Download Resource 2

Scottish Numeracy Energiser
NIACE for Learning Connections
Session 2
Handout 1
Are you stuck?
Don’t know where to start?
Put pen to paper
Make a list of everything you know
Make a list of everything you need to find out

Alternatively draw a mind map
Look for connections between the above
Draw arrows to link facts

Repeat the above process

Stuck in the middle?

Specialise - step–by–step approach
Simplify the problem by looking at particular features in a systematic way
Generalise – holistic approach
Have the particular features got anything in common: can you see a pattern
emerging?

Still stuck?

Take a break
Distance lends perspective
Change tactics
Look at the problem from a different angle: work backwards

Ask a friend
Your friend may have more experience, greater knowledge or new insights. It is also
easier to spot others mistakes and wrongful assumptions.

If all the above fail
Accept that there is no single solution
There may be a number of different solutions each with its own merit depending on
the particular circumstances

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Scottish Numeracy Energiser
NIACE for Learning Connections
Session 2
Handout 2
Billiard Table Investigation
This billiard table has four pockets one at each corner
The table is divided into equal squares
The ball is always struck from the same corner and travels at 45 degrees to the
sides.
The ball always rebounds at 45 degrees to the sides.
Which pocket will the ball fall into?
Ask your own questions and investigate.
Some ideas
What would happen if the table was of a different shape or a different size?
Are there sizes of tables where the ball will travel across every square?
From Investigator 1, 1984, produced and published by SMILE (Secondary
Mathematics Independent Learning Environment)
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Scottish Numeracy Energiser
NIACE for Learning Connections
Session 2
Handout 3
Making Assessment Meaningful
tutor’s
perception
learner’s
perception
external
perception
Be clear about the purpose of each task or exercise you use for assessment. Are
you assessing:
conceptual understanding – for example, what makes three three, what makes
an angle an angle, the significance of base 10.
 perceptual understanding – the ability to visualise shapes, volumes, numbers
 directional awareness – a sense of how to move oneself in relation to other
entities, and vice versa
 maths awareness - a sense that numbers reveal something about universal
principles
 number knowledge – an understanding that mathematical systems develop in
social and historical contexts; familiarity with the most immediately applicable
ones: for example, how many cm in half a metre, what number comes after 23
 operational skills - knowledge of how numbers behave when they are put into
various relationships with each other, and the ability to apply that knowledge,
for example to multiply 8 by 9
 maths literacy - for example, how to write down the sum to work out the total of
24, 32 and 41
 ability to strategise – whether or not the learner has techniques to be able to
start to solve a mathematical problem, and can recognise which to use when
 decision-making skills – the ability to assess a situation, and make decisions
about it using numbers.
Assessment is perceived as constructive and helpful where it reveals what learners know
and can do already, not just what they don’t know or find difficult. Assessment that focuses
primarily or exclusively on problems and shortcomings is demoralising and disempowering.
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Scottish Numeracy Energiser
NIACE for Learning Connections
Session 2
Handout 4
Top tip
A good way to engage learners is to get them to devise their own ways of reaching a
given answer. This way, they reveal a lot about what they know/can do already.
In this crossword, for example, everyone can work at their own pace/level. This is,
therefore, a ‘differentiated’ activity. (In this case, it’s the learners who do the
differentiating, rather than the tutor.)
Task:
Fill each blank square with one digit only from 0 to 9.
1
2
5
3
6
7
9
4
8
10
11
Now complete the clues using … (The tutor sets a condition e.g. multiplication,
division.)
Across
1.
3.
5.
7.
10.
11.
Down
1.
2.
4.
6.
8.
9.
To create a blank crossword of any size
 Insert table, choose number of rows and columns
o Select format from the toolbar
 Select borders and shading
 Select shading black
o Apply to cell
Number the squares (use a small font size so that learners don’t get confused).
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