Notes & FAQs

Tasks for this target will require students to create equations and inequalities in one variable to solve problems. Other tasks will require students to create and graph equations in two variables to represent relationships between quantities.

Tasks for this target will require students to solve linear equations and inequalities in one variable... Tasks asking students to choose the appropriate method will contribute evidence to Claim 2 and 4.

 In Algebra, students are working toward fluency with linear equations & inequalities.  The inclusion of letter coefficients raises the level of abstraction and the level of rigor in Algebra 1.  There is also a greater emphasis on students creating the equations & inequalities from a given context or problem.  Those contexts can help students understand why they are taking the steps they do as they decontextualize & recontextualize (SMP#2).

The Item Specifications reference both.  There are two evidence statements for linear inequalities and tow that involve linear equations.  Teaching both using algebra tiles and and multiplying by a negative one is one way to solve both.  You might consider reminding students of the difference between them, and then teach both letting students decide which type  they are from a given contextual problem.  This supports the key difference of students creating the equations they are working to solve (A-CED 1&2).  By the way, students technically have not done inequalities since the seventh grade, which might be a reason to focus a bit more attention there, but once again the the solution strategy can be the same  depending on how it is taught.

Besides being a level 1 (equations or at best a level 2 (inequalities) understanding, there is no reason to have to start with one-step equations.  While one might think it is a scaffold for students, the brain works to create a “space” for new learning.  When multi-step equations are added to a one-step equation understanding, some students fall apart. Start with the more complex first, and use algebra tiles and context as scaffolds instead.  Students will still need to see a couple of one-step equations thrown in, bu they should say these are too easy at some point after working on multi-step equations - which is good as one-step equations are from the 6th grade level if not before.

Middle school spent time on equations.  Just enough work with linear equations in one variable should be done to remind students of that work and be prepared to apply it in manipulating linear equations and systems as they change forms and solve problems.  Eighth grade emphasized linear functions over linear systems; therefore, work should be more focused on linear systems.  If students need re-teaching of linear functions, then re-engaging with linear systems literally gives them twice the practice so why not begin there?  Time should be balanced between solving/graphing linear equations and comparing them.  In fact, comparing functions is a part of every level of the Achievement Level Descriptors 1-4.  This is yet another argument to focus on systems.

While linear functions are a large part of middle school and high school, there is no need to "die on this hill."  Here is why - linear functions are the focus almost the entire year.  Unit 2 (Functions 1/Overview) should have included linear growth.  Unit 4 (Exponentials) will compare linear growth to exponential growth.  Unit 5 (Quadratics) will compare linear growth to "quadratic" growth.  Unit 6 (Two Variable Stats) should re-engage linear functions and statistics both from 8th grade.  Unit 7 (Functions 2) ask students to compare all three types of functions including linear and introduces new functions, which can also be compared to linear functions.  The moral of the story? Emphasize systems throughout the year whether the system contains two linear functions (this unit) or two different functions where one is linear (the remaining units).

While this may be up to individual or site interpretation, we would encourage a data comparison to find what is most effective for students. That said, I might encourage the following:

1. Linear equations and inequalities in one variable to build a conceptual and procedural foundation for what comes next.

2. Create equations & inequalities, graph them & compare them. Taking care to compare similar and dissimilar representations. This provides a contextual & conceptual foundation for the work. Avoid saving all the word problems for last as procedures are not well understood and application becomes too difficult.

3. Discuss explicit & recursive formulas throughout as students often struggle with one or both, then use them with series to transition from linear (arithmetic) to exponential (geometric) functions in the next unit.