Lesson Links from Irv Leskowitz - May 2004

MATHEMATICS, as promised

One good place to start building math skills is dealing with fractions, and a good way to startteaching  fractions is to determine your student’s level of fractions “literacy.”  Your student may know the meaning of the word fractions but may not recognize how fractions and the concepts of percent, proportion and ratio are related.  But you should not be surprised to find that he/she knows about batting averages (percent) or team winning percentages.  Understanding the meaning and usage of terms related to fractions gives the student a key to understanding discussions of such economic and financial matters as budget allocations and tax rates as well as the results of voting polls and othermeasurements. 

Exercise 1. Fraction Skills Assessment*

• Ask your student a few questions about some measurements:
  
  An ounce is what fraction (part) of a pound?

  A payment of $400 is what fraction of a monthly mortgage debt of $1200?
  
  One foot is what fraction of a yard?  Etc.

• In each pair of fractions shown here, circle the greater; if they are equal, circle both.

  1/3  or  ½               7/15  or  5/8                 9/17  or  6/16       Etc.

Exercise 2. Terminology* (See Note below.)  

• Point out that the numerator is the number of parts you have, while the denominator is the number of parts in the whole.  This concept can be nicely demonstrated by drawing a square and dividing it into 4 equal parts, 3 of which you shade.  The fraction ¾ tells what part of the figure is shaded, and ¼ tells what part is unshaded.  Expand the lesson by drawing figures divided into numerous equal parts.

• Demonstrate the significance of numerator and denominator by asking your student to identify which figure of each pair is greater.

  9/12  or  9/24­­         6/36 or  6/30           14/18  or  8/9        Etc.

Exercise 3. Forms of fractions*

Ask your student to tell whether each of the following is a proper fraction, an improper fraction, or a mixed number.

7/9      1 6/8      13/13      14 3/4      7/120      Etc.         

(Note: Your student may not be familiar with fraction terminology; start by using top number and bottom number rather than numerator and denominator.  Introduce the latter terms when you think your student is ready for them.) 

VOCABULARY EXPANSION

This is an exercise for the advanced student. For each of the words in Column A you will find an antonym or a synonym in one of the numbered columns on that line.  Once the right words have been identified you can discuss why the others are not correct :

Etc.

Where does the  ‘  go?**                       

The apostrophe is small but plays two big roles in written language.  It shows that a person (or thing) possesses something, and it is used in contractions.  Before using this or a similar exercise, a discussion of the use of the apostrophe would be in order.  In the following sentences insert an apostrophe where necessary or remove where it doesn’t belong.  Circle sentences that do not require an apostrophe and those in which the apostrophe is correctly used.

1. Oregon is famous for its advanced environmental policies.
2. The mothers’ of Baker Street had a bake sale.
3. Arizonas scenery is its most important tourist attraction.
4. Whose book is that?
5. Thats the one I want.
6. Its the people of a country that make its history interesting.    
7. Whose the one that asked for pizza?
8. The 1999 storm that hit Connecticut was it’s worst in 20 years.

Etc.

Using some and any**

In a statement, use some.        
Example:         I have some money.

In a negative sense, use any.    
Example:         I don’t have any money.

In a question, use either.                      
Example:         Do you have any money?
Example:         Do you have some money?

1. Use some or any to complete these sentences.

a. Joe needs ____ money.
b. Do you have ___ food?
c. I didn’t get ___ mail.

Etc.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Notes: “Etc.” as used above calls for the addition of as many examples at the level you deem appropriate         

* Howett, Jerry, Contemporary’s Number Power, Contemporary Books, Inc., 1988.
**  Azar, Betty S., Basic English Grammar, Prentice Hall Regents, 1996

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