Category Archives: Grade 10

Linear System Group Assignment

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Purpose

In groups, we designed our own linear relationship which consists of two different equations that graph nonparallel diagonal lines. We put the equations in Slope-intercept form and used it to represent them graphically and algebraically to solve where the points meet, where both values satisfy both equations.

Curricular Response

a. Describe as much of the mathematical vocabulary your group used during this activity as you can remember. How can using precise vocabulary improve understanding?

Some of the vocabulary words that were used to address these mathematical problems were substitution, and the addition methods which are two algebraic methods used to solve linear equations. Everyone immediately knew the formula y=mx+b was the slope-intercept form without having to search it up. We knew that b represented the y-intercept, and m the slope. Knowing precise vocabulary not only can improve you’re understanding of the unit but how or when to use it and how it is represents in math. There are words that we use in our daily lives that have a different definition in math. For example: acute means sharpness or when we describe pain but in math an acute angle is an angle that measures to less than 90 degrees.

b. Justify your mathematical decisions. Give reasons for your choice of equations and for your choice of algebraic method.

We picked a point on the graph that wasn’t too high in value and shade decisions on the second equation from there. We decided to use the substitution method to find the solution since the y variable was alone on one side of the equation, being in slope-intercept form, we can easily plug it into the y of the second equation. The addition method would have been the more time-consuming but still possible.

Core Competency Self-Assessment

I take on roles and responsibilities in a group; I do my share. I was always participating and was especially involved in creating our own linear equation and solving . Some other members helped with the graphing, plotting the points, organizing the graph to make it neat. When someone needs assistance I always offer to help. I encourage others to share their voices and value diverse perspectives. I always try go get all group members involved in the activity by passing the, the marker if they are left out, ask them to join our discussion or about opinions on on the topic. Sometimes I feel that they are hesitant but they shouldn’t be excluded from the group.

Linear and Non-Linear Equations

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Linear Equations

Equation 1:

This graph represents a linear equation because, in the equation, the variables have an exponent of one, and based on the rules of linear relations they can only be to the power of one in order to create a linear line. Visually, you can tell the line above is straight and stays continuously straight (when zoomed out it displayed a continuous straight line).

The equation is also similar to the standard form ax + by = c (only a difference in the mathematical symbol + and -)

Equation 2:

Since this equation only demonstrates the value of x, there is no y-intercept and the slope is undefined, we can assume it is a vertical straight line right away. The variable x has an exponent of one which indicates that the equation is a linear relationship.

Non-Linear Equations

Equation 3:

This graph represents a non-linear equation. We can tell this by checking if there are any exponents of the variables. In the equation, x is raised to the power of 3 (or cubed) which indicates that it is a non-linear relation. In the graphical format, the line is curved, not straight, a linear equation would display a straight line on the coordinate plane.

Equation 4:

In this equation, we can easily tell it is a non-linear relationship since both x and y variables are squared or raised to the power of 2. The equation graphed is not a linear (straight) line, nor does it have a slope. The equation graphed is a circle with a radius of 4 which is self-explanatory by itself.

Self Assessment

I explored mathematical ideas using technology when I applied my knowledge of graphing and linear equations to Desmos in order to figure out whether or not the equation represented a linear or a non-linear relationship. Using technology to my advantage, visually comparing each of the graphs allowed me to easily identify the difference between the two relationships. I analyzed data and used criteria to draw conclusions when I tried to figure out whether or not the equations represented a linear or non-linear equation by analyzing the graphical format on whether or not the line is straight. I used the basic criteria of how we can identify linear and non-linear equations in ways such as looking for exponents on variables or by graphing different equations on the coordinate plane, it was easier to visualize and make clear conclusions. I justified my conclusions with evidence when I was certain my conclusions were correct. After collecting all the data, I justified my conclusions on all 4 equations with graphs, as well as using my knowledge of the unit, writing it down on Edublog. Since all 4 equations plot, a distinct line of the graph my explanations for each of them is slightly different. I tried to point out what stood out and how it made them a linear or non-linear relationship.

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

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  1. When I am sad, angry or frustrated about school, doing something I find relaxing helps me be more productive or calm. I used to calm myself down by playing a musical instrument, the piano in my case. Pressing on the keys sort of took my stress away as well as the music it made. Doing something I am good at after being stressed about school which is usually caused by my dissatisfaction with my grades help remind myself that I have things I am actually good at and it doesn’t always have to be academic. In order to keep my productivity I take a few breaks especially when I feel burnt out. When I have free time I like to either watch movies or go out for walks because staying physically active (but not too excessively) reduces stress.

2. When distractions are getting in the way of my work, I often find a quiet place to study in places like the Library where I believe is the most appropriate environment where everyone is maintaining their voices at a low level, where it is peaceful and where everyone is focused on their own work. However, I sometimes find it hard to focus when it is too quiet and during those times I listen to music that doesn’t include lyrics because they are distracting, or go to a cafe with my laptop to prevent myself from losing focus. I find that being in a public space increases my productivity because I get a little bit more tensed up.

3. When I am feeling anxious about a test, I can calm myself by revising as much as I could and preparing for the test as much as possible because it reduces my anxiety by a great margin. When I feel extremely worried I don’t show any emotion because everything happens inside for me. I always text my parent on the day of the test because I need assurance to feel relieved, they are always so encouraging. Right before a test, I revise as much as I could during the time remaining or space out so that I’m not thinking about the test at all because once I focus on something the worry comes back. But overall there is nothing more effective than being ready and prepared for the test.

4. When I am feeling down about school, I remind myself that school is inevitable and that there is no point in feeling upset about something you have to get through anyway. I believe school is one of the most vital parts of preparing for adulthood. I try my best to enjoy it since I don’t have control over it, this includes homework, assignments and just being present at school. I know there are people who find school much more difficult and stressful than what I’ve experienced in the past. I always give everything my best because I gain so much fulfillment when I put in the effort and I know that school is worth it and that if everyone else could do it I could get through it too. It will benefit me in the future and even if I tend to push myself or put myself down when I am dissatisfied with my grades at times, I refuse to waste my energy on complaining about it. However, I try not to ignore these emotions because later when all these emotions build up you will reach a point where you have no willingness to do anything or try anything new anymore. Instead, I tell myself that effort doesn’t always guarantee success and that it is completely okay to fail at times as long as you always give it your best.