Mr. Ohashi's Math 8 Website

Eighth Grade Math at Eckstein Middle School

Tuesday, 1/23: Power Rules and Coefficients (Day 7 of 18)

Learning Target: Use power rules to simplify expressions with coefficients.
Handouts: Power Rules & Coefficients (Turn in: Wed, 1/24)

Today, we worked with the power rules again, but this time there were coefficients with the powers! A coefficient is a number that is being multiplied times a variable. In each of these situations, you have to compute with the coefficient separately from the variable. Here are the three examples that we wrote down in our notes:

Notice that we broke down the problem into steps. You will not be required to do this in the future, unless it helps you to remember what to do! Eventually, you will get to a point where you will simply compute with the coefficients, compute with the powers using the power rules, and then write down the answer! For the multi-step problems, however, you will still be required to show work though!

Your homework is to finish #1-8. Don’t forget that we have a quiz on Friday!

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Monday, 1/22: Exponent Rules (Day 6 of 18)

Learning Target: Use power rules to simplify expressions.
Handouts: Mixed Power Rules WS (Turn in: Tues, 1/23)

We worked with exponent power rules again today, but you learned two new things. First, we talked about the difference between (–11)2 and –112. Most people think that these are the same, but if you do them on your calculator you will find out that they are not! Here is how you should think of them…

(–11)2 = (–11) × (–11) = 121

–112 = –(112) = –(11 × 11) = –121

These have subtle differences, but important differences! You had a chance to expand these expressions out in a table to really look at how and why these work the way that they do. There are also a couple of tricks that you might pick up as you do them! Here are the notes that we wrote down for them:

The other new thing we did today were two-step power rule problems. On #3 of the classwork, you needed to apply the power rules twice in order to simplify the expressions. Use the order of operations to determine what your first step is. I want you to show your work on these, and then cross out your answer from the list of possible answers on the side margin.

Your homework is to finish #1-7.

Friday, 1/19: Exponent Power Rules (Day 5 of 18)

Learning Target: Use patterns in powers to develop rules for operating with exponents.
Handouts: The Rule For Dividing Powers WS (Turn in: Mon, 1/22)

We continued to work with power rules today. We divided powers by expanding them out, crossing out the numbers that undid each other, and then simplifying the numbers that were left as a single power. We quickly found a rule that worked for all of these!

The harder rule was the second rule. We know that when you do not have an exponent next to a number, it means that it is raised to the first power. But what happens when you have a number that is raised to the power of zero? You got a chance to explore that and you found out that any number to the zero power always comes out to the same value… one!

We wrote these two new rules in our notes:

For classwork, you should have finished #1-6. Also, we will have our first quiz on exponents on Friday of next week. Have a great weekend!

Thursday, 1/18: Exponent Power Rules (Day 4 of 18)

Learning Target: Use patterns in powers to develop rules for operating with exponents.
Handouts: Three Power Rules WS (Turn in: Fri, 1/19)

Today we were computing with powers. In the first case, you were multiplying two powers with the same base. In the second case, you were multiplying two powers with the same exponents. In the third case, you were raising a power to another power.

In all three cases, you had to expand them out and then simplify them down to a single power. A table and an example were included for each to help you. You then had to come up with a rule that would allow you to figure out the simplified power without having to expand it out!

What we found was that each had a simple rule to get the simplified single power. We wrote them in our notes:

Your homework is to finish #1-6.

Wednesday, 1/17: Scientific Notation (Day 3 of 18)

Learning Target: Use scientific notation to write very small numbers.
Handouts: Very Small Numbers WS (Turn in: Thurs, 1/18)

Today, we continued our work with scientific notation. However, instead of working with very big numbers, we worked with really small numbers! I’m talking about numbers that are so close to zero that they have a lot of zeroes after the decimal point! When we write these numbers in scientific notation, the power of ten will be negative to show that we have to move the decimal point in the other direction. It basically means that we are dividing the number by ten several times!

Here are the examples that we wrote in our notes. Use the bouncing arrow to help you keep track of the number of times that you are moving the decimal!

Remember two key facts: A negative power of ten means that the number will be small and a positive power of ten means that the number will be big. Remember, the power of ten tells you how many places to move the decimal, not how many zeroes there are!

Your homework was to finish #1-10.

Tuesday, 1/16: Scientific Notation (Day 2 of 18)

Learning Target: Use scientific notation to write very large numbers.
Handouts: Very Large Numbers WS (Turn in: Wed, 1/17)

Today, we looked at scientific notation. Numbers in science are often very large. For example, the mass of the earth is 5,970,000,000,000,000,000,000,000 kg. Big numbers like this are overwhelming and too time consuming to write out, so there is a shorthand way to write them: 5.97 x 1024 kg. This is called scientific notation. Here are the notes that we wrote:

To write a number in scientific notation, take the digits on the left side until all that are left are zeros. Next, put the decimal after the first digit. Finally, multiply the number by the power of ten required to move the decimal from its original spot to where it needs to be now.

When given a number in scientific notation, take the first number and move the decimal over as many times as the power of ten. The common misconception with kids is that you just “attach zeros” on the end based on the power of ten. This is not the case! We are moving the decimal based on the power of ten!

Your homework is to finish #1-12.

