Mr. Ohashi's Math 8 Website

Eighth Grade Math at Eckstein Middle School

Monday, 10/23: Linear Relationships Quiz 1 Review (Day 9 of 38)

Learning Target: Review linear relationships in order to get ready for the quiz.
Handouts: Quiz 1 Review (Turn in: Tues, 10/24)

We have a quiz tomorrow! It is on all of the work that we have done for the past two weeks. For the quiz, you should be able to:

  • Understand rates and unit rates
  • Identify proportional relationships and write equations for them
  • Identify the slope and explain its meaning in the story
  • Identify the y-intercept and explain its meaning in the story
  • Distinguish between the independent and dependent variables
  • From a story problem, make a table, graph, and equation
  • From an equation, make a story, table, and graph

Your homework is to finish #1-8 from the Quiz Review (the bonus questions are optional). Remember, the Quiz Review must be done before you can take the quiz!

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Friday, 10/20: Graphing Equations (Day 8 of 38)

Learning Target: Produce a graph to match the equation of a linear relationship.
Handouts: Horizontal & Vertical Lines (Turn in: Mon, 10/23)

We continued graphing equations today, but we saw two new types… horizontal lines and vertical lines! Here are the two examples we wrote in our notes:

For the example on the left, we have the equation y = 2. We can see that the y-intercept is 2, but notice that there is no x in the equation. That means that the slope is 0 (like we are adding 0x). So we plot a point at 2 on the y-axis, and the pattern of the points is up zero and right 1. This forms a horizontal line! This makes sense because if the slope is zero, then the line will not incline/decline but stay flat! You can also look at the points that make up the line. Notice that they all have 2 as their y-coordinate. That is because the line represents all of the points where y is 2!

For the example on the right, we have the equation x = 3. Notice that it is x= and not y=. This means that there is an x-intercept at 3 instead of a y-intercept. This line represents all of the points where the x-coordinate is 3, so it forms a vertical line!

If you need a review on graphing the usual linear equations, you can watch the video below:

For classwork, you should have finished #1-4. Have a great weekend!

Thursday, 10/19: Graphing Equations (Day 7 of 38)

Learning Target: Produce a graph to match the equation of a linear relationship.
Handouts: Graphing Equations (Turn in: Fri, 10/20)

So far, we have been graphing some pretty easy equations. The numbers have been easy to work with and we have only been working in the positive section of the coordinate grid. Today, things got a little bit harder.

To graph equations like the ones above, you have to follow the two steps – plot the y-intercept on the y-axis, and then use the slope to plot the pattern of the line. When your slope is a fraction, think of the number on top as the “rise” (how many squares to go up) and the bottom number as the “run” (how many squares to move right). If the slope is negative, then the rise goes down, but you still move to the right.

Also, if the slope is a whole number, you can make it into a fraction by putting it over 1. And if there is no number next to the x, remember that it means that there is a one there… so your slope is 1 over 1!

If you would like to watch me explain it in a video, check it out below:

When you make your graph, I look for four things (in addition to having a correct graph, of course!). First, plot the points to show the pattern of the graph all the way across the entire coordinate grid. Second, use a straight edge to draw your line through the points. Third, put arrows on the ends to show that the lines continue in both directions forever. And finally, label the lines to show which lines match up to which equations.

Your homework is to finish up #1-3!

Wednesday, 10/18: Starting with Equations (Day 6 of 38)

Learning Target: Produce a table, graph, and story to match the equation of a linear relationship
Handouts: Starting with Equations (Turn in: Thurs, 10/19)

So far, our work with linear relationships always started with me giving you a story problem. You then had to create tables, graphs, and equations to match. Today, I switched things on you! This time, you are starting with an equation, and you have to create the tables, graphs, and stories! This is not too hard, because we know where to find the starting point (y-intercept) and rate (slope) in our equation!

