Linear System Group Assignment

purpose

Our group needed to create our own linear systems by showing them in a graph and in algebraic equations.

Curricular Response

During this activity my group and I used mathematical vocabulary such as variable, standard form, slope-intercept form, and one solution. My group and I talked about the variables multiple times mainly because we were trying to find out what it is but also because we kept forgetting where to place it at times. We used the terms standard and slope-intercept form when we were discussing what form it would be easiest to change our equation to. We used the term one solution because we needed to create an equation that was one solution and not infinite or no solution.

using precise mathematical vocabulary improves understanding because it is specific. When you use precise vocabulary you can’t mistaken it for other words because it has one main meaning which thus helps you understand what you are talking about.

My group and I chose to solve our equation with substitution. We chose this method because the equation was already set up to do so. We did this by plugging in y=-x+9 into y=3/2+4.

Core Competency Self-Assessment

– I work with others to achieve a goal.

During the time my group and I worked together i displayed respect and inclusivity to my peers to achieve our goal of completing our linear equations. We communicated effectively to understand each other’s points of view to create the best solution. We all equally did our part in working and completing the equation.

– I am kind to others, and support others when they need it.

As my group and I were solving our equation, we constantly assured and helped each other understand the equation and the steps that went into solving it. We also politely pointed out mistakes in the equation while we were solving it.

Linear and Non-Linear Equations

Linear Equations

Example 1:

This is a linear equation. I can tell from the graph because the green line is straight. I can tell from the equation, because all the variables have an exponent of one.

Example 2:

this is a linear equation. I can tell from the graph because the blue line is straight. I can tell from the equation, because all the variables have the same exponent of one.

Non-Linear Equations

Example 1:

This is a non-linear equation. I can tell from the graph because the red line is in a circle and not in a straight line. I can tell from the equation, because the variables have an exponent of two.

Example 2:

This is a non -linear equation. I can tell from the graph because the green line is not a straight line, it is curved. I can tell from the equation, because the variable x is to the power of three.

Self Assessment

• I explored mathematical ideas using technology when I used the website Desmos to create graphs for the linear and non-linear equations I chose on teams.

• I analyzed data and used criteria to draw conclusions when I figured out which equations on teams were linear and which were non-linear.

• I justified my conclusions with evidence when I explained how I could tell each graph and equation was or was non a linear equation.

Personal Awareness and Responsibility: How I manage school-related stress.

– When distractions are getting in the way of my work I take a breather, take time to focus, and move to another place.

– I respectfully advocate for my needs by asking for help, taking a break, and communicating verbally.

– Some of the things I do to stay mentally and physically healthy include going for runs, Hanging out with my family, and watching movies.

– My support network is helpful to me because they support my decisions, help navigate me, and love me unconditionally.