‘Questioning the Answer’
Enables group work
Generates rich discussion
Encourages creativity
Improves literacy skills
Identifies misconceptions
Facilitates mathematical understanding
Allows students to appreciate each others’ mathematical thinking
The general brief is for students to ‘design’ mathematics questions that
connect to a given answer in such a way that the progression of the phases
provides a scaffold which starts to enable the above features.
Students working in pairs, and producing agreed questions, will enable
effective conversations at that level. The use of a visualiser is very beneficial
for the whole class to appreciate and discuss each other’s questions.
Prompting and probing questions by the teacher will facilitate the process.
The discussions that emerge will be rich and
thought provoking. Whether they are between
the students, between teacher and pairs of
students or between teacher and the whole
class, the dialogue that develops will be a
prominent aspect of this activity.
Developed by:
Matthew Stennett, Advanced Skills Teacher (Shirebrook School)
Peter Needham, Consultant (Derbyshire LA)
Trialled with:
Y9 and Y10 students (Shirebrook School)
Additional support with resources:
Sandra Rimmer, Admin Assistant (Derbyshire LA)
Karen Shepherd, Admin Assistant (Derbyshire LA)
George Mullins, Subject Support Assistant for Mathematics (Shirebrook School)
Phase 1
(Let’s see what happens!)
Question Design Sheet
NAMES:-
EASY
QUESTION
Our Question is:
This is the mathematics we need to answer our
question:
MEDIUM
QUESTION
Our Question is:
This is the mathematics we need to answer our
question:
TOUGH
QUESTION
Our Question is:
This is the mathematics we need to answer our
question:
ANSWER…………………………………………..
Students to work in pairs. Each pair to be given one ‘Question Design’ sheet.
“Write 8 in the answer box at the bottom”
“The answer is 8. In pairs, design a question that you think is easy and
gives an answer of 8. Write your question in the ‘easy question box’”
Students will only need one or two minutes to do this.
Allow the students to interpret ‘easy’ is their own way. No need to discuss or give
examples of ‘easy’.
Choose some questions, as designed by the students, to share with everyone. A
visualiser will be extremely useful here.
Most likely the questions will be of the form ‘2 + 6’, ‘2 x 4’, ‘10 – 2’ and there will
also be an absence of vocabulary e.g. ‘calculate’, ‘work out’, ‘find the product’ etc.
Any questions which display a little more creativity and/or a different area of
mathematics then share briefly. Too much focus on someone’s originality here
will encourage plagiarism.
At this stage use only the part of the worksheet for writing questions. Ignore
the ‘mathematics needed’ section.
“Now design a question where the answer is still 8 but which must be
more difficult than your easy question. Write this question in the ‘medium
box’”
Allow adequate time as before. Circulate and offer prompts to pairs encountering
‘mental blanks’. Many pairs will most likely, at this stage, produce questions
similar in nature to their easy ones but longer e.g. ‘5 + 6 – 4 + 1’. Others may start
to involve arithmetic questions showing 2 or more operations (in some cases these
may be incorrect due to absence of brackets).
Some pairs may start to include the necessary vocabulary whilst others might
have now started to delve into other areas of mathematics (averages, rotational
symmetry).
Some pairs might now be creating word problems which provide a context for the
question. Share examples with the class and discuss merits of each question.
Share some which might display misconceptions.
“Does this one give an answer of 8?”
“What adjustment needs to be made to the question to ensure that it
does give an answer of 8?”
“Does this question display the necessary words? What words could we
use to make it look like a question on a worksheet/textbook/test?”
“Is this question an easy question or a medium question?”
This opens up the discussion regarding the features/perception of questions
which are deemed to be more difficult than the easy ones.
“What areas of mathematics are there amongst our questions?”
Ask the students to now write the areas of mathematics in the relevant box for
each of the two questions. This to be done without any guidance.
Responses will generally be simplistic and sometimes clumsy. As a class, share the
range of mathematics involved and start to suggest correct terminology. For this
phase there is no need to continue to the ‘tough question’ but feel free to
venture there.
Phase 2
(Now let’s be creative!’)
“The answer is 15”
Provide the prompt sheet (Mathopoly) and allow a few minutes for the
students to appreciate the range of mathematics available.
“Which other areas of mathematics might have been considered for ‘the
answer is 8’?”
(The design of this prompt sheet is to provide an ‘eye catching’ resource rather than a bland list
of mathematical topics, although there are many ideas that can emerge for alternative uses of
this format)
“The answer is now 15. Design an easy and a medium question which gives
an answer of 15. Make sure that each question covers a different area of
mathematics.”
Again, share questions and discuss as per phase 1 but pay attention to the range
of mathematics emerging and to what the students are now entering on their
sheet in the ‘this is the mathematics we need’ section.
Focus on the design of the question and the use of vocabulary. Some questions
emerging will be contrived and unrealistic. Share these and discuss.
“Now let’s try a tough question. Be creative!”
Phase 3
(Stepping up a gear)
This phase introduces answers with units, letters, percentages etc.
“The answer is 10cm”
Repeat Phase 2.
The students should now be aware of what is expected of them.

