## Reflection: Checks for Understanding Comparing Linear Combinations in Ax +By= C to y=mx +b - Section 1: Warm Up

Making an effort to use more contextual problems has made a big difference for my students with respect to understanding when to model a situation as a Linear Combination and when to use Slope-Intercept Form. After completing a series real world like problems, my students can better interpret word problems in terms of their underlying mathematical structure. They know that:

• Some problems give a starting value and a rate of change
• Some problems combine different quantities, each of which can vary and should be described using a different variable

Once they understood the differences and similarities between these two types of linear models, they were generally more successful converting from one form to the other. However, they often raised reasonable objections like, "if they are the same and I understand it this way, why change it?"

The biggest benefit to converting to slope-intercept form is that my students find it easier to graph using this form. I am not yet satisfied with their progress graphing a linear combination using both the x- and the y-intercepts. As a result, I am trying to incorporate equations in standard form more regularly into my curriculum. I think that this will better prepare my students for the assessments that they will take at the end of this year.

Changing Between Structures (MP7) of Equivalent Linear Equations
Checks for Understanding: Changing Between Structures (MP7) of Equivalent Linear Equations

# Comparing Linear Combinations in Ax +By= C to y=mx +b

Unit 3: Linear Functions
Lesson 9 of 20

## Big Idea: Recognizing the mathematical structure of a context involving a linear model helps students to write equations whose form is consistent with their thinking.

Print Lesson
1 teacher likes this lesson
Standards:
Subject(s):
Math, standard form of an equation, slope intercept form, guided notes, Exit Slip, linear combinations, Mixture Problem, Graphing using x and y intercept method
55 minutes

### Rhonda Leichliter

##### Similar Lessons

###### What is Algebra?
Algebra II » Modeling with Algebra
Big Idea: Algebra is built on axioms and definitions and relies on proofs just as much as geometry.
Favorites(41)
Resources(19)
Fort Collins, CO
Environment: Suburban

###### Inequalities: The Next Generation
12th Grade Math » Polynomial and Rational Functions
Big Idea: Does the zero product property work for inequalities?
Favorites(3)
Resources(19)
Troy, MI
Environment: Suburban

###### Graphing Systems of Linear Inequalities (Day 1 of 2)
Algebra I » Linear Inequalities
Big Idea: Students will combine their knowledge of systems of equations and linear inequalities to represent the solution in a simultaneous equation scenario.
Favorites(14)
Resources(16)
Washington, DC
Environment: Urban