maximum and minimum values. They will represent these situations with statements and reason about them in discrete and continuous contexts. 
Day 3: Students consider situations with more than one condition and learn that inequalities may have multiple solutions. They will use real-world scenarios to reason about and reduce the range of possible solutions. They will reason asbtractly and use graphs to represent their work. 
Day 4: In this lesson, we will focus on situations where the mathematical solution doesn't make sense in real world context. We will also use inequalities to make comparisons between unknown quantities. 
Day 5:  In this lesson, we work on inequalities with negative numbers and generalize our understanding of inequalities to go beyond the equation. We work on using substitution to find the direction of an inequality after determining a boundary point to generate inequalities about problems grounded in real-world contexts. 
Week 2: 
Day 1: We will continue our work using inequalities with negative numbers and generating inequalities to represent complex situations. We work on building conceptual understanding and intuition to solve related equations in order to understand inequalities rather than static rules or algorithms. 
Day 2: We will apply our formalized concept using models to connect to students interest. Students start with questions they want to answer and decide how to use inequalities to represent the situation mathematically. 
Day 3: We will begin our work with equivalent expressions. This will allow students to tackle more complex equations using existing skills by reducing equations to the form px+q-r. We will use graphic representations to begin to understand how to work with complex equations and define them through their parts. 
Day 4: We will apply the distributive property to our work by using it to expand inequalities, expressions, and equations by distributing a coefficient to multiple terms within a set of parenthesis. 
Day 5: In this lesson, students have a chance to recall one way of understanding equivalent expressions, that is, the expressions have the same value for any number substituted for a variable. Then they use properties they have studied over the past several lessons to understand how to properly write an equivalent expression using fewer terms. 
Week 3: 
Day 1: We will continue building fluency on writing equivalent expressions by exploring common error patterns and using mathematical models to identify the flaws.  Then we practice adding and removing parentheses in equations to determine ow they impact meaning in expressions with four terms. 
Day 2: We will have opportunities to demonstrate fluency in combing like terms through looking for and making use of structure. We will also work to apply the distributive property in more sophisticated ways. 
Day 3: We will move on from the hanger model and practice using equations to represent a problem and think about balanced moves as ways to manipulate equations using inverses and reciprocals. Then we will explore using negative number sin these equations which would not have been possible with a hanger model. 
Day 4: In this lesson we continue reinforcing the connection between three key Algebraic ideas: a solution to an equation is a number that makes the equation true, performing the same operation on each side of an equation maintains the equality in the equation, and therefore two equations related by such a move have the same solutions. Then they use these to practice generating and explaining their own solutions. 
Day 5: In this lesson, we will practice being strategic about which of our tools and strategies to use by realizing that there are multiple solution paths for an algebraic equation. We will also explore different structures of equations. 
Week Four:
Day 1: We will generalize from inequalities to equations and realize that equations can also have more than one solution. We will learn that equations can have many, one, or no solution.  We will practice generating equations of these types. 
Day 2: we will generalize this pattern and learn how to identify structural features of an equation that tell them which of these outcomes will occur when they solve it. They will learn to stop solving an equation when they reach a point that communicates the outcome. They will practice paying attention to and noting each step of the problem solving process. 
Day 3: In this lesson, we will take a macro approach and focus on large complex problems to apply our use of solving equations and lay the groundwork for the idea of substitution. 
Day 4: We will practice applying the skills form this unit to real-world situations, share multiple ways to solve a single problem, and use our skills to decide which deals will save us the most money using equations. 
Day 5: We will take an end-of-unit assessment where students independently solve problems to demonstrate mastery.