Online  Basic Accountability in Math (BAM) Lesson (Algebra and Functions Strand 3 - AF)  (03af.html)  
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Word Problems.    Multi-Choice Practice.  (10 possible points).

 

Bill rode his skateboard (with a helmet) 25 miles in 80 minutes.  How many miles can he ride his skateboard in 60 minutes (at the same pace)? Aurora HC212 8 digit, Solar / Battery power calculator
Formula:    25 =  x 
            80   60    
            25 * 60      = 80x   cross multiply
            25 * 60  80 = x     isolate for x 
            x            = 25*6080                               
 
Calculator: 25x6080=
Start off by setting it up mathematically.
Setup:    25 mi   =  x mi  
          80 min    60 min  
      25 miles in 80 minutes is expressed as 25 mi
80 min
How many miles in 60 minutes is expressed as  x mi 
60 min
First step: Cross multiply:   60*25 = 1500   (60 times 25. done below)
            so    1500 = 80x
            1500 equals 80x (80 * x)
2nd  step:  Isolate x by dividing each side by 80. 
            1500  = 80x       80x 
80 80 80 cancels to x
Third step: Rewrite as x = 1500   
80
4th  step:  Divide 1500 by 80, equals 18.75. 

T
he answer is 18.75 miles in 60 mins (mph) .
1
1. cross multiply:   60x25 = 1500 
   so    1500 = 80x
         1500 equals 80x

Calculator: press 60X25= (60x25 = 1500)

(= sign gives result)

Note the ,x,-,= signs.

 
2

 

divide 1500 by 80 by pressing

80=

(divide sign, 80, equal sign)

result is 18.75 miles in 60 mins.

(fast for a skateboard)

 

Choose the letter of the correct answer:

A. 17   B. 18   C. 18.75   D. 20  and enter it in the answer box below:             
  

  

 

Answer Box.    Check it with the Test Button.

 
 

2

 
Rocky rode his mountain bike in the Trans-Alps race,  and,  on some downhill trails, he went 1 2 miles in minutes.  How many miles per hour is that?    (practice calculating answer, testing it by displaying answer.  Watch how "rounding up" is done.)
  answer:    12 * 60 =      rounded    

  12    =                                              
 
    60
 x = 12  * 60

Calculator: 12 x60 =

 

Answer Box.   If answer is  .5 or higher,  add 1 to answer (round up).


 

3

 
You will be given equations in  the form of:

   If n = 2 and x = 1/2, then n(4 - x) =

This is solved by substituting 2 for n, 1/2 for x, performing the    operation within the parentheses, then doing the arithmetic.

       n(4 - x)  = 2(4 - 1/2)          .. substitute, then solve  
                                              within parentheses.
       2(3.5)    = 4 - 1/2 = 3.5      .. do arithmetic
       2(3.5)    = 2 * 3.5 = 7        .. (2 times 3.5 equals 7)

Here's an equation for you to solve.
 
* ( -   4) =  

Keep Pressing "Display Answer" until you learn how to solve equation.  After you have learned how to solve this equation, enter answer into Answer Box below  and press "Test".  (10 points for each correct answer).   Progressively harder.

  Problem:    * ( -    4 ) =      

 Display Answer

 

Answer Box.   If multiplying with 0, the answer is 0.  No points given if you display answer.

4

 

 
Given  what does xequal when x = -2?     Ans.  -2^2 = -4   (Rule 1)
                              x
equal
when x = -1?     .....  -1^2 = -1   (Rule 1)
 
                             xequal when x =  0?"    .....    0^2 =  0   (0*0)
                              x equal when x =  1?     .....    1^2 =  1   (1*1)
                              xequal when x =  2?     .....    2^2 =  4   (2*2)

                              x equal when x =  2?     .....    2^1 =  2   (Rule 2)
                              x0   equal when x =  2?     .....    2^0 = 1   (Rule 3)
 
21/2  =   2^-2  =   ( * = ) =  0.5 * 0.5 = 0.25                 (Rule 4)
 
Rule  1:    A negative number raised to any power stays negative.

         2:    Any  number  raised to the 0 power is 1.

         3a:  A positive  number raised to the 1 power is   itself. 
         3b:  A negative number raised to the 1 power is  itself.

