Week of November 10 - 14

This week we will continue our lessons over proportions by discussing percent of change and similar figures.  There are two types of percent of change, percent of increase and percent of decrease.  Percent of change is found by dividing the amount of change in the situation by the original number.

Example:  Sam's grade during the 1st six weeks was an 85.  The 2nd six weeks he had a 92.  What was the percent of change from the 1st six weeks to the 2nd six weeks?

percent of change = 92 - 85   =     7    =  0.0823... x 100 = 8.2%
                                   85             85

To convert the number to a percent you multiply it by 100.

Wednesday, we will complete a test review for our first test of the 3rd six weeks and finish the week with a Common Assessment over Proportions and Percents.

Bonus Question for the Week

A real estate agent received a commission of $9375 on the sale of a home. If the commission
represents 7 1/2% of the selling price, how much did the house sell for?

Copy the problem, work it, and turn it in by Friday, November 14th for 10 Bonus points.

Percent Proportion

We ended last week by discussing the Percent Proportion.  The percent proportion is a tool you can use for all percent problems.  It is

   %    =   part  
 100       whole

The percent sign, part, and whole are all places where you plug in information from a problem.

There are 3 types of percent problems.  Problems where the % is missing, the part is missing, and the whole amount is missing.  Here are 3 examples:

What is 25% of 80?

20 is what percent of 80?

20 is 25% of what number?

Each of these problems can be solved by using the percent proportion.

Problem 1   25   =    x         Problem 2    x    =   20         Problem 3    25   =   20  
                  100       80                          100       80                           100        x

To solve each problem you cross multiply and divide by the value with the variable.

Problem 1    25   =    x   
                   100       80

                 100 x  =  25 (80)
                 100x  =  2000
                  100        100

                       x = 20

All 3 forms of the percent problems are solved the same way.

Most problems don't look like the examples.  They look more like this one:

The Incredible Chocolate Chip Company has discovered that 36 out of 400
chocolate chip cookies do not contain enough chocolate chips. What percent of
the chocolate chip cookies do not have enough chips?

In this problem we are looking for the percent so it will be like problem 2.

   x    =   36  
 100      400

400x = 3600
400       400

   x = 9%

For more information click here.

Ratio, Rate, Unit Rate, and Proportions

This past week we have been discussing how to simplify a ratio, and to identify a rate, how to find a unit rate, and how to find the missing value in a proportion.

A ratio is a comparison of 2 like quantities.  Ratios need to be in simplest form and they can be written 3 different ways.

Example:


This ratio can be written as 1:3, 1 to 3, or as a fraction 1/3.

A rate is a ratio that compares quantities of different units.
A unit rate is a comparison of a quantity to 1.

Example:

Unit rates become very important when doing price comparison.  We always want to get the best buy.

Example:

    

Which flash drive is the best buy?

5.99/8 = $0.75 per GB                                                         24.95/64 = $0.39

The 64 GB hard drive, according to price, is the better flash drive.

A proportion states that two ratios that are equal to each other.  To solve a proportion you find the cross products and solve for the missing variable by dividing.

Example:

Images from Google.

Week of Oct. 27th

This week we are going to try using our digital textbook to review and learn about ratios, unit rates, and proportions.

Monday - We will review the definition of a ratio, find equivalent ratios, and simplify ratios with different units.  This information can be found in Chapter 6 Section 1 of the digital textbook.  If you can not remember how to log in to the book click here.

Tuesday - We will find unit rates and use them to find other equivalents.  We will be discussing unit cost, price comparison, better buy, etc.  Our lesson will be Chapter 6 Section 2 in our digital textbook

Wednesday - We will learn to solve proportions.  We will solve them like an equation.  We will also have our 3rd Quiz over our Fraction to Decimal Equivalents.

Thursday - We will complete a hallway activity in groups over unit rate and proportions.  This activity will test the students ability to determine items that are a better buy.

Friday - Parent/Teacher Conference Day - Holiday for Students
If you would like to come and discuss how your child is doing in class please send me an email with a time you would like to come visit and I will schedule you into a slot around that time.  If your child seems to be doing fine you do not have to come unless you just want to.

Also, remember Monday, Nov. 3rd is a Teacher Staff Development day so it is also a Student Holiday.

Simple Interest

Today we learned how to calculate Simple Interest.  Simple interest is easy to calculate.  You use the formula I=Prt where I stands for Interest, P = principal (the amount of money you start with), r = rate (the percentage of interest that is used on the money), and t = time (that amount of time the money is earning interest).

Example:  I = _____, P = $1500, r = 5%, t = 3 years

          I = Prt
          I = 1500 x 0.05 x 3
          I = $225

Example:  I = $500, P = $2100, r = _____ , t = 4 years

          I = Prt
          500 = 2100 x r x 4
          500 = 8400 r

           500  =   8400 r 
          8400       8400

             r = 0.059...
             r = 5.95%

Just plug the information in to the equation and solve.

Week of Oct. 20th

This week is the middle of the 2nd six weeks.  Schools seems to be going quickly.  This week might be a long week for some though, we will be having 2 assessments this week.

Monday - Simple Interest

- This lesson will be an application of 1-Step equations.  Simple Interest can be figured using I=PRT (Interest = Principle x Rate x Time).

- Also, any student that did not perform satisfactorily on Test 2-1 will be taking a retest. 

Tuesday - Common Assessment

- We will be taking our first Common Assessment which will cover equations, inequalities, percents, and simple interest.

Wednesday - Test 2-2 Review

- We will review our unit test over equations and inequalities.

Thursday - Test 2-2

- Students will take their second test of the six weeks.

Friday - Begin creating a Digital Portfolio

- Portfolio's are becoming more and more necessary to use as part of a college application.  It is a collection of works by the student that demonstrates student growth.

This week is Homecoming and each day there is a way to show your spirit.

Bonus Problem of the Week

Jenna invests $13,000 into separate bank accounts, one earning 6% simple interest and the other earning 3% simple interest. If at the end of one year she earns $682.50 in interest, how much did she invest in each account?

Copy the problem, solve, and turn in by Friday, Oct. 24th for 15 Bonus Points.

2-Step Equations

Thursday and Friday we learned how to solve 2-Step Equations.  We began by reviewing the two types of 1-step equations:  equations with addition and subtraction, and equations with multiplication and division.

Our main goal in solving equations is to get the variable by itself, or isolate the variable.  With addition problems you add the opposite, with subtraction you change the subtraction sign to addition and the next number to its opposite then you add the opposite.

              x + 6 = -4                                           x - 8 = 4
    x + 6 + (-6) = -4 + (-6)                            x + (-8) = 4
                    x = -10                              x + (-8) + 8 = 4 + 8
                                                                              x = 12

With equations involving multiplication and division you do the opposite operation to isolate the variable.

             4x = 24                                  x    =  -3
                                                           5
            4x  =  24 
             4        4                                 5 x   =  -3 (5)
                x = 6                                   5
                                                               x = -15

With 2-Step equations you have both of the steps in the same problem.  To solve a 2-step equation you reverse the order of operations.  The last thing you did to solve an order of operation problem is add/subtract to the first thing you undo in an equation is add/subtract.

              2x + 6 = -10                                                     m  - 5 = 3
    2x + 6 + (-6) = -10 + (-6)                                           3
                     2x = -16                                         m  + (-5) + 5 = 3 + 5
                                                                            3
                     2x  =  -16                                                      m   =  8
                      2         2                                                        3
                       x = -8
                                                                                     (3)  m  = 8 (3)
                                                                                            3

                                                                                             m = 24