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:
Your homework is to finish #18 from the Quiz Review (the bonus questions are optional). Remember, the Quiz Review must be done before you can take the quiz!
]]>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 yintercept 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 yaxis, 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 ycoordinate. 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 xintercept at 3 instead of a yintercept. This line represents all of the points where the xcoordinate 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 #14. Have a great weekend!
]]>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 yintercept on the yaxis, 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 #13!
]]>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 (yintercept) 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 #13. Your homework is the Homework Worksheet.
]]>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 #12. 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!
]]>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 yintercept)! 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 #13. Your homework is the Homework Worksheet.
]]>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 #15.
]]>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 #17. Your homework is the Homework worksheet.
]]>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 #110. Have a great weekend!
]]>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 preassessment 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!
]]>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 multistep 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
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 #15 from the classwork.
]]>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.
]]>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 liketerms 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 #14 by Monday. Have a great weekend!
]]>Today was the schoolwide 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.
]]>Up until now, all of the algebra equations that we have solved had one solution. In other words, there was only one value that x could be to make the equation true. Today, that was not the case! Here are the two examples that we wrote in our notes:
In the first example, we get a contradictory statement… 14 does not equal 11! Since this can never be true, it tells us that there is no possible value of x that can make the equation true. So we say that there is “no solution”.
In the second example, we get a statement that is always true… of course 16 equals 16! Since this is always true, it tells us that any value of x can make the equation true. So we say that there are “infinite solutions” because x could be any value and it would work!
If you would like to see and hear me explain it in a video, check out the clip below:
Your homework is to finish up #15.
]]>We had a quiz today! Your homework was called After The Quiz. It was more practice solving the equations that we learned on Friday, undoing fractions by multiplying by the reciprocal!
]]>We have a quiz tomorrow, so today was our day to review! For the quiz, you should be able to:
• Solve multistep equations
• Solve equations with x on both sides of the equal sign
• Solve equations whose answers are fractions (reduced)
• Simplify by combining like terms
• Simplify using the distributive property
• Set up and solve algebra equations for story problems
• Check your algebra answer
Your homework is to finish #17 of the Quiz Review. Remember, Quiz Review must be finished before you are allowed to take the quiz!
]]>Today we had equations where x was being multiplied by a fraction. To understand how to undo the fraction, you first had to remember something about fractions…
When you learned how to divide by a fraction, you learned that you have to multiply by the reciprocal of that fraction (the fraction flipped upside down). So dividing by a fraction is the same an multiplying by the reciprocal!
To undo x times a fraction in an algebra equation, you have to multiply by the reciprocal of that fraction! And what you do to one side of the equal sign, you have to do to the other! Here is the example that we wrote in our notes:
In class, you should have finished #13. Have a great weekend!
]]>Today, we had more practice with solving algebra equations. There were more story problems and area/perimeter problems. And when you got to #5, you got to choose the difficulty level of the algebra equations. If you need more practice, take Level 1 – it has more problems, but they are easier. If you are pretty good with algebra, take Level 2 – it has fewer problems, but they are harder.
Your homework is to finish #15 from the classwork.
]]>Today we reviewed the distributive property and added it to our mix of algebra skills! Remember, when a number is next to parentheses, it means that you need to multiply. When there are multiple things inside the parentheses, then you need to multiply the number times each of those things! Here are the examples that we wrote in our notes:
When we have an algebra equation with parentheses, use the distributive property to simplify it first! Then you can go through the steps of solving it.
In class, you should have finished #12. Your homework is the Homework Worksheet. Also, we have our first official quiz on Tuesday.
]]>Today, the work got one step harder! Not only did you have to solve algebra equations, but today you also had to write them! You were given story problems. You had to translate the words into an algebra equation, then solve the equation.
Your homework is to finish #17.
]]>We continued to solve algebra equations today, but this time the answers were not
whole numbers! Here is the example that we did in class:
So if you are solving an equation and do not get a whole number, give the solution as a fraction (not a decimal!). Also, I expect you to always reduce your fractions! If you get an improper fraction, you can keep it improper (I actually prefer it that way, as opposed to a mixed number), just make sure it is reduced!
In class, you should finish #12. Your homework is the Homework Worksheet. We are adding an extra step tomorrow!
]]>Our algebra work got one step harder today!
