Fractions: Counting by three-fifths

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Count by 3/5's and explore patterns in the sequence of groups of three-fifths. bar


  1. Count by 3/5s.
  2. Make a list of groups of three-fifths.
  3. What do you notice about the numbers?
  4. Organize them into rows with each row starting with a whole number equivalent.
  5. What patterns do you notice?


Count orally: three-fifths, six-fifths, nine-fifths, twelve-fifths, fifteen-fifths, eighteen-fifths, ...

Record the group and number of fifths in each group ...

Number of groups 0 1 2 3 4 5 6 7 8 9 10 11 12


Number of groups 13 14 15 16 17 18 19 20 21 22 23 24 25


Patterns for the denominator ...

Patterns for the numerator ...

What about group 100?

Group ...

What patterns can you find when you arrange them in a grid starting a new row for each whole number equivalent. Like below.

Groups of three-fifths fractions

Sample with some notes

Groups of three-fifths fractions

Some patterns:


What will a graph look like for the relationship for groups and number of fifths?

What will be the difference if the number of groups are graphed as x-values and totals as y-values vs. the number of groups as y-values and totals as x-values.


Source: Extending Choral Counting. Mathematics Teacher: Learning & teaching PK-12.
by Brandon G. McMillan & Theodore Sagun. 8 August 2020.



Grid 20x20



Dr. Robert Sweetland's notes
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