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Gr. HS Unit: Relationships Between Quantities and Reasoning with Equations

Unit Overview

By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. Unit 1 of Algebra I builds on these earlier experiences by asking students to analyze and explain the process of solving an equation, to reason quantitatively, and use units to solve problems. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities in both one and two variables, and use them to solve problems. They master solving linear equations and applying related solution techniques. They also solve simple exponential equations that rely only on the application of the laws of exponents (exponents are integers). All of this work is grounded on understanding quantities and on relationships between them.

Essential Questions:

  • When and how is mathematics used in solving real world problems?
    • How are equations and inequalities used to solve real world problems?
  • What characteristics of problems would determine how to model the situation and develop a problem solving strategy?
    • What characteristics of problems would help to distinguish whether the situation could be modeled by a linear or an exponential model?
    • When is it advantageous to represent relationships between quantities symbolically? numerically? graphically?
  • Why is it necessary to follow set rules/procedures/properties when manipulating numeric or algebraic expressions?
    • How can, the structure of expressions/equations/inequalities, units of measure used, and mathematical properties help determine a solution strategy?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.

Available Model Lesson Plans

The lesson plan(s) have been written with specific standards in mind. Each model lesson plan is only a MODEL - one way the lesson could be developed. We have NOT included any references to the timing associated with delivering this model. Each teacher will need to make decisions related ot the timing of the lesson plan based on the learning needs of students in the class. The model lesson plans are designed to generate evidence of student understanding.

This chart indicates one or more lesson plans which have been developed for this unit. Lesson plans are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignment: A.CED.2, N.Q.3

This lesson plan focuses on the characteristics of problems to determine how to model the situation and develop a problem solving strategy.

Available Model Lesson Seeds

The lesson seed(s) have been written with specific standards in mind. These suggested activity/activities are not intended to be prescriptive, exhaustive, or sequential; they simply demonstrate how specific content can be used to help students learn the skills described in the standards. Seeds are designed to give teachers ideas for developing their own activities in order to generate evidence of student understanding.

This chart indicates one or more lesson seeds which have been developed for this unit. Lesson seeds are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignnment: A.CED.1, A.CED.3, A.REI.3

Practice
The activity in this lesson seed provides a non-scaffolded problem which requires students to create, solve and interpret the solution for a linear inequality in one variable.

CCSC Alignnment: A.CED.2

Developmental Activity
The activity in this lesson seed would serve as a good introductory activity for a lesson on creating exponential equations in two variables.

CCSC Alignnment: A.CED.1, A.REI.3

Practice
The activity in this lesson seed provides practice with solving a non-scaffolded problem. The problem provides an opportunity for students to demonstrate proficiency with Standards for Mathematical Practice:

  • Make sense of problems and persevere in solving them
  • Reason abstractly and quantitatively
  • Construct a viable argument