Completing a table for a linear relationship is pretty easy for tables that start at zero and go up by ones. But what about tables that don’t? In that case, you have to plug each x value into your equation and calculate the y value! Since this is just calculator work, it is easy (but you still have to show your work!)

For classwork, you should have finished #1-3. Your homework is the Homework Worksheet.

Tuesday, 10/17: Linear Relationships (Day 5 of 38)

Learning Target: Produce a table, graph, and equation to match the story of a linear relationship.
Handouts: More Linear Relationships (Turn in: Wed, 10/18)

We continued our work with linear equations again today. But this time, there were some new twists! One of those new twists showed up in the example we did in our notes:

In example 2, the amount is decreasing. This means that the unit rate is negative. In these cases, you would have subtraction in the equation instead of addition! We also saw that the graphs of these situations look a little different than we are used to. They start up higher and go down as you move to the right.

Another twist involved the choice of variables that you used to write the equations. Sometimes in math, we use different letters for the variables so it is easier to see what they stand for. This can make the equations easier to understand later, but can be tricky to write!

And the last new twist is the I did not write in the scale on your graphs, so you have to figure out what increments each axis must go up by. Remember, it must start at zero! I showed you a trick – divide the biggest number you have to graph by the number of squares. This will give you an estimate for your scale.

In class, you should have finished #1-2. Your homework is the Homework Worksheet. You also got your Algebra Quiz 2 back today. You have a week to do corrections on them and turn them back in!

Monday, 10/16: Linear Relationships (Day 4 of 38)

Learning Target: Produce a table, graph, and equation to match the story of a linear relationship.
Handouts: Linear Relationships (Turn in: Tues, 10/17)

Today we extended our understanding of proportional relationships to linear relationships. The graph of a linear relationship forms a straight line (just like a proportional relationship), but it does not necessarily have to go through zero!

To write an equation for a proportional relationship, all you needed to know was the constant of proportionality (the unit rate). But, because linear relationships do not start at zero, you need to know two things to write an equation for them – the unit rate (called the slope) and the starting amount (called the y-intercept)! Here are the notes that we took:

Notice that the equation for a linear relationship looks almost exactly the same as the equation for a proportional relationship. The only difference is the added b (the starting amount).

Remember these things that I am looking for when graphing points…
1. Labels on each axis that tell the reader what the numbers represent.
2. Correctly plotted points and a line.
3. A title to explain what the information is.

In class, you should have completed #1-3. Your homework is the Homework Worksheet.

Tuesday, 10/10: Proportional Relationships (Day 3 of 38)

Learning Target: Represent and solve problems involving proportional relationships.
Handouts: Representing Proportional Relationships (Turn in: Mon, 10/16)

We continued our work with proportional relationships today and added writing equations for them. To write an equation for a proportional relationship, all you need to know is the constant of proportionality! Just stick it into the equation next to the x! This makes sense, since we are multiplying it by x to get y.

Your homework is to finish #1-5.

Monday, 10/9: Proportional Relationships (Day 2 of 38)

Learning Target: Identify and work with proportional relationships.
Handouts: Proportional Relationships (Turn in: Tues, 10/10)

Today we worked with proportional relationships. In a proportional relationship, one variable varies directly with the other. In other words, you can multiply one set of values by a certain number to get another set of values. The number that you are multiplying by is called the constant of proportionality. Here are the notes that we did in class:

The relationship is only proportional if the constant works for every single x value to get the y value! The constant does not always have to be a whole number. Today, you saw that sometimes the constant of proportionality is a decimal and sometimes it is a fraction!

In class, you should have completed #1-7. Your homework is the Homework worksheet.