Questions which are realistic and not contrived.

Well phrased questions

A range of mathematics in use.

Questions which are now becoming more demanding but which still show a
progression from ‘easy’ to’ tough’

Opportunities to appreciate questions designed by peers.
Other ideas for answers which can be presented in phase 3
1. Different units hrs, mph, g, km, cm2, ml, etc
2. Algebra 5x, 4x-3y, 7
3. Fractions, decimals and percentages 4/5, 60%, 0.7
4. ‘C is the odd one out’
Phase 4
(Directing the creativity)
This phase starts to direct the students’ creativity to areas of mathematics
determined by the teacher. Examples:
“The answer is 10cm and somewhere amongst your three questions, you must
involve perimeter and area.” (Important to stress that the answer required is in
cm).
“The answer is £3.50 and, somewhere amongst your three questions, you must
involve percentages and fractions.”
“The answer is 17 and, somewhere amongst your three questions, you must involve
equations and substitution.”
“The answer is (3,8) and, somewhere amongst your three questions, you must
involve co-ordinates, equations and reflections.”
“The answer is 12 and, somewhere amongst your three questions, you must involve
mode, a bar chart and probability.”
“The answer is 30 degrees and, somewhere amongst your three questions, you
must involve an isosceles triangle, a trapezium and exterior angles of a polygon.”
“The answer is 7.6cm (1 dp) and, somewhere amongst your three questions, you
must involve circumference and Pythagoras.”
Additional notes:
This activity can be used at the end of a unit for students to display understanding
of the mathematics encountered in the unit. This can still be done in pairs or, for
assessment purposes, individually.
Some of the questions designed will relate to identified assessment criteria (APP)
and will thus provide evidence towards the criteria.
With KS4 students there will be opportunities to discuss the difficulty of
questions in relation to GCSE grades. These materials can be used with any year
group.
Copies of the design sheet and the mathopoly sheet follow on the next two pages.
NAMES:-
MEDIUM QUESTION
EASY QUESTION
Our Question is:
This is the mathematics needed to answer the question:
Our Question is:
This is the mathematics needed to answer the question:
TOUGH QUESTION
Our Question is:
This is the mathematics needed to answer the question:
ANSWER…………………………………………..
The following pages show a selection of questions as designed by a class of Y9
students. The original ‘question design’ sheet included a section to identify the
level of the question but it was later decided that the idea of easy, medium and
tough in relation to the students’ own mathematical understanding was more crucial
rather than being distracted by levels and grades.
The class discussions that took place around
some of these questions reflected the depth of
mathematical thinking taking place and the
appreciation of each others’ explanations.
This first example is taken from phase 4 where the students were told to ensure
that area and perimeter were evident amongst the questions. No prompts or
assistance were given. The ‘tough’ question, in particular, shows excellent
mathematical thinking.
This example is from phase 3 where the students suggested possible answers. The
medium question, in particular, displays a good level of understanding with
percentages. (The easy question, though, is questionable!)
This example, also from phase 3, shows a good progression to the tough question
which incorporates simplifying and use of ‘lowest form’ and then converting to a
percentage.
This example is from phase 3. The tough question, in particular’ provoked much
discussion. The students who designed the question realised that they only needed
to show one of the base angles. When shared with the class there were some
students who commented that there wasn’t enough information in the question…..
but others then responded that it was an isosceles triangle!
This example is from phase 3 and, just like the previous example, incorporates
some geometry
The following example are taken from the first lesson (phase 1) and illustrate the
simplistic responses as well as the beginning of some creative thinking.
The following examples are from phase 2 and start to show other areas of
mathematics and better use of vocabulary.
The following examples are taken from phase 4 (The answer is 10cm) where
perimeter and area each needed to be evident in some of the questions. The
questions show a better use of vocabulary. Some questions give an answer of 10cm2
and the students have addressed this by writing, in the question, ‘show your answer
in cms’. This prompted much discussion. A number of students initially found it
difficult to design an area question where the answer required is in cm. One
student designed such a question then announced that she had to ‘bend the
question’ in order to find a missing length from a given area!