Mr. Ohashi's Math 8 Website

Eighth Grade Math at Eckstein Middle School

Wednesday, 9/27: Infinite Solutions & No Solutions (Day 13 of 18)

Learning Target: Solve algebra equations that do not have exactly one solution.
Handouts: How Many Solutions? Worksheet (Turn in: Thurs, 9/28)

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 #1-5.

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Tuesday, 9/26: Algebra Quiz 1 (Day 12 of 18)

Learning Target: Take the Algebra Quiz.
Handouts: After The Quiz Homework (Turn in: Wed, 9/27)

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!

Monday, 9/25: Algebra Quiz Review (Day 11 of 18)

Learning Target: Review algebra to get ready for the quiz.
Handouts: Algebra Quiz 1 Review (Turn in: Tues, 9/26)

We have a quiz tomorrow, so today was our day to review! For the quiz, you should be able to:
• Solve multi-step 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 #1-7 of the Quiz Review. Remember, Quiz Review must be finished before you are allowed to take the quiz!

Friday, 9/22: Undoing Fractions (Day 10 of 18)

Learning Target: Use algebra to solve equations with fractions in them.
Handouts: Undoing Fractions (Turn in: Mon, 9/25)

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 #1-3. Have a great weekend!

Thursday, 9/21: More Algebra (Day 9 of 18)

Learning Target: Simplify, then solve algebra equations.
Handouts: Algebra Levels (Turn in: Fri, 9/22)

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 #1-5 from the classwork.

Wednesday, 9/20: The Distributive Property (Day 8 of 18)

Learning Target: Simplify, then solve algebra equations.
Handouts: The Distributive Property (Turn in: Thurs, 9/21)

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 #1-2. Your homework is the Homework Worksheet. Also, we have our first official quiz on Tuesday.

Tuesday, 9/19: Algebra Story Problems (Day 7 of 18)

Learning Target: Use algebra to solve story problems.
Handouts: Algebra Story Problems (Turn in: Wed, 9/20)

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 #1-7.

Monday, 9/18: Equations with Fraction Answers (Day 6 of 18)

Learning Target: Solve equations with non-whole number solutions.
Handouts: Equations with Fractions (Turn in: Tues, 9/19)

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 #1-2. Your homework is the Homework Worksheet. We are adding an extra step tomorrow!

Friday, 9/15: Combining Like-Terms (Day 5 of 18)

Learning Target: Simplify, then solve algebra equations.
Handouts: Combining Like-Terms (Turn in: Mon, 9/18)

Our algebra work got one step harder today!

Today we learned how to “combine like-terms” 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 #1-3 in class. If not, get it done this weekend! Have a great weekend and see you next week!

Thursday, 9/14: Finish Pre-Assessment

Learning Target: Use algebra to solve equations with x on both sides of the equal sign.
Handouts: Both Sides WS (Turn in: Fri, 9/15)

Today we finished the Pre-Assessment 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!

Wednesday, 9/13: x on Both Sides (Day 4 of 18)

Learning Target: Use algebra to solve equations with x on both sides of the equal sign.
Handouts: More Algebra Equations (Turn in: Thurs, 9/14)

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 #1-2 in class. Your homework is to the Homework Worksheet. Tomorrow, we will be finishing up the pre-assessment that we started last week!

Tuesday, 9/12: Solving Algebra Equations (Day 3 of 18)

Learning Target: Use algebra to solve for unknowns in equations.
Handouts: Solving Algebra Equations (Turn in: Wed, 9/13)

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 #1-2 in class. If you didn’t, then you have some extra homework! Your homework is the Homework Worksheet!

Monday, 9/11: Undo Tables (Day 2 of 18)

Learning Target:Undo algebra equations in order to solve them.
Handouts: Undo Tables WS #1-2

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 #1-2.

Friday, 9/8: Positive & Negative Numbers (Day 1 of 18)

Learning Target: Review positive and negative number computation.
Handout: Positive & Negative Numbers (Turn in: Mon, 9/11)

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 #1-5, so if you didn’t get that far in class, you should complete those problems by Monday. Have a great weekend!

Thursday, 9/7: Pre-Assessment

Learning Target: Take a pre-assessment to see what you know.
Handouts: Math Questionnaire WS (Turn in: Fri, 6/8)

We took a pre-assessment 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!