Category Archives: Math 10

Linear System Group Assignment

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Purpose

Our group needed to invent our own linear system and show how to represent it graphically and algebraically.

Curricular Response

The Mathematical vocabulary we used during our group assignment were: Linear system, X value, Y value, true, solution, diagonal, values, point, addition method, and substitution method. A linear system is a set of equations involving one or more of the same variable. Solution is the point in which 2 linear equations cross paths, it is shown as an x and y coordinate. addition method is a method which you add 2 equations together in standard form with the goal of having an answer with only 1 variable. substitution method is when you isolate one of the variables, for example; x= 2-3y. My group isolated Y= 2/3x+5. It is super important that you use the correct vocabulary to improve your understanding because when you are thinking of what to do you can have those key words that make sense for a certain part in the math you are conducting. it is also helpful for others understanding if you are explaining anything to them to use the right vocabulary.

My group decided to start by plotting the solution and then drawing the lines for the linear system. We did this because we though it would be easier since we knew the 2 equations would be correct and follow the rubric. Then we wrote the equations for line A an B in slope intercept form. We did this because it would be easy to then turn it into standard from if we needed to. We then isolated the Y variable because we chose to do substitution method. Our equation was 2/3+5=2x+9. The next step was to get rid of the fraction to make the equation easier to do, so we multiplied the whole equation by the denominator of the fraction. From there we were able to easily find the X value by using simple algebra and then plug the X value into one of the original equations to find the Y value.

Core Competency Self-Assessment

During this assignment I worked well with my group to achieve a common goal. I did this by being open to everyone in my groups opinions and ideas and also giving my own ideas in a constructive way.

I asked questions ad responded in an active and supportive way. I did this by always listening to what my group members have to say and trying it. I also gave my own ideas when I pointed out that we have to get rid of the fraction before we can continue the substitution method.

    Linear and Non-Linear Equations

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    Linear Equations

    Example #1

    This is linear.

    I can tell this is linear from the graph because the line is straight at all times.

    I can tell this is linear from the equation because the variable has an exponent of 1, if variable has an exponent of anything except 1 it is non linear.

    Example #2

    This is linear.

    I can tell this is linear from the equation because the variables have an exponent of 1 attached to them, a non linear equation would have an exponent greater or less than 1 attached. All of the variables in an equation need to have an exponent of 1 for it to be linear.


    I can tell this from the graph because the line is straight, even if it’s diagonal it is still linear.

    Non-Linear

    Example #1

    This is non linear.

    I can tell this is non linear from the equation because the variables in the equation have an exponent that’s not 1 meaning the equation is non linear.

    I can tell this is non linear from the graph because it is not going in a straight line.

    Example #2

    This is non linear.

    I can tell this is non linear from the equation because the 2 has an exponent that is not 1 meaning its a non linear equation..

    I can tell this is non linear from the graph because the line is not straight, also something cool about this is although it may look like it’s touching the y axis in the negatives it never touches it.

    Self Assessment

    I explored Mathematical ideas using technology when I experimented with linear and non linear questions by graphing them on the Desmos app.

    I analyzed data and used criteria to draw conclusions when I did a test to see if a non linear graph ever touched the line by zooming in but it did not. I also analyzed the data of other equations to see if they were linear or not.

    I justified my conclusions with evidence when I gave reason to each of the 4 graphs on whether they were linear, or not and why.

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

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    👹

    When I get stuck on a problem, I have strategies for what to do next: they include, looking at the question form a different view. Asking for help.

    When I need to boost my mood or refocus I listen to music or eat food.

    I can prevent school related stress by managing my time efficiently

    Some ways I stay mentally or physically healthy by working out and going on walks.