Product of Powers and Power of Powers

We discovered how to simplify expressions using powers by expanding the expressions and then rewriting the answers. This led us to two simple rules: The Product of Powers rule states that if powers being multiplied together have the same base, you can add the exponents. The Power of Powers rule states that when raising a power to a power, you multiply the exponents.

Tonight's Homework: Home Book page 45 (81, 85-95) and 51 (74-77) and the pink 8.4B worksheet.

Scientific Notation and Exponents

Students received their scores from the test over systems. Most did a terrific job on the test.

We went over the rules for computing with scientific notation. For most, this was a review lesson, so students had few questions. Class time was given to get started on tonight's homework.

Tonight's Homework: Home Book pages 38-39 (23-25, 45-47, 49-51) and the gray worksheet 8.4A

Move Over Systems of Equations--Here We Come, Exponents!

Students received feedback on their systems of equations work sample today. Most students did an amazing job! Needless to say, I was impressed, and I believe students were pleasantly surprised with their ability to do well!

Next, students turned in their Shapes of Algebra books today, and then took the test over systems of equations.

Tonight's Homework: Complete the yellow worksheet on simplifying powers.

One Work Sample Done, One to Go!

Students were given a problem to solve in class today which will serve as their algebraic work sample problem. Another problem will be given later in the year, and will cover one of the following areas: geometry, probability or statistics.

Tonight's Homework: Study for the test over systems of equations, which will be given in class on Friday. Do Home Book, page 32 (2-44, even).

Looking at Exponent Properties, Day 1

In preparation for Friday's test and Thursday's work sample, students set up equations from story problems to create systems of equations. Although we didn't take the time to solve each problem, we did review the key points in extracting information to write equations. Most felt much more capable of writing equations after this exercise.

We switched gears completely and looked at powers. Powers consist of a base and an exponent. We discovered a few simple rules that govern the world of computing with exponents. These rules are summarized in your home book. Be sure to review these often over the next few days.

Tonight's Homework: Start preparing for Friday's test over systems of equations. Home Book, page 42 (1-21, all)

Ugly System Problems on the Loose!

We took care of a lot of loose ends today, and geared up for this week's work sample and concept test. Students were given a study guide to help them prepare for the upcoming test. Those needing extra help are urged to stop in during resource, lunch or after school, so test results can be as high as possible.

Tonight's Homework: SOA, page 68, again. This time, solve the systems listed on the page, using any method you choose. These answers will be on the ugly side, but just trust the process. You CAN do these!

Graduation Video Problem

Students completed another series of problems that involve the use of systems of equations. We will take the test over concept 10 towards the end of next week.

Tonight's Homework: Graduation Video worksheet (all parts). In addition, you may wish to do at least 3 of the problems on pages 23-24 of the Home Book for extra practice and credit.

More Systems Word Problems

We looked at problems related to place value and used our knowledge of algebraic systems to set up a system and then solve it. We talked about pitfalls that students often encounter when setting up these problems and how to avoid them. Next, we tackled the problems that deal with air or water currents. Using a picture helps see what you are solving for, as does careful analysis of the units (labels).

Tonight's Homework: Home Book (read pages 19-21, do 1-14 on pages 22 and 23). In addition, feel free to do both sides of the pink worksheet you received in class today. It will not be collected for credit, but answers will be given in class on Tuesday.

Systems in the Real World

Students continued investigating real-world applications of problems that can be solved using systems of linear equations. Today, we talked about purchasing food from a deli and how that could be set up as a system of equations.

Tonight's Homework: SOA ACE 4 (48, 49, 61-64) and CME p. 365 (5), 366 (9 and 10) and 376 (2). In the CME book, use any of the 3 methods to solve the equations. I would suggest substitution and combinations, but graphing would be okay to use, if that's your preference.

Algebra Rock Bands???

Students worked in groups to solve a problem related to producing music CDs. They used a system of equations to answer a series of questions about profit, cost and revenue. This set of questions was designed to help students understand how real life problems can be solved by using algebra.

Tonight's Homework: Complete the Rock Band and Love Story worksheets if you did not get them done in class. In addition, do SOA page 68 (all problems).

More Practice on Solving Systems with Combinations (Elimination)

Students watched two clips from Khan Academy to review the rules for solving systems of linear equations using the combination/elimination method. Students then worked with table mates to ensure that they understood how to do these types of problems. Those who needed help on using the substitution method also had time to get it. Here's the link to one of the videos we watched today:

http://www.khanacademy.org/video/solving-systems-by-elimination-2?topic=core-algebra

Tonight's Homework: Complete the front side of the blue worksheet you received in class. Check steps are required. If you did not finish the substitution worksheet, you may finish it over the weekend and turn it in on Monday for full credit.

More Practice on Solving Systems with Substitution

Because I was at a district meeting, the class used today's math time to work on getting better at using the substitution method of solving systems of linear equations. Although tonight's homework assignment might be long, having 45 minutes in class to complete a major chunk of it should have proved to be beneficial. Of course, that is only true for those who used their time wisely . . . :)

Tonight's Homework: SOA page 58, parts A - D. No check steps required. Complete the cherry-colored worksheet you received in class today. Check steps are required for odd problems only.

Introduction to Solving Systems of Equations Using Combination/Elimination

Our schedule for today was changed at the last minute, making it a regular rather than M-PAC schedule. Students were introduced to the combinations method of solving equations today, but won't be formally practicing it until Friday.

Tonight's Homework: SOA ACE 4 (15 - 26, but solve all of these using the combination method).

Solving Systems of Equations by Substitution

Now that we are experts at graphing lines and determining the point of intersection, we tried a new method that might take less time. This method is the substitution method, and it is well described in the video found at this web site:
http://www.khanacademy.org/video/solving-systems-by-substitution-1?topic=core-algebra
It is also described in Investigation 4.3 of your SOA book.

Tonight's Homework: SOA ACE 4 (8 - 20). Be sure to include check steps for problems 15 - 20.

Solving Systems of Equations by Substitution

Students used the handheld computers to check the weekend's homework. While doing so, they were able to learn how to use a trace function on the computer to locate exact x and y coordinates of the intersection point in a system of linear equations. Next, we learned how to use the substitution method to find the intersection point of two lines. Lastly, students received feedback on their performance on the concept nine test. Most did extremely well.

Tonight's Homework: Complete both sides of the blue worksheet you received in class today. Be sure to do each problem twice--once by graphing and once by using the substitution method.

Testing over Concept 9 Completed Today

Students took the test over linear inequalities today. (I'm crossing my fingers that the principal's announcement about pantsing did not cause scores to go down.)

Tonight's Homework: Complete both sides of the pink worksheet. The directions were changed slightly--you will not use the palms to graph the equations. Just graph the two lines for each problem and name the point where they intersect, if there is one.

Solving Systems of Equations by Graphing

Today we learned about vocabulary related to systems of linear equations. Students took notes about the key components of a system of linear equations. In a nutshell, systems of linear equations can have one of three possible outcomes: the lines intersect at exactly one point, they never intersect, or they are different names for the same line.

Tonight's Homework: SOA ACE 2 (1-6, 13-22) and prepare for tomorrow's test over linear inequalities.

Reviewing Key Points About Graphing Linear Inequalities

We spent some time reviewing what will be on Friday's test. Students have 5 different worksheets and several pages in the Shapes of Algebra book to reference as they study for the test over linear inequalities.

Tonight's Homework: SOA page 82. Start preparing for Friday's test.