Friday, 1/12: Exponents Review (Day 1 of 18)

Learning Target: Review the basics of exponents.
Handouts: Exponents Review (Turn in: Tues, 1/16)

We started a new unit today! This unit is all about exponents. Today, we started with some basic review of exponents:

In class, you should have finished #1-8. Have a great three-day weekend!

Thursday, 1/11: Systems of Equations Quiz 2

Learning Target: Review system of equations to get ready for the quiz.
Handouts: Systems of Equations Unit Reflection (Turn in: Fri, 1/12)

Today, we took the last quiz of this unit! Your homework is the Unit Reflection, where you have to rate your understanding, answer some reflection questions, and finish the pre-assessment.

We will start a new unit tomorrow!

Wednesday, 1/10: Systems of Equations Quiz 2 Review (Day 15 of 16)

Learning Target: Review system of equations to get ready for the quiz.
Handouts: Systems of Equations Quiz 2 Review (Turn in: Thurs, 1/11)

We have a quiz tomorrow! For the quiz, you should be able to:
• Solve a system of equations using elimination method
• Use systems of equations to solve story problems
• Use systems of equations to solve linear relationship problems

Today was our review day! Your homework is to finish #1-7 from the Quiz Review.

Tuesday, 1/9: Using Systems of Equations (Day 14 of 16)

Learning Target: Use system of equations to solve problems.
Handouts: Using Systems (Turn in: Wed, 1/10)

Today, we had to apply our skills with systems of equations in a variety of different situations. We had story problems, like we did yesterday. We also had problems involving the linear relationship work that we did earlier this year. For these problems, you had to write linear equations for pairs of situations and then use algebra to find the point of intersection. You need to find the y-intercept and the slope – it was really good review!

Your homework is to finish #1-6. Don’t forget that we have a quiz coming up on Thursday!

Monday, 1/8: Systems of Equations Story Problems (Day 13 of 16)

Learning Target: Solve story problems using systems of equations.
Handouts: Systems Story Problems (Turn in: Tues, 1/8)

Today our focus was on solving story problems by setting up and solving a system of equations. For the past week or so, you have had story problems where I gave you possible equation options to choose from to match. Today, you had to write them on your own!

There is no magical formula that works for every single story problem. You have to read the problem and figure out what the two equations are. Sometimes each of the equations equal a total amount of items. Sometimes the equations will equal a variable.

Your homework is to finish #1-6. Don’t forget that we have a quiz on Thursday, so make sure that you are understanding!

Friday, 1/5: Elimination Method (Day 12 of 16)

Learning Target: Use elimination to solve a system of equations.
Handouts: Solving Harder Systems (Turn in: Mon, 1/8)

Today, we used the elimination method again, but we had to do a step first. This time, we couldn’t just add or subtract the two equations because it wouldn’t eliminate any of the variables! Instead, our first step was to multiply one of the equations by a number so that one of the variables matched up with the variables in the other equation. Here is the example that we did in our notes:

Notice that we multiplied the first equation by 3. This was strategic because it allowed us to have the same number of y’s! Now, we can just add the two equations together to solve for x like we did yesterday!

If you would like to see me explain it, check out the video below:

Your homework is to finish all of #1 (although I assigned #1-2 for 3rd period). Have a great weekend!

Thursday, 1/4: Elimination Method (Day 11 of 16)

Learning Target: Use elimination to solve a system of equations.
Handouts: More with Elimination (Turn in: Fri, 1/5)

We continued using the elimination method today, but it got a little trickier. Yesterday we learned that we can add two equations together to eliminate one of the variables. Today, we found that we can also subtract two equations to eliminate one of the variables.

Notice that our original equations both have 4y. If we were to add the two equations, it would not eliminate any of the variables. However, if we subtract them, we would eliminate the y’s, because 4y minus 4y leaves you with nothing! We can then get the other variable just like we did yesterday.

If you’d like to see me explain it, check out this video:

Today’s assignment had elimination by adding and subtracting all mixed up. You need to look at the equations first and determine if you need to add them or subtract them to eliminate one of the variables.

Your homework is to finish #1-3. Also, we will have a quiz on all of this work on Thursday of next week!

Wednesday, 1/3: Elimination Method (Day 10 of 16)

Learning Target: Use elimination to solve a system of equations.
Handouts: Using Elimination (Turn in: Thurs, 1/4)

Up until now, we have been using substitution to solve systems of equations. Today we learned a new method! We have had situations where both equations were in standard form, but one of the variables was always easy to solve for and then substitute into the other equation. Today, that was not the case! However, all of today’s problems could be solved by adding the two equations together. See the example we wrote in our notes:

Because the first equation has 6x and the second equation has -6x, adding the two equations together leaves us without any x’s! This makes it easy for us to solve for y! Then to get x, we substitute the y-value into one of the two original equations. Notice, that this method only works because adding the two equations together eliminates all of the x’s! If we could not eliminate a variable by adding the two equations together, then we would not do it!

If you want to watch me solve it, check out the video below:

In class, you should have finished at least #1-4 (just #1-3 for fifth period), which includes some story problems!

Tuesday, 1/2: Review (Day 9 of 16)

Learning Target: Review how to solve systems of equations.
Handouts: After Break Review (Turn in: Wed, 1/4)

Welcome back to school! Today was a review day to refresh our memories on the systems of equations work that we were doing before the break. We will be learning new stuff tomorrow though!

Your homework is to finish #1-6 (although I assigned #1-7 for third period).