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Why do this problem?
This problem offers an opportunity for students to practise routine
multiplication whilst being required to consider common factors and
multiples. The task provides an engaging and challenging
environment which encourages students to think about efficient
strategies for solving a set of related problems.
Relating to this
, the action of filling in the table given the
headers is straightforward; probing the table and then working out
the headers is the inverse or undoing action. It is challenging to
look for the least amount of information required in general
to enable the undoing
action to be completed.
Introduce the class to the problem using the
In order to really get to grips with the task, students need
to spend quite a long time developing efficient strategies for
solving the Level 3 challenges.
If a computer room is available, students could work in pairs
using the interactivity. Another option, if students have access to
computers outside school, is to ask them to work on the different
challenges for homework.
If computers are not available, the task can be recreated by
asking each student to create a multiplication grid of their own,
and then draw a blank grid for their partner. As in the
interactivity, the challenge is to ask for as few entries as
possible from the grid in order to work out what the headers
Once students have had plenty of time to develop strategies,
the key questions below provide a good basis for discussion.
Finally, once students have had a chance to share ideas, they
could revisit the interactivity to test out each other's
Is there a strategy for completing the Level 3 challenge
Are there any numbers you could uncover that immediately tell
you the row and column headers?
Are there any numbers you could uncover that narrow down the
row and column headers to two alternatives?
Does it make a difference if you choose which cells to reveal
at the start or if you choose as you go along?
There are natural extensions within the problem - working on
the 10 by 10 grid provides a real mental workout.
Why was it necessary to include a grey (unavailable) number in
one of the headers of the versions of the problem which included
uses a similar structure but the context is
factorisation of quadratic expressions.
This version of the interactivity
uses multipliers up to 10 and
allows unlimited reveals, so it could be used to allow students to
get a grasp of the structure of the problem before moving on to the