Using Probing Questions in
Mathematics lessons
What do
you think?
Year 8
Level 6
Assessment Criteria
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Criteria you are looking for.
Assessment Criteria for Year 8 Level 6
• Using and applying mathematics to
solve problems
• Numbers and the number system
• Calculations
• Algebra
• Shape, space and measures
• Handling data
Using and applying mathematics to solve
problems
• Use logical argument to establish the truth
of a statement.
How do you know
that expression
matches the
pattern?
Well, it works
for the 3rd
arrangement.
Which pattern?
The red squares
or the white
squares, or both?
What if I make a
different pattern?
Numbers and The Number System
• Use the equivalence of fractions, decimals
and percentages to compare proportions;
calculate percentages and find the outcome
of a given percentage increase or
decrease.
• Divide a quantity into two or more parts in a
given ratio; use the unitary method to solve
simple word problems involving ratio and
direct proportion.
Well, from that I
can work out lots
of other
equivalents
I know that:
1
 0.1  10%
10
I notice a link
between sets of
fractions, decimals
and percentages.
I bet you can’t
work them out
for one third!
Which fraction is it
closer to?
What about
20
?
61
I can find a
fraction between
1 and 1
3
2
How do
you do it?
I don’t think you
can find out exactly
how many
students there are.
The ratio of students
with mp3 players to
those without is 3:1
I wonder if
there could be
30 students.
I bet there’s
25 boys.
Algebra
• Plot the graphs of linear functions, where y
is given explicitly in terms of x; recognise
that equations of the form y = mx + c
correspond to straight-line graphs.
I have trouble
deciding on what
scale to use.
I need to graph
y = 2x + 4.
I wonder how I could
get a set of points to
plot.
Don’t you just put
2 on the x-axis
and 4 on the yaxis, then join
that up?
I know we need an x and
y axis, but I can never
figure out how big to
make the graph.
I have to draw
y = 3x + 5. I
wonder if it’s
steeper.
I need to graph
y = 2x + 4.
I wonder how I could
do it without this
computer.
If one number is
the gradient,
what’s the other
number for?
I can never
remember which
number affects
the gradient.
Shape, Space and Measures
• Identify alternate and corresponding angles;
understand a proof that the sum of the angles of
a triangle is 180° and of a quadrilateral is 360°.
• Classify quadrilaterals by their geometric
properties.
• Enlarge 2-D shapes, given a centre of
enlargement and a positive whole-number scale
factor.
• Use straight edge and compasses to do
standard constructions.
• Deduce and use formulae for the area of a
triangle and parallelogram, and the volume of a
cuboid; calculate volumes and surface areas of
cuboids.
This should help us
to find out the sum
of angles of a
quadrilateral.
Should we use
something like
corresponding and
alternate angles?
How do I convince
someone that the sum
of the angles in a
triangle is 180o?
Don’t you have to
draw in some parallel
lines somewhere?
I think that kind of
trapezium would
have three acute
angles.
I don’t think
you can get
any
quadrilaterals
with three
acute angles.
I think I can
draw an isosceles
trapezium.
Wouldn’t that
be just a
parallelogram
?
I notice that when
you enlarge a
shape, some things
change and some
stay the same.
I wonder what
the scale
factor is.
I want to find
the centre of
enlargement.
How do we know if
the shape is being
enlarged or…umm
shrunk?
Why do we need to use
compasses anyway?
I think bisecting
the angles of a
rhombus would
be easy.
I can never remember
when I should keep
the same compass arc.
I think the formula for
the area of a triangle is
related to the formula
for the area of a
parallelogram.
I know there’s a
formulas for a
triangle. I wonder if
there is a formula for
the area of every 2D
shape?
AREA = 12 cm2
I think I can
work out the
dimensions of
this triangle.
It’s hard to find the
area of some types
of triangles, but
others are really
easy.
Handling data
• Construct, on paper and using ICT;
– pie charts for categorical data;
– bar charts and frequency diagrams for discrete and
continuous data;
– simple time graphs for time series;
– simple scatter graphs.
Identify which are most useful in the context of
the problem.
• Find and record all possible mutually exclusive
outcomes for single events and two successive
events in a systematic way.
I wonder if showing our
results in a graph would
be most useful to show
the answer to this
hypothesis?
I think we need
to group the
data. What
class intervals
should we use?
Hypothesis: The older you are,
the more television you watch.
I think I want to
use the graph
which is the
easiest to
interpret.
I think we
should use the
type of graph
that is the
most helpful.
I want to make
a pie chart how can we work
out the angles
again?
Height of
Seedling (cm)
Frequency
0 – 4.9
3
5.0 – 9.9
8
10.0 – 14.9
15
15.0 – 19.9
6
I’m not sure if we
should draw a pie
chart. This is
continuous data,
isn’t it?
Are those class
intervals OK.
They don’t look
quite right.
I wonder how
many different
outcomes there
are?
Rule: Spin and Add the numbers
How do you
know if you have
all the
possibilities?
I think we have to
find all possible
outcomes, whether
they are different
or not.
What’s the best
way of recording all
the possible
outcomes?
Thanks to Emile Pinco, Head of Mathematics at Churchdown
School, for compiling this resource
Based on material from the Secondary Strategy’s ‘Focused
Assessment Materials’ (APP) and ‘Progression Maps’
Some images from www.stfx.ca