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A1-A-1-1

Page history last edited by Brenda Butz 6 years, 2 months ago

A1.A.1.1 Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context.


In a Nutshell

Students will use prior knowledge of solving equations with to solve and understand real-world problems which could include geometry, statistics or scientific formulas.

Student Actions

Teacher Actions

 

  • Students will develop accurate and appropriate procedural fluency as they solve for a variable in equations of varying types (one-step, two-step, and multistep) and manipulate equations by applying mathematical properties learned in pre-algebra.

  • Students will develop a deep and flexible conceptual understanding as they apply the proper formulas to solve mathematical and real-world problems from areas that may include geometry, science, and statistics.

  • Students will  develop strategies for problem solving and mathematical reasoning by choosing appropriate equations and applying logical strategies to solve mathematical and real-world problems.

  • Students will develop the ability to communicate mathematically by correctly interpreting and explaining their solutions in the original context of the problems.

 

  • Use and connect mathematical representations by providing students with a variety of models for a given problem including graphs, tables, diagrams, text and equations.

  • Build procedural fluency from conceptual understanding by giving students real world problems involving equal relations that have a wide range of complexity.

  • Pose purposeful questions and elicit evidence of student thinking as the teacher works with students, assessing their thinking behind their steps as they solve for a variable, using questioning to encourage students to think more deeply and look for alternate ways of solving.

  •  Implement tasks that promote reasoning and problem solving by helping students to accurately interpret the solution in the original context of the problem and to consider the reasonableness of their solutions in the context of the problem

Key Understandings

Misconceptions

  • Know how to use the properties of equality and inverse operations to isolate the chosen variable to form a new equation so that a problem can be solved using the new equation as a formula.

 

                   Example: Solve for C.  F=9/5C+32

 

  • Solve and apply linear equations with formulas to find the area, length, perimeter, circumference, etc., on geometric models.

 

 

                   Example: Using the formula for the perimeter of a rectangle, solve for the base in terms of the height                       and perimeter, and interpret the solution to an equation in the original context by using the new                                 equation

P = 2b + 2h

P = 2(b + h)

P/2 = b+h

b = (P/2) - h

 

                 Example: If the perimeter of a rectangle is 80 cm and the height is 20 cm, then what is the base using                      the new formula?

  • Students may misuse the proper property of equality while solving for a variable. 

  • Students may misinterpret the wrong variable for the solution. 

  • Students may use the incorrect formula to solve a problem.

  • Students may have solved for the incorrect variable when multiple variables are in an equation prior to calculating a solution.
  • Students may misinterpret the variable in the context of the equation.

  • Students fail to check the validity of the solution in the original problem.

 

 

OKMath Framework Introduction

Algebra 1 Introduction

 

 

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