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 fractions
Initially 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.