For example, a student who can recognise that 3/7 is equivalent to 6/14, which is less than one-half (7/14), will be in a strong position to both create an appropriate proper fraction and successfully challenge opponent plays.

The player in control (Player 1) decides whether players will create proper fractions greater than one-half or less than one-half for that round.

The proofs of the above theories show that the proposed method is feasible for fraction reduction; namely, the simplest

proper fraction can be obtained by this method for any fraction.

"Sprint" (2 min; introduced in Lesson 10) provided strategic, speeded practice on four measurement interpretation topics: identifying whether fractions are equivalent to 1/2; comparing the value of

proper fractions; comparing the value of a proper and an improper fraction; and identifying whether numbers are

proper fractions, improper fractions, or mixed numbers.

Simply that

proper fractions with N as denominator, where N has factors other than 2 or 5, will produce repeating sequences of length (N - 1) or less.

Locating

proper fractions on number lines: Effect of length and equivalence.

Using this algorithm Fibonacci showed that it was possible to express all

proper fractionsInitially the student should start working with dividing whole numbers by

proper fractions to develop the notion that division does not always yield a quotient that is smaller than the dividend.

(Teachers will need to decide whether or not to specify that only proper fractions--or perhaps

proper fractions plus improper fractions equivalent to 1--"count" for some of these activities.) Similar decimal versions of Digits and Dice may be created.