Explaining the Number of Fractional Parts Used Determines the Size of Fractional Parts

T.I.P.S.

Students will begin to lay the foundation for fractions in second grade. Students have experienced fractions in first grade through geometric shapes. Students should understand that the inverse relationship between the size of the fractional part and the number of equal parts in the whole when given the same size whole. The greater the number of parts, the smaller the size of the parts and the smaller the number of parts, the greater the size of the parts. Second grade students do not use or write in fraction notation (a/b) as they use written words to describe the relationship of fractions. Students should also have a great understanding that each fractional part of an object is the same size in area and the same shape and that the orientation of the partitioned parts does not affect the size in area or shape of the parts.  

Example

You will need paper and two different colored pencils or markers to complete this activity. Look at the following shapes. Which shapes could you draw a line through to show halves?

With a different color pencil, draw 1 another line to partition each shape above into fourths.

a)  What happened to the number of equal parts in each whole when you drew the second line?

b)  What happened to the size of the equal parts when you drew the second line?

c)  Explain what would happen to the size of each part if you continued to divide the shapes into more equal parts. 
Hint
Possible Solutions

TEKS

2.3 Number and operations. The student applies mathematical process standards to recognize and represent fractional units and communicates how they are used to name parts of a whole. The student is expected to: (B) explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part 

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