Friday, 10/6: Unit Rates (Day 1 of 38)

Learning Target: Use unit rates to solve problems.
Handouts: Unit Rates (Turn in: Mon, 10/9)

We started a new unit today – linear relationships! We reviewing the two types of variables that we will see, and also reviewed rates and unit rates:

While working, we found that the independent variables and dependent variables are always located in the same places on tables and graphs! In a table, the independent variable is always listed first in the left column and the dependent variables is listed second in the right column. In a graph, the independent variable is always on the horizontal axis and the dependent variable is always on the vertical axis. This makes sense, since DRY MIX reminds us that the independent is the x variable and the dependent variable is the y variable!

For classwork, you should have finished #1-10. Have a great weekend!

Thursday, 10/5: Algebra Quiz 2 (Day 18 of 18)

Learning Target: Take an algebra quiz.
Handouts: Algebra Unit Reflection (Turn in: Fri, 10/6)

We had a quiz today! Your only homework is the Unit Reflection – you have to rate yourself on how well you learned the algebra concepts, answer some reflection questions, and then correctly answer problems from the pre-assessment that you took at the beginning of the year. It is a great way for you to see how much you have learned in just a few short weeks! We will be starting a new unit tomorrow!

Wednesday, 10/4: Algebra Quiz 2 Review (Day 17 of 18)

Learning Target: Review algebra work in order to get ready for the quiz.
Handouts: Algebra Quiz 2 Review (Turn in: Thurs, 10/5)

We have a quiz tomorrow, so today was our review day! Your homework is to finish what you didn’t get done in class (although the Bonus problems are optional!).

For the quiz, you should be able to:
• Solve multi-step algebra equations
• Use the distributive property with negative numbers
• Solve algebra equations with fractions in them
• Recognize when an equation has one solution, no solutions, or infinite solutions
• Set up and solve equations for story problems and diagrams

Tuesday, 10/3: Mixed Algebra Review (Day 16 of 18)

Learning Target: Simplify, then solve algebra equations.
Handouts: Putting It All Together (Turn in: Wed, 10/4)

Today’s assignment had a mixture of all of the algebra work that we have been doing over the past few weeks. Our goal was to get a day of practice to get ready for Thursday’s quiz!

Your homework is to finish #1-5 from the classwork.

Monday, 10/2: Mixed Distributive Property Work (Day 15 of 18)

Learning Target: Simplify, then solve algebra equations.
Handouts: Mixed Distributive Property Work (Turn in: Tues, 10/3) and Quiz Corrections (Turn in: Mon, 10/9)

Today, we used the distributive property with negative numbers and then solved algebra equations. There are a lot of little things that can go wrong when you are solving these, so work carefully!

In class, you should have finished all of #1. Your homework is the Homework Worksheet. I announced that the data for Algebra Quiz 2 is this Thursday 10/5.

You also got back Algebra Quiz 1 today. You must do corrections on problems that you got wrong by solving them correctly on the Corrections paper and then writing a brief explanation of how to do the problem correctly. It is due on Monday of next week.

Friday, 9/29: Distributing Negatives (Day 14 of 18)

Learning Target: Use the distributive property to simplify expressions and equations.
Handouts: Distributing Negatives (Turn in: Mon, 10/2)

Today we worked with the distributive property, but this time with negative numbers! Things get tricky when you are doing the distributive property with negative numbers, so pay close attention to the negative signs. Here are the examples that we did in class:

When there is no number in front of the parentheses, you can think of it as a 1. This will make it easier for you to distribute! Notice that in the last two examples, we had to do the distributive property and then combine like-terms to simplify the expression completely.

In the example on the right, we not only had to simplify but also solve! Work carefully, because there are now a lot of little things that can mess you up!

Your homework is to finish #1-4 by Monday. Have a great weekend!

Thursday, 9/28: Goal Setting Day

Learning Target: Set goals for math class this year.
Handouts: Mixed Algebra Practice (Turn in: Fri, 9/29)

Today was the school-wide goal setting day! In each class, you set goals that you want to accomplish this year. In math class, you set three goals – one for effort, one for citizenship, and one for academics.

Your only homework is to complete the Mixed Algebra Practice worksheet.