Number Sense in Fractions

Students also need to develop their number sense in fractions – combining them & partitioning them and using them in a flexible way. We will see some activities for doing this.

1. Equivalent Fractions

   1. Given any fraction, make several fractions equivalent to it. Eg ¾6/8, 9/12, 12/16 etc

   2. Given any fraction make an equivalent fraction with a “given” numerator or denominator

2. Comparing Fractions

   1. Comparing fractions with same denominator

   2. Comparing fractions with same numerator

   3. Comparing fractions by using the idea of equivalent fractions

3. Adding & Subtracting fractions

   1. With same denominator

   2. With different denominators

4. Skip Counting with fractional difference 1</a>

   1. For ½0, ½, 2/2, 3/2, 4/2 …….0, ½, 1, 1 ½, 2, 2 ½ ….

   2. For ¾0, ¾, 6/4, 9/4, 12/4, 15/4 …..--> 0, ¾, 1 ½, 2 ¼, ……

5. Skip Counting with fractional difference 2 (direct)

   1. For ½0, ½, 1, 1 ½, 2, 2 ½ ….

   2. For ¾0, ¾, 1 ½, 2 ¼, ……

6. Converting between Improper Fractions & Mixed number

   1. Convert an improper fraction into a mixed number

   2. Convert a mixed n umber into an improper fraction

7. Add 2 mixed numbers

   1. Adding the integer part & the fractional part can be added separately

8. Subtracting a mixed number from another mixed number

   1. Where the integer part & the fractional part can be subtracted separately and then combined. E.g 3 ¾ - 2 ½ -> 3 -2 & ¾ - ½ -> 1 & ¼1 ¼

   2. Where both have to be converted to improper fractions and then subtracted

9. Partitioning Fractions

   1. 7/203/20 + 4/20 -> 3/20 + 1/5

   2. 7/205/20 + 2/20¼ + 1/10

Subitising Fractions

Teachers also need to train students in subitising fractions, in the sense of quickly identifying simple fractions, just by looking at their visual representation. Simple fractions are those whose numerator & denominators are less than 5, hence identifiable by sight.

Oral Counting

Examples are counting in one fourths starting from two, in one thirds starting from 1 and counting in two thirds starting with zero.

These exercises bring out the patterns underlying fractions also, which most students never realise.

Benchmark Fractions

In whole numbers we call 5s & 10s as benchmarks wither to compare or to perform operations.

Similarly in fractions, halves & wholes can be thought of as benchmarks. Halves can be 1/2 or 2/4 or any equivalent. Wholes can also be in the form 2/2, 3/3 etc. We can estimate results of fraction operations by using these benchmark fractions.