Mr. Ohashi's Math 8 Website

Eighth Grade Math at Eckstein Middle School

Thursday, 12/14: Systems of Equations Quiz 1 Review (Day 7 of 16)

Learning Target: Solve systems of equations to get ready for the quiz.
Handouts: Systems of Equations Quiz 1 Review (Turn in: Fri, 12/15)

We have a quiz tomorrow! Today was the quiz review. For the quiz, you should be able to solve systems of equations using algebra and by graphing. We have learned four different situations that involve substitution, so you should be familiar with them all!

Your homework is to finish #1-7 of the Quiz Review. Remember, you have to have the review complete in order to take the quiz!

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Wednesday, 12/13: Substituting for x (Day 6 of 16)

Learning Target: Find the point of intersection of a system of equations algebraically.
Handouts: Substituting for x (Turn in: Thurs, 12/14)

Today we learned how to solve a new type of system of equations. This time, instead of having an equation with y=, we had an equation with x=. We can solve this with substitution, just like before, but this time we are substituting things in for x instead of y. Here is the example that we did in class:

Notice that when we substitute in for x, we get an equation with just y’s. This means that we solve for the value of y first. To find x, we take our y value and put it into the equation with x=.

If you want to see it in a video, you can check it out…

Your homework is to finish #1-4. Don’t forget that we have a quiz on Friday!

Tuesday, 12/12: Substitution and Systems of Equations (Day 5 of 16)

Learning Target: Find the point of intersection of a system of equations algebraically.
Handouts: Solve and Sub (Turn in: Wed, 12/13)

We continued our work using algebra to find the point of intersection of two lines. So far, we have always had at least one of the equations with y=, making it easy to substitute into the other equation. Today, that was not the case… but we can make it so!

Notice, the first thing we do is take one of the equations and get y alone on one side of the equals sign. That gives us our y= equation! Now we can solve the system of equations like we have been doing all week! Once we find x, put it back into one of the original equations to get y – but notice that we have to solve the equation to get the value of y!

If you want to see it in a video, you can check this out…

Your homework is to finish #1-4.

Monday, 12/11: Infinite Solutions & No Solutions (Day 4 of 16)

Learning Target: Find the point of intersection of a system of equations algebraically.
Handouts: How Many Solutions (Turn in: Tues, 12/11)

We solved systems of equations again today, but this time we had some situations that we have seen earlier this year…

If the two lines run parallel to each other, then they never intersect, so there is no point of intersection and we say that there is “no solution”. In algebra, we have no solution when we end up with a number that equals a different number. We did an example in our notes of what it looks like on a graph and what it looks like with algebra:

If the two lines are on top of one another (they are the same line), then every point on the lines are points of intersection! In that case, we say that there are “infinite solutions”. In algebra, we have infinite solutions when we end up with a number that equals itself. We did an example in our notes of what it looks like on a graph and what it looks like with algebra:

Your homework is to finish #1-5. Also, we will have a quiz on systems of equations on Friday!

Friday, 12/8: Substitution and Systems of Equations (Day 3 of 16)

Learning Target: Find the point of intersection of a system of equations algebraically.
Handouts: More with Substitution (Turn in: Mon, 12/11)

Today’s algebra wasn’t that much different than yesterday’s algebra, except now you will be using the distributive property with negatives!

Notice that when you use the distributive property, you have to multiply everything in the parentheses by -4. This is where a lot of kids mess up, so work carefully!

Your homework is to finish #1-3. Have a great weekend!

Thursday, 12/7: Substitution and Systems of Equations (Day 2 of 16)

Learning Target: Find the point of intersection of a system of equations algebraically.
Handouts: Using Substitution (Turn in: Wed, 12/14)

Yesterday we learned that we can use algebra to find the point of intersection of two lines if they are both in slope-intercept form. Today, we learned that we can also do it when one of them is in slope-intercept form and one is in standard form.
To do this, we use substitution again, but it looks a little different…

In the example above, we have an equation in slope-intercept form (y=3x+2) and an equation in standard form (-5x+3y=14). Since we know that y is equal to 3x+2, we can replace y in the second equation with 3x+2. This gives us an equation that is very long… but solvable! Use the distributive property, simplify, and then solve for x. To find y, put the value of x (in this case, it is 2) into the equation with y=.

If you’d like to watch me explain it in a video, check it out here:

In class, you should have finished #1-3. The algebra is getting a little harder each day, so make sure that you are working hard to stay with us!

Thursday, 12/6: Solving Systems of Equations (Day 1 of 16)

Learning Target: Find the point of intersection of a system of equations algebraically.
Handouts: Solving Systems of Equations (Turn in: Thurs, 12/7)

The focus of the next few weeks will be on systems of equations. A system of equations is when you have two or more equations at the same time. When we solve a system of equations, we are looking for the coordinates of the point of intersection.

We spent time this week graphing pairs of equations and finding where they intersect, but today, we found the point of intersections by using algebra! To find the point of intersection algebraically, you have to use substitution…

The first equation tells us that y equals 8x-11. We can therefore substitute 8x-11 in for y into the second equation, which gives us an equation with only x’s that we can solve! Once we find the value of x, we can put the value into either of the original two equations to find the value of y!

If you’d like to see this done in a video, check out the one I made below…

Your homework is to finish up #1-3.

