Equality of Challenge Initiative
Differentiated Extension Activities in Maths for Exceptionally Able
Students
by Helen Ryan, Castletroy College, Limerick
One of the more effective ways of making inclusive provision for exceptionally able students is through
extension tasks in mainstream classes. This example of subject planning for exceptionally able students
through extension activities is in the area of maths.
This activity arose from an examination of the provision for gifted and able students in the school. One of
the outcomes of this review as was the development of a specific initiative for such students in the form of
differentiated extension activities in mainstream maths classes.
In September 2010 it was decided such an initiative would be run with first year Maths students. As a
result of the Drumcondra Numerical Ability it was possible to identify students who are exceptionally able
in the area of numerical ability (over 90 percentile). The First year Maths teachers, in consultation with the
Project Maths advisor, devised learning tasks for Term 1 which could be used as extension activities in
the classroom to challenge the very able students.
These included
•
Problem of the Day (each day for 6 weeks) with particular emphasis on problem solving and
critical thinking. The problems have direct relevance to the syllabus: e.g. probability, fundamental
principle of counting, algebraic equations and problems, indices – examples are included below
•
Purchase of a class set of small white boards for peer teaching which involved encouraging
students to work in small groups (usually 3 or 4). The use of a small white board makes it very
easy for students to rub out their mistakes and continue with questions.
•
Peer correcting which involved students working in groups of 2 correcting each other’s work and
assisting each other in identifying problems they may encounter.
•
Students writing their own rules: e.g. integers, teachers not pre teaching the rules, instead
encouraging students to write their own rules and methods of doing questions. Teacher then
compiling all suggestions from students and generating a class rule.
•
Teaching extensions from base topics: e.g. laws of indices with order of operations, equations in
algebra. This involves looking at the syllabus of work for first year Maths and deciding to
introduce more difficult challenging parts of the syllabus in Year 1.
o
o
Example 1 involved introducing Law of Indices including a = 1 in October.
o
Example 2 involved teaching students to form their own algebraic equations from
problems while teaching the first year Algebra programme. In the common First Year
Maths test given at Christmas questions with these extensions were placed on the
test. The decision as to whether include them or not in the marking scheme was left
to the individual teacher.
•
Use of work sheets from Whiteboard Maths from www.whiteboardmaths.co.uk.
Examples of the Extension Tasks
Monday 8th November 2010
Task:
How many ways can you arrange FOUR books on a bookshelf?
Solution:
There are 24 ways to arrange FOUR books on a bookshelf.
Tuesday 9th November 2010
Task:
A cat is at the bottom of a 20 foot well. (Don't worry, he's got lots of food, water, toys
down there.)
Each day, he climbs up 5 feet...
And each night, he slides down 4 feet.
How many days will it take him to reach the top of the well?
Solution:
Think it's 20 days? Up 5... down 4... that's 1 foot up a day...
Wednesday 10th November 2010
Task:
Use the numbers
1, 2, 3, 4, 5, 6, 7, 8, 9
to fill in the bubbles so that the sum
around each hexagon adds up to 30.
You can use the numbers more than
once... and you won't need to use all
of them.
Solution:
Here's one solution:
Thursday 11th November
Task:
If you have FOUR people in a room and each person shakes hands with every other
person exactly once, how many total handshakes happen?
Solution:
If there are FOUR people in a room and each shakes hand exactly once with everyone
else in the room...
There will be 6 handshakes
Friday 12th November
Task:
What number comes next?
1, 3, 6, 10, 15, 21, ___
Solution:
28