Today we learned how to “combine liketerms” to make a long, complicated equation into an easier one. You can do this by taking multiple groups of x’s on the same side of the equal sign and combining them together into one group of x’s. You can also take multiple groups of regular numbers on the same side of the equal sign and combine them together to make one group of regular numbers. Once we have simplified each side, you will notice that it is now an easy algebra equation to solve!
Here is the example that we did in class:
Pay careful attention to the subtraction signs! They are attached to the number after them, and should be thought of as negative signs!
You should have completed #13 in class. If not, get it done this weekend! Have a great weekend and see you next week!
]]>Today we finished the PreAssessment that you started last week. Afterwards, your homework was the Both Sides Worksheet, which gave you more practice solving algebra equations. Your homework is to finish the front and back of it!
]]>We continued our algebra work today, but the equations got a little bit harder! Today, the equations had x on both sides of the equal sign. To solve these, our first step was to undo all of the x’s off of one of the sides. It doesn’t matter which group of x’s you undo, but sometimes dealing with the x’s on one side is easier than the x’s on the other! Once you have done that, you will find that you have an equation like we solve yesterday!
Here is the example that we did in our notes:
If you’d like to see it in a video, check this out:
You should have finished #12 in class. Your homework is to the Homework Worksheet. Tomorrow, we will be finishing up the preassessment that we started last week!
]]>Today we solved equations by undoing them, but instead of using undo tables, we undid them using the steps of algebra! Here are the notes and the two examples that we wrote down in class:
Solving algebra equations is exactly like completing undo tables. You have to undo the equation in the reverse order that it was put together. To show the work, you need to show what operation that you are performing… and do it on both sides of the equal sign! I am very picky about how you show your algebra work, so do it correctly and completely!
You should have finished #12 in class. If you didn’t, then you have some extra homework! Your homework is the Homework Worksheet!
]]>Today we started solving algebra equations. My demonstration in class showed how solving an algebra equation is a lot like opening a birthday present! The giver put the gift in a box, wrapped it, and then put a bow on it. To open the present, you take the bow off, unwrap it, and take the gift out of the box. Notice, you are undoing all of the steps in the reverse order!
Today we solved algebra equations using undo tables. In an undo table, you have two columns – sequence and undo. In the sequence column, you start with x and then list the operations performed on x in the order that they were performed using the order of operations.
To solve the equation, you undo the operations in the undo column. Start with the last number in the sequence column and then undo each operation as you work up the table. Your answer is what you end up with at the top! Here are the notes that we took on them in class:
To see it in action, check out my video:
Your homework is to finish up #12.
]]>We had our first real math lesson today! You got a blue packet of notes for our first unit. We will complete it together as we go through this unit, and you can use it to help you on tests and quizzes! Our first unit is on solving algebra equations.
Today, our focus was on positive and negative number computation. We wrote down the following rules for working with them:
We also did a quick review of the order of operations:
For the classwork, you do not have to complete the entire worksheet! I assigned #15, so if you didn’t get that far in class, you should complete those problems by Monday. Have a great weekend!
]]>We took a preassessment today in math class. Your only homework is a math questionnaire that asks questions about you so I can get to know you better! Also, if you didn’t turn in your syllabus today, remember to get it signed and turned in soon!
]]>Welcome to the first day of 8th grade math! We went over the class expectations and the syllabus. I would like you to get the syllabus signed by your parent/guardian and return it to math class.
Your homework was a goal setting worksheet. I want you to rate yourself in various areas based on your work in math class last year, then I want you to come up with some goals for math class this year!
]]>In case you want to get a head start on school shopping, here are the supplies needed for math class this year:
School Binder with a Math Section

You probably already have a school binder, but make sure that you have a section for math to hold assignments, handouts, and class notes. Also, make sure that you have a pencil pouch so that you don’t lose your pencils and erasers! 
Sheets of Lined Paper 
Sometimes we will do work on math worksheets and sometimes we will do our work on a separate sheet of lined paper (especially when we get into algebra), so you will need to have lined paper with you! 
Pencils and Erasers 
You will need a pencil in math class every single day, so make sure that you bring at least one. This is where having a pencil pouch will come in handy! 
Calculator 
You will need a calculator with a square root button and a cube root button. I recommend the Texas Instrument TI30x iis (pictured on the right). They are around $15 and worth it! You will not be allowed to use a cell phone as a calculator in class. 
Ruler (SeeThrough) 
We will need a straightedge for various different concepts in math class this year. I recommend having one that is seethrough, because it will be easier to use since you can see where you are placing it on the paper. 
Please let me know if you have any questions or have difficulty obtaining any of these materials!
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