Using the 5Es instructional approach for teaching in two contexts: Mathematics
(a) enquiry processes
(b) for understanding/skills practice
The 5Es approach offers a format for effective teaching that follows how students learn. It can be applied to the teaching of: (a) processes
such as enquiry and problem solving; and (b) promoting deeper understanding of ideas and concepts and skills development. The
following examples illustrate how the 5Es can be applied to these contexts.
Teaching strategy
(a) processes – problem solving and enquiry
The tiling problem
Engage
Provide an interesting, often
visual input to stimulate learner’s
interest in the topic.


Explore
Offer hands-on opportunity for
interaction with materials or
ideas, with minimum instruction,
but the expectation of follow up
Ask students to describe and
reflect on experience.
Draw out key aspects of
students’ responses; help them
to focus on the next stage of the
enquiry – this may involve
prompting to formulate a
question or the introduction of
additional ideas
Provide support in the pursuit of
the extended work (enquiry or
development work); especially
where new skills are introduced
{use resources provided PPT tiling problem}
Introduce the ‘L’ shape problem: how can you fit 2 x 3 ‘L’
shapes into a 6 x 4 rectangle?
Provide paper and card cut outs
Take feedback from pupils:

establishing that 6 ‘L’ shapes are needed to fill the
rectangle

showing the range of solutions

discussing with pupils how to record and communicate
their solutions

considering systematic ways of proceeding; changing
one pair of ‘L’ orientations at a time
Explain
Extend
Evaluate
Encourage reflection on the
learning to include answering of
a research question and/or
reflection on the learning
process
Show some photographs of tiling and frieze patterns
And/or offer pupils some tiling jigsaw puzzle problems
Pupils have an opportunity to further explore the problem (in
pairs if desirable), recording their solutions with a view to
presenting their results with images and text. Their work can
be recorded:
o With (traditional) shaded pencil drawings
o Digital photographs of shapes or multilink cubes
(perhaps presented as a slide show or movie)
o Shaded tables, using software such as MS Word or
PPT
With pupils consider:
o The achievement of a full solution set, identifying any
missing configurations or repeats
o The effectiveness of the mathematical communication
(see above criteria)
(b) teaching for understanding/skills practice
Addition of two digit numbers
Provide a context:
Invite two pupils to come to the shop to buy their lunch: they
have £1.00 to spend and can choose 2 or 3 items, priced in
the range 30p to 70p – they have to choose and decide what
they can afford.
Invite all students to take part in the shopping activity in 2s
or 3s. (Provide ‘real’ labelled items and ‘real’ money if
appropriate)
Ask students to feedback on their experience. Identify the
different strategies they used to calculate the additions and
how they checked their answers.
Introduce further strategies, perhaps including pencil and
paper methods, 100 squares and number lines.
Set the next task, depending on the students’ achievement
with the explore . . . . .
o Shopping for two lunches, maximum £3.00
o Buying an outfit (shirt and jeans); maximum £35.00
Students undertake further shopping task involving practice
with either more 2-digit numbers , or 3-digit numbers.
They can take number lines, 100 squares, pencil and paper.
Calculators for checking only!
Try and compare different methods.
Students consider how successful they were in terms of
accuracy of computation, time taken to complete additions.
Students consider which method/s were best for purpose.