Ordering fractions
a) 
^{1}/_{10} , ^{1}/_{3} , ^{2}/_{5} , ^{1}/_{2} , ^{6}/_{10} , ^{2}/_{3} , ^{3}/_{4} , ^{6}/_{5}
NOTE: an error may be a transposition or fraction out of order.

2 marks(all correct)
or
1 mark(1 error)

Total  2 marks 
Extension:
Ask students to explain their reasoning for how they know one fraction is less/more than another.
A number of students placed most of the fractions in correct order, but made 12 errors. Most students knew to have the tenths as the smallest denominator, and most of those onetenth as the smallest fraction.
Common error  Likely misconception 
^{1}/_{2} , ^{1}/_{3} , ^{1}/_{10} , ^{2}/_{3} , ^{2}/_{5} , ^{3}/_{4} , ^{6}/_{5} , ^{6}/_{10}  Whole number (numerator first)Ordering the fractions by the numerator and then the denominator. Students are applying whole number ordering principle to the top and them the bottom indicating a lack of understanding of the nature of a fraction as a rational number. 
^{6}/_{10} , ^{1}/_{10} , ^{6}/_{5} , ^{2}/_{5} , ^{3}/_{4} , ^{2}/_{3} , ^{1}/_{3}, ^{1}/_{2}  Whole number (denominator first)Ordering the fractions by the denominator and then the numerator, indicating a lack of understanding of a fraction as a single rational number. Students have some understanding that a larger denominator means a smaller fraction, but they think this is true for the numerator as well. 
^{1}/_{10} , ^{6}/_{10} , ^{2}/_{5} , ^{6}/_{5} , ^{3}/_{4} , ^{1}/_{3} , ^{2}/_{3}, ^{1}/_{2}  Whole number (denominator first)Ordering the fractions by the denominator and then the numerator as above. Students have some understanding that a larger denominator means a smaller fraction, and that a larger numerator means a larger fraction. 
^{1}/_{2} , ^{1}/_{3} , ^{2}/_{3} ( ^{2}/_{5} , ^{1}/_{10} , ^{6}/_{5} , ^{3}/_{4} ) ^{6}/_{10} *variable order in brackets  Whole number (larger numbers)Ordering fractions by the larger the top and bottom numbers the larger the fraction (these numbers could be added or multiplied together). 
Based on a trial set of 27 Y7/8 students.
NOTE: Students should be able to order all 8 fractions to indicate understanding of ordering simple proper fractions. Two important ideas in this resource are:
 where they place ^{2}/_{5} , ^{6}/_{10} , and ^{6}/_{5} ; and
 how they justify their choice.
Understanding partitioning and the partwhole relationship
Students who have any of the whole number misconceptions identified previously need to develop a partwhole understanding of fractions before trying to devise a system to compare or order fractions.If required, students could go back to partitioning and explore constructing the parts (unit fractions), combining these parts to make nonunit fractions that are between 0 and 1 (also called proper fractions), and naming these new fractions (partwhole fractions).
Simple fractions correctly placed all fractions
For students who correctly placed all fractions, ensure that they can also order other odd numbered fractions and top heavy (improper) fractions such as ^{3}/_{13} , ^{11}/_{27} , ^{13}/_{9} , ^{29}/_{3} , etc.
For further information about Fractions and number lines, lick on the link Fractional thinking: conceptual map.
Numeracy resources:
Book 7: Teaching Fractions, Decimals and Percentages, 2006:Trains (p.19) Early additive/Advanced additive/Early multiplicative.