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 California High School Exit Exam (CAHSEE) Mathematics Section



 Success in Math requires knowledge of Measurement / Metrology, including the conversion between the US and the Metric System.  Therefore this lesson includes  comparing weights, capacities, geometric measures, times, and temperatures within and between measurement systems.  (e.g., miles per hour to kilometers per hour to feet per second,  and cubic inches to cubic centimeters).


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 "Measurement and Geometry" (MG) Strand" is to reinforce the learning of these skills.  The approach of this lesson-quiz is to "hard-calculate" the answer, thus earning a "sense of range." 

This lesson relates to the 7MG1.1 Standards of Comparing  measurement systems.

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 Metric conversions are essential. The developers of this lesson ask that you 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. Make a list of metric distances to check out. 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.


      WPM Hold down    


 This is an example of how to use a miles-to-km calculator below.  You are traveling North on 101 to San Francisco which is 150 miles.  Mileage is  given in miles (mi) and  Kilometers (km) on the sign.   How many km?    Use the calculator below.  Enter 150 into the mi box, press "Compute"
Miles <---> Kilometers Converter

         (4 dec precision)
   Enter amount to be converted in appropriate box.  Click  "Compute".

 If your answer has decimal positions, ignore them for now.  How to "round-off" taught later.


Answer:   Type answer in the form of  nnn,   3 integers only.  No decimal point.  No numbers to the right of the decimal point.   Check your answer with the Test Button.  (10 points)



It is fair to show you other ways to convert numbers, such as hand calculator, pen-paper multiplication, and using the Windows Calculator shown here  

(To access the calculator,  from the Start button below, select "Run", then type "calc"  without the parentheses.)






Type 150 in the bar, press the "*" (multiply sign - circled in red), then 1.609, and press the <Enter> key.     

        Or on paper:      150 
                      x 1.609


You could also use Excel by typing  =150*1.6093  into a cell.

  Or any other number conversion programs found on the web, with Google, by typing "number conversion"

It is important to develop a "number sense",  a sense of proportion.  Km are a bit more that 1.5 times Miles.  So do a "range check" when calculating.

Calculate 150 * 1.609 a 2nd way to verify your answer. How did you do it?  Write a short answer below.




Rounding off.   Drill and Practice.  (100 possible points).  In the box below you will be given a value in miles to convert to km.  However, this lesson is about "rounding off"  to the 'ones' position.  The "ones" position (the rounding digit), is occupied by "0".    

In this example, the "0" in the 160.95 value is the rounding digit.  The digit just to the right of it is "9", and since it is  > 5, the "0" becomes "1" (one is added to it -- called the "5-up" rule).  So rounding off  "160.95"  to the "ones position" becomes 161.  Rounded off, the answer is 161 km.
                !!! !!-- 5 in the hundredth's position
                !!! !--- 9 in the tenth's     position
                !!!----- 0 in the one's       position
                !!------ 6 in the ten's       position
                !------- 1 in the hundred's   position

this with me: "(1 * 100 position) + (6 * 10) + (0 * 1) + (9 * .1) + (5 * .01) equals 160.95.  Since there is a '9' in the tenths' position, it become rounded off at 161."   Rounding off 160.95 to the one's position (0), requires a look at the digit to its right (9).  If > 5, increment it by 1. It is, so it becomes 161.  

        Miles <---> Kilometers Converter

          (4 dec precision)
   Enter amount to be converted in appropriate box.  Click  "Compute".

Miles. Type the  number above into "mi" box of the converter.  Note how many kilometers it equals, then round off to the one's place.


 Round off the km value to the nearest one's place, and enter in the box to the left.  Enter the rounded number as integers (without a dec. point and following digits).  Check it with the Test Button.




Cubic inches to Cubic Centimeters.  Calculator demonstration only.  Non-graded.  

1 cubic inches = 16.38 cubic centimeters (cc) (2.54^3)
1 cc           = 0.61  cubic inches.

Explanation: an object with 1" height, 1" width, and 1" depth contains a cubic inch. This is a cubic inch.

 It has an X-axis (width), Y-axis (length), and Z-axis (height).   The Red Bar goes inside the cube vertically.  It breaks the top and bottom planes.  The Blue Bar enters horizontally, breaking the right, then left planes.  The cube also rotates.  Watch it to see that the bars cross through its center.

A 1" cube will contain 16.38 cc or 16.38 ml (milliliters) of liquid.  Its dimensions allow it to be called an inch-cubed. 

If you  filled this cube with liquid, it would almost contains 3 oz. of liquid, less than half an 8 oz. glass.


    Cubic Inches  <--->  Cubic Centimeters (cc) Converter

           (2 dec precision)
   Enter amount to be converted in appropriate box.  Click  "Compute".

Short answers to Word Problems    

1.  A 1968 classic Volvo Model 122 has 122 cu. in. displacement engine.  How many cc is that? 
2.  1000 cc = 1 Liter (L).  How many liters displacement does a 122 cu. in. engines have?
3.  A Mercedes SL 190 Sports Coupe has a 1900 cc engine. How many cu. in. of  displacement?
4.  A small bottle of Eucalyptus Oil contains 5 cc (equals 5 milliliters).  How many cu in?
5.  The Nissan Altima has a 2.5 L engine. Is it smaller than a Ford 300 cu. in. one?
6.  Extra credit:  Access a conversion program on the web  Fill in the blanks.
    1 L bottle contains ____ ounces (US. Fluid) which equals _____ cubic inches. 
Type answer below:            


                              Miles to Km conversion                   = 7MG1.1  (operational)
                              Km to Miles conversion                   = 7MG1.2  (under development)
                              Cubic inches to cubic centimeters = 7MG1.3  (under development)
                              Cubic centimeters to cubic inches = 7MG1.4  (under development)


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.   (c) Copyright, 2003 - 07