Thursday, December 4, 2008

FRACTIONS, FRACTIONS, FRACTIONS EVERYWHERE - A MIDDLE SCHOOL ACTIVITY

What middle schooler doesn't get that warm and fuzzy feeling when we tell them we're going to play with fractions! Here's a small investigation to capture that mood of euphoria...

RULES OF THE GAME:

• No Calculators - No decimals!
• All fractions must be expressed in lowest terms
On a number line mark off 0 and 1 and approximately locate points A and B whose coordinates are 1/4 and 1/3 respectively.

1. Write the fraction that divides the segment between A and B into two equal parts. How can we verify that this point satisfies the desired condition.
Complete: This fraction is the _______ of 1/4 and 1/3 and is ____-way between 1/4 and 1/3. The corresponding point is the _________ of segment AB.

2. Write the two fractions that divide the segment between A and B into three equal parts.

3. Do the same for four, five and six equal parts.

4. Reach/Extension: Describe a general procedure for dividing the segment AB into any desired number of equal parts (mathematically speaking, we would say n equal parts).