How do we handle wide ability ranges in a single class?

Preparatory questions and links:

Focusing questions:
What strategies have you used in the past to handle different ability levels?
What strategies do you use to assess ability level? Do you pre-assess before a unit?
Do you group by ability or have mixed groups?
How do you service advanced students who have mastered content? Next level or alternative topics?
What strategies have you used to help students represent/understand specific concepts?
Manipulatives - do students use them on a math test? When do students stop using manipulatives?
Does the programme/text you use (eg. Bridges, Everyday Math, etc.) provide for differentiation? Examples?

Useful links:
Differentiated Instruction for Math
3rd, 4th and 5th grade Math Differentiation
Differentiating content in math:
Differentiating process in math:
Differentiating product in math:
Rationale for manipulatives:
Visual Manipulatives
Illuminations web site: contains Lessons, Tools and Web Resources
Wired Math (gr 7-10
XP Math:

(Provided by @tcash )

Threaded discussion from 15th July 2010 -
Threaded discussion from 19th July 2010 -

Links mentioned in the discussions, with contributor:
brittgow Potato Olympics for Year 6/7 (Australia)
ccoffa Dan Meyer's TEDxNY Talk: Math class needs a makeover (Video)
tcash What is Differentiated Instruction?
math2go Kathie Nunley's Layered Curriculum

kcollazo Math mastery learning ideas from Laura Chandler
tperran Strategies for Differentiation
ColinTGraham Six Open-ended Investigations (British) [requires free registration]
Saskateach The Bansho alternative to "drill-and-kill" (ColinTGraham Japanese explanation here !)
ccampbel14 SNAP Math Fairs
Also check out Family Math Nights and Math Field Day at the bottom of cybraryman1's Math Page

Resources (costing money!) mentioned in the discussions, with contributor:
brittgow Maths 300 (Australian)
Saskateach Young Mathematicians at Work series (Catherine Fosnot et al)

mrdfleming Maths Makes Sense (Canadian)
Saskateach Making Math Meaningful (Canadian)
tcash Bridges in Mathematics (American)
Saskateach The Teaching Gap (Book)
ColinTGraham Thinking Maths - Teacher's resource from Cognitive Acceleration Research
in the UK
ccampbel14 Great Ways to Differentiation Mathematics Instruction - top 2 in list - Primary & Secondary

Other links which may be useful
Math Workshop : Using Developmental Grouping to Differentiate Your Instruction suggested by mrdfleming
Learning Outcomes vs. Differentiation - blog post by MaggieSwitz suggested by whatedsaid & brittgow
Tiered Lessons: One Way To Differentiate Mathematics Instruction suggested by tcash
Recent forum on TES Differentiating for mixed ability - how? suggested by ColinTGraham