        
4.    A negative power becomes its positive reciprocal.

Raising Negative Numbers:    Example:  Raise -2 to the 5th power.   (Apply Rule 1:  A negative number raised to any power stays negative.)    So -25  equals -32.    On my calculator, I typed -2^5=  and got -32.   By pen-and-paper, I did 2*2*2*2*2 = 32 then prefixed it with a minus (-) sign.  (unary operations performed last.)
                            - - - - - - - - - -  - - - - - - -

Raising a Number to 0 power:    Raise 2 to the 0 power.   (Apply Rule 2:  Any number to the 0 power is 1.)   
So 20 equals  1.
                 - - - - - - - - - -  - - - - - - -
Raising a Number to 1 power:    Raise 2 to the 1 power.   (Apply Rule 3:  Any number to the 0 power is 1.)   
So 21 equals  2.
                 - - - - - - - - - -  - - - - - - -
Raising a Number to a negative power:   Given  2-2  or  2 ^ -2.   The -2 becomes  = .  ( Rule 4:  -3  power becomes 1/3, etc.) 
                  
Thus,  2 ^   =  *   =    =  0.25. 
 

Here's an equation for you to solve.                                       
 
    =   ^ =   
                                   Base           Exponent

Press and hold down the  "See Answer"  to view answer. Drill yourself on exponentiation until you learn it well!   (Discover  negative, zero, and positive base  and exponents!)  Then do the problem below; enter answer into Answer Box and press "Test".  (10 points for each correct answer).  Don't press "See Answer" for quiz credit.   Progressively harder.
  Problem:    ^ =      
 

Answer Box.   Raising any number to the 0 equals 1;  to the 1st  power gives itself.  No points given if you display answer.


 California High School Exit Exam (CAHSEE) Mathematics Section

 

 

Success in Math requires knowledge of Algebra and Functions, strand #3 of the CAHSEE. This is about expressing word problems in algebra, including order of operations, and simplifying equations.

 

The California High School Exit Exam -- "CAHSEE" --  Mathematics Section verifies that the student has learned these skills for life and career.  The focus of this exam on the "Algebra Functions" (AF) Strand" is to reinforce the learning of these skills.  The approach of this lesson-quiz is to "immerse" the student into the process, using gaming and hueristic methods optimizing traditional methods, thus making this skill-set part of their "body of knowledge"!  

This lesson relates to the 3AF1.1 Algebra Functions Standards. 

A good working set of Math skills is vital for success in vocations, professions, trade schools, and higher education, specifically, in this case, skills in solving algebra word problems are essential. The developers of this lesson ask that students spend sufficient time with it until you hit the mastery level!

The "greater the hands-on involvement" the "greater  learning"! -- Learn by doing! Use as many ways as you canto learn. This lesson aims to teach you several ways to calculate, ways to apply Math, a problem-solving process, a 'sense of range', practical applications, and reinforces, by repetition, your math skills.

Keep your hand on the mouse, and take control of your learning! Double-check and "range check" every answer. Push the edge of your learning. Go beyond the lines. Think of word problems to solve by algebra! Share this program with your friends. Teach them to pass this lesson! Extra credit given for helping other students learn this lesson!

Show us what you can do! (acknowledgement to La Canada HS for CAHSEE logo.)

Press "Replay" to start over.


 

 

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email addr .    johnsmith@aol.com 

             


Note to educators, this lessons uses Visual, Interactive, and Virtual techniques to involve the student in the lesson. The goal is that the greater the involvement, the greater the comprehension.  It also uses "hands-on" calculators, "discovery" techniques, short-written answers, drill-and-practice, heuristic type learning, guided responses, and answer-reinforcement.  All of these methods instill a "sense of range" in the student -- look at  value and convert it in their head! -- by translating values, a student effectively operates in both number systems, and can demonstrate that skill on an exam.   The goal is to apply the technology to optimize Online, Interactive learning to supplement, and reinforce class-room / personal contact instruction. This project is in Continuous Quality Improvement and Innovation mode, and your suggestions / improvements therefore are welcomed.  Joseph@Auciello.net   (c) Copyright, 2003 - 07