Mental Mathematics
Aims
• To consider the purpose of the starter in
the daily maths lesson
• To consider possible content of the
starter
• To look at some starter activities
Background and context
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Concern that children’s mental calculation skills and recall of facts were
generally weak.
Framework referred to the first part of the lesson as:
– • Oral work and mental calculation (about 5 to 10 minutes)
(Whole-class work to rehearse, sharpen and develop mental and oral skills)
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Focus was on strengthening children’s oral and mental skills through
regular daily practice.
1999 Framework lists a number of activities that might form part of this
oral work and mental work.
Oral and mental ‘starter’ and was often judged by Ofsted to be the
strongest part of mathematics lessons.
Successful starters were short, focused activities that prepared the
children for the main teaching activity by getting them to think
mathematically.
These ‘starters’ were objective-led activities that supported children’s
learning and moved it on.
Current situation
• Range of purposes and related activities has increased.
• Focus on oral and mental calculation has widened and become
a vehicle for teaching a range of mathematics.
• Too often, the ‘starter’ has become an activity extended beyond
the recommended 5 to 10 minutes.
• In these situations, there can be more teacher talk than there is
oral and mental work
• Some evidence that the focus on oral and mental calculation
has been lost and needs to be reinvigorated.
• The ‘starter’ to a lesson remains an effective way of engaging
children at the start of a lesson through a brisk, well-focused
activity that helps to secure children’s knowledge and sharpens
their skills.
• Some evidence that mental work is only done in the starter
• Some evidence that teachers see mental mathematics as giving
children a test
Starter
• Activities may continue to be rehearsal
activities.
• Rehearsal and practice are designed to
strengthen knowledge and skills.
• Important that children have sufficient
opportunity to consolidate all the mathematics
teaching they have received.
• Mental work fulfils many other purposes.
The six Rs of oral and mental work
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Rehearse
Recall
Refresh
Refine
Read
Reason
Rehearse
• Practise and consolidate existing
skills. (usually mental calculation
skills, including using and
applying)
• Vocabulary and language of
number
• Properties of shapes or
describing and reasoning.
Recall
• To secure knowledge of
number facts, (developing
speed and accuracy)
• Recall quickly names and
properties of shapes
• Recall quickly units of
measure or types of charts or
graphs to represent data.
Refresh
• To draw on and revisit previous learning
• To assess, review and strengthen
children’s previously acquired
knowledge and skills
• Return to aspects of mathematics with
which the children have had difficulty
• Draw out key points from learning.
Refine
• To sharpen methods and procedures
• Explain strategies and solutions
• Extend ideas; develop and deepen the
children’s knowledge
• Reinforce their understanding of key
concepts
• Build on earlier learning so that strategies
and techniques become more efficient and
precise
Read
• To use mathematical vocabulary
• To interpret images, diagrams and symbols
correctly
• To read number sentences and provide
equivalents
• To describe and explain diagrams and features
involving scales, tables or graphs
• To identify shapes from a list of their properties
• To read and interpret word problems and puzzles
• To create their own problems and lines of enquiry.
Reason
• To use and apply acquired knowledge, skills
and understanding
• To make informed choices and decisions
• To predict and hypothesise
• To use deductive reasoning to eliminate or
conclude
• To provide examples that satisfy a condition
always, sometimes or never and say why.
Activities for Mental Work?
Useful Strategies for developing
mental skills
 Ensure children have understood a question by:
-repeating the question more slowly
-rephrasing the question
-presenting the question visually
-asking the children to put the question into their own words
-giving an example of a possible answer
-give them thinking time
 Help all children to answer by asking them to:
-say an answer in unison
-show an answer with their fingers
-point to a number on a grid, target board or line
-asking questions with a range of possible answers
-waiting before expecting an answer
-getting the children to tell their partner the answer
-giving children digit cards to hold up
-writing answers on personal whiteboards
-taking an answer but asking the children to discuss whether it’s correct
Key messages
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Cover all areas of maths
Think of the 6Rs
Involve all children
2 or 3 sessions in a week should be to
do with your target area in maths
• Counting and rapid recall should occur
every day