Exponent Review with Jeopardy!

As we prepare for the upcoming concept test, we took some time to review some of the major ideas related to computing with exponents. We played jeopardy as a class, and determined that everyone feels pretty good about most of the topics covered in Lessons 8.1 through 8.4.

Tonight's Homework: Complete the practice test for concept 11. The test will be given in class on Wednesday, March 3rd.

Exponential Decay Models

Today, we compared the exponential decay model with the exponential growth model. What we discovered is that the major difference in the formulae is that the growth factor is greater than one, while the decay factor is less than one. Students worked in groups to collect penny flipping data. Flipping pennies simulated what happens when radioactive atoms decay. Students flipped the pennies until they were able to eliminate all pennies from the flip pool.

Tonight's Homework: Graph the penny flipping data in a double line graph which includes a title, key, and labels. Please complete the following problems from the book: Lesson 8.5 ( 1 - 13 ) and Lesson 8.6 ( 1 - 13 ).

What's Exponential Growth?

Today we talked about how using exponents could be a useful thing in real life. Most students in class reported having a savings account. Using different interest rates, students calculated by hand how much money would be in the bank if they invested $100 at 1.24% interest for several years. Next, the same process was used to calculate how much they would have after 5 years if they could invest the same $100 at 18% interest. After being convinced that using hand calculations was pretty laborious, we looked at the exponential growth model formula and discovered that this was a much faster way to come up with the answers to these types of problems. One problem we encountered was that different calculators had different buttons to press in order to make things work efficiently ( ^ vs. y to the x buttons, for example).

Tonight's Homework: None.

Applying Exponents to Real World Situations

Students worked most of the period today on a set of problems that relate to real life situations where math can be used to figure out reasonable answers. Some of the problems required students to use systems of equations (from chapter 7), while other problems relied on the use of exponents or scientific notation to determine the answers.

Tonight's Homework: Complete all problems on both sides of the white handout you received in class today.

More with Exponents

Students were shown how to use unit analysis to help them with complex problems that might or might not include the use of exponents and scientific notation. Being able to use unit analysis skills is very important when working on problems related to business, chemistry, physics, and other technical fields.

Tonight's Homework: Lesson 8.4 ( 53 to 65, but not 63 )

Scientific Notation

One of the ways we use exponents in real life is when we deal with very large numbers (like the distance to the sun) or very small numbers (like the size of an electron in an atom). We often will express these numbers using scientific notation. Numbers written in scientific notation always are expressed as a decimal number between 1 and 10 multiplied by a power of 10.

Tonight's Homework: Lesson 8.4 ( 16 - 46, even ) and the pink worksheet about Wanda and Roy.

Dividing with Powers

Once again, we looked at dividing expressions involving powers. There are several rules to consider, including:
•Quotient of Powers Property
•Power of a Quotient Property
Both of these are outlined on page 463, with examples worked out for you on pages 463 and 464.

Tonight's Homework: Lesson 8.3 ( 4 - 18 even, 19 - 47 first column only, 49, 50 )

Exponents Galore

Today's class was abbreviated because of the school-wide Winter Social. We reviewed homework, and then worked on two review worksheets, One covered integer operations, and the other covered multiplying and dividing with powers.

Tonight's Homework: Finish the two worksheets. Enjoy the long weekend!

Negative and Zero Exponents

Students cleaned out papers from there binders today, making their binders much lighter and tidier, I hope.

We looked at how to simplify expressions with negative exponents today, as well as those with exponents equalling zero. We practiced doing about 20 problems to ensure students were able to multiply and divide with powers.

Tonight's Homework: Lesson 8.2 ( 14 - 44, even )

Power Review

Students took the application portion of the concept 10 test. Afterwards, we reviewed vocabulary related to powers (base, exponent, and power) and the rules to follow when multiplying powers with identical bases. We then looked at a specific example where a power is raised to a power, and created a rule to follow for these types of problems. Be sure to review lesson 8.1 for details, especially if you missed class today.

Tonight's Homework: Lesson 8.1 ( 25 - 54, last column only ).

Systems of Equations Test Day, part 1

Students turned in homework from pages 444 and 445, and then proceeded to complete the first part of the test over Concept 10. Because this test takes just a little longer to complete (check steps were required for most problems), students will complete the application portion of the test on Wednesday.

Tonight's Homework: None, for a change. Enjoy the night off from math!

Preparing for Concept 10 Test (with treats!)

Students voted to eat their treats, earned by Sami, today in class while figuring out the number of calories in the chicken chunks and mustard sauce. Students were asked to complete the problem, following problem solving guidelines, in class today.

The test over concept 10 will be given in class today. Be sure to prepare for it by looking over the practice test!

Tonight's Homework: Page 444-445 ( 1 - 14, all ). ( Multiple choice questions, but show work when you can. )

Wrapping Up Systems of Equations

Today, students had time in class to work on one of two tasks:

• solve a series of word problems related to systems of equations
• complete the practice test for Concept 10

Both of these worksheets will be due at the beginning of class on Friday.

Tonight's Homework: Complete both of the above assignments. (Hopefully you got most of the work done in class today!)

Rock Band Problem

Today, students worked in groups to solve a series of problems related to a rock band wishing to create a product to sell. Using a system of linear equations related to the cost and profit functions of creating a CD, students determined answers to questions. The problem was also solved by using a graph to describe the different functions. This work, if not completed in class today, is to be finished at home tonight.

Tonight's Homework: Finish the Rock Band activity (if you need to do so). Also, complete the story problem worksheet you received in class today.

Looking at Special Systems of Equations

There are two sets of circumstances that provide interesting results when using systems of equations to solve for a variable. One situation provides us with a statement that looks like 0 = 10, which is obviously false. In cases like these, there will never be a time when the lines cross. This indicates that the lines are parallel (this can be verified by looking at the slopes of the lines). The answer to these types of problems in "no solution" or "no point of intersection".

In the second case, we will get a statement that looks like 0 = 0, which is always true. In these situations, graphing the equations will provide us with two lines sitting in the exact same place, meaning we've discovered two equations for the same line. These lines are called coincidental lines, and the answer for these types of problems will be "all real numbers".

Tonight's Homework: Lesson 7.5 ( 12 -28, even, 30, 36 )

More Applications for Systems of Equations

Students looked at more word problems that involve the use of systems of equations. Examples included admission rates of adults and children to a fair, speed of a jet flying with or against the wind, and the number of bushes and tress purchased by a landscaper. Solving these problems are relatively easy if you can get the problems set up.

Tonight's Homework: Lesson 7.4 ( 52 - 56 )