Tuesday, 12/5: Linear Relationships Quiz 4 (Day 41 of 41)

Learning Target: Take a quiz on functions and linear relationships.
Handouts: Unit Reflection (Turn in: Wed, 12/6)

We had a quiz today! Your homework is the Unit Reflection, where you have to answer some reflection questions and correctly answer each of the problems on the attached pre-assessment. We will start a new unit tomorrow!

Monday, 12/4: Linear Relationships Quiz 4 Review (Day 40 of 41)

Learning Target: Review functions and linear work to get ready for the quiz.
Handouts: LR Quiz 4 Review (Turn in: Tues, 12/5)

We have a quiz tomorrow! For tomorrow’s quiz, you should be able to:
• Determine if a relationship is a linear
• Determine if a relationship is a function
• Write a function rule for a set of inputs and outputs
• Take equations in standard form and write them in slope-intercept form
• Find the solution to a system of equations by graphing

Today was our review day. You need to finish #1-9 of the review in order to take tomorrow’s quiz!

Friday, 12/1: Graphing Systems of Equations (Day 39 of 41)

Learning Target: Graph to find the solution to a system of equations.
Handouts: Systems of Equations (Turn in: Mon, 12/4)

Today we learned about systems of equations. A system of equations is when you have more than one equation. When we work with a system of equations, we are usually looking for the solution to the system… which is a fancy way of saying that we want the point of intersection!

When two lines intersect at one point, the coordinates of the point of intersection is the solution to the system of equations. When two lines are parallel, they never intersect! Then we say that there is “no solution”. When one line is on top of the other line, they intersect at every place on the line! Then we say that there are “infinite solutions”.

Don’t forget that when graphing equations in standard form, you have to use algebra to rearrange the equation into slope-intercept form before you can graph it. One equation in each part of #1 is in standard form. Show your algebra work on these! Here is the example that I showed in my Powerpoint in class:

In class, you should have finished #1-3. We will have a quiz on Tuesday. Have a great weekend!

Thursday, 11/30: Linear vs Non-Linear (Day 38 of 41)

Learning Target: Distinguish between linear and non-linear relationships.
Handouts: Linear vs Non-Linear (Turn in: Fri, 12/1)

We have already learned how to distinguish between relations that are functions and not functions using the vertical line test. Today, we had to distinguish between linear and non-linear graphs. A graph is linear if it is one straight line. So if the graph is curved or has corners to it, it is not linear.

In the classwork, you had to determine if the graphs were linear or non-linear. Then you had to determine if they were functions or not functions. You found that a graph can be both linear and a function, be neither linear nor a function, or be one or the other!

Your homework is to finish #1-5.

Wednesday, 11/29: Equations in Standard Form (Day 37 of 41)

Learning Target: Work with equations that are written in standard form.
Handouts: Equations in Standard Form (Turn in: Thurs, 11/30)

Today we worked with linear relationships again, but the equations looked different than what we are used to. We are used to seeing equations that have y alone on one side of the equal sign. This form of an equation is called slope-intercept form, because the equation shows you the slope and y-intercept.

Today’s equations had both x and y on the same side of the equal sign. This form is called standard form. This form does not tell you the slope or the y-intercept, so you have to do some algebra work before you can graph it. You will need to use algebra to get y alone on one side of the equal sign, then you can see what the slope and y-intercept are. Here is what we wrote in our notes:

If you’d like to watch me explain it, check out the video…

You are required to show your algebra work! Work carefully, because there are a lot of little steps that can trip you up (negatives, reducing slope, etc)

Your homework is to finish up #1-6.

Tuesday, 11/28: Functions & the Vertical Line Test (Day 36 of 41)

Learning Target: Identify and understand what a function is.
Handouts: More with Functions (Turn in: Wed, 11/29)

We continued our work with functions today, but our focus was on their graphs. We know that a graph is not a function if there is an input that gives us different outputs… which means that the points have the same x value and different y values. If you look on a graph, this shows up as points lined up on the same vertical line! So if we have more than one point on the same vertical line, then the relation is not a function!

Now we can easily test to see if a graph is a function by just looking at it! If there is a vertical line that touches the graph in more than one place, then it is not a function! We call this the Vertical Line Test. Here are the examples we wrote in our notes:

In class, you should have finished #1-8. Your homework is the Homework Worksheet. You also got your quiz back today, so Quiz Corrections are due a week from today!

Monday, 11/27: Math Assessment

Learning Target: Take a math assessment.
Handouts: After Assessment WS (Turn in: Tues, 11/28)

Welcome back from break! Today, you took a math assessment in the library! Your homework is the After Assessment worksheet.

Wednesday, 11/22: Functions (Day 35 of 41)

Learning Target: Identify and understand what a function is.
Handouts: Intro to Functions (Turn in: Tues, 11/28)

Today we learned a new concept, functions. A function is a relation where every input gives you exactly one output. Within each function is a rule, so when you put a value into the rule, you get an output.

The example I showed you in class was a website with an interactive function machine. You input a value and it gives you the output. You have to figure out what the function rule is!

Here are the notes that we took in class:

Notice that we think of tables for functions a little differently than we did for tables of linear relationships. Instead of finding the rise and run for the rows in the table, we look at each x value and try to determine the rule that gets its corresponding y value. Also, remember that the definition of a function is a relation where each input has exactly one output. That means if you put the same input into the function, you should get the same result both times. If not, then it is not a function!

In class, you should have finished #1-5. You will turn this in on Tuesday 11/28.

On Monday, you will go directly to the library for math class because we are taking an assessment on the computers! It will not affect your grade, but it will give you a chance to show what you have learned so far!

Have a great Thanksgiving break!