In one lesson, one task can “differentiate” or be suitable for many different students of many different levels.
The trick is in choosing the right task.
A quick example – are you familiar with the numbers game from SBS “Letters and Numbers”. Given a set of 6 numerals you aim to make a target number using any mathematical operations.
https://mathsstarters.net/numbersgame
Quite a tricky task – especially with some number sets!
(Here’s a “cheats” link to finding answers!! http://www.crosswordtools.com/numbersgame/)
So how can we differentiate??
Easier
 Take away the target number – get kids to make any numbers they can
 Give categories of target number ( a number between 200 and 400, a number using both addition and subtraction, a number with a 5 in the tens column, )
 “Rig” the target number so it is easy to get to
 Give clues “Can you make 33 and then times by 10”
Harder
 Set a time limit (the TV game uses 30 seconds)
 Make it a race or competition: give scores (10 for getting it right, 9 if you are one off, 8 if you are two off…..)
 Find more than one way of making the target number
 Must includes (must include a ÷, must include the 9)
This task could cover some of these Australian Curriculum outcomes.
Year 2  Year 3  Year 4  Year 5  Year 6  Year 7 
ACMNA027
ACMNA028 ACMNA029 ACMNA030 
ACMNA052
ACMNA053 ACMNA054 ACMNA055 
ACMNA072
ACMNA073 ACMNA075 ACMNA076 
ACMNA098
ACMNA099 ACMNA291

ACMNA123
ACMNA134 
ACMNA151
ACMNA280

Is that enough differentiation for you??
How do we choose a task to differentiate?
The task must be:
Based on big ideas/concepts – the big ideas open to more creative thinking and solutions compared to a question that requires a single answer. Compare the difference between “adding 5 and 8”, and finding a set of numbers that total 13.
Have possibility for multiple solutions – a single solution immediately limits a task to that solution. Multiple solutions inspire creativity, persistence or extension of thinking.
Allow for student choice, creativity and thinking – different students think in different ways, and from different angles. In order to differentiate we need to tap into these alternatives rather than always following the book. Allow the students to surprise you.
Ideally it should also
Require minimal instruction from the teacher – Present the requirements of the task and let them at it. Don’t waste time by telling the students what to do or how to do it. Step back and allow them to explore the task. Step in with scaffolding and encouragement when necessary.
Relate to real life in either content or skills. Make it relevant and give a purpose to the task and it becomes more engaging.
Student choice
It seems that teachers’ biggest fear is that student will make the “wrong” choice. What is the “wrong” choice? Something too easy? Something too hard? If it is too easy the student will build fluency and confidence (and get bored) – and hopefully soon choose to challenge themselves with something a little more complex. If it is too hard the student will quickly readjust and find something that more within their abilities, or seek help. In either case some subtle redirection, or encouragement may help students to make a different choice next time.
Student choice empowers the student to take responsibility for their actions and outcomes. Most students have a very good idea of their abilities and their “ranking’ compared to other students. Most students make appropriate work choices, most of the time. Giving student choice also adds another layer to their learning. Rather than simply responding to teacher direction, they are participating in creating their direction, and enhancing the skills that contribute to life long learning.
Teacher skills
The biggest skill needed to teach in this way is the ability to step aside and allow the students the lead role in their learning. Rather than the students responding to the teacher, the teacher is responding to the students. The teacher is there to coach and support with guidance and encouragement. It requires flexibility and willingness to adapt to questions, needs and directions of students. It requires a good knowledge of the concepts of mathematics and how they work together to build understanding. And it requires a good knowledge of the students themselves – their abilities and attitudes.
Why differentiate?
Apart from the current buzz words like “teaching to students’ abilities”, “allowing all to achieve,” etc etc…..
Differentiation encourages us to teach people, not content. It encourages us to teach skills, not memorise procedures. It engages and motivates students to learn, to challenge themselves, and to develop skills in thinking, managing themselves and their work, make responsible choices and to celebrate their achievements.