Transcript Year 8 Level 5 Probing Questions Version A

What
do
you
think?
Using Probing Questions in
Mathematics lessons
Year 8
Level 5
Assessment Criteria
Click on a link to Jump to the Assessment
Criteria you are looking for.
Assessment Criteria for Year 8 Level 5
• 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
• Identify the necessary information to solve
a problem; represent problems and
interpret solutions in algebraic,
geometrical or graphical form.
There’s a lot of
information there. I
wonder what’s
important?
Bacteria in a petri dish
double the area they
cover every day. If the
dish is full
after 16 days, on
what day was only one
quarter of it full?
I don’t think
there’s enough
information
here
I’m going to
work out a
quarter of 16.
I wonder what
the half time
score was?
2
1
I’m going to work out
all the possible half
time scores.
What would
happen if the
final score was
different?
Where do I start?
A boy ate 100 cookies
in total in five days.
Each day he ate 6 more
than the day before.
How many
cookies did he eat on
the first day?
I think I could
use algebra.
I’m just going
to guess.
I wonder if I could
use symbols?
Bugs Bunny has three
carrots of lengths
10cm, 12cm and 15cm.
How can he use
these carrots to
mark off a length of
17cm?
I wonder what other
measurements Bugs
could get?
I think I’ll draw a
diagram.
Numbers and The Number System
• Add, subtract, multiply and divide
integers.
What about
multiplying and
dividing?
I think addition
always makes
numbers bigger
I think subtraction
always makes
numbers smaller!
I think you’re
both wrong!
Did you use
more than one
operation?
Hey! I got
– 144.
Did you use
+, –, x or ÷ ?
I can guess
what keys you
pressed to get
that answer!
What if x was a
– 0.2?
If x = 2, I can
put these
cards in order
What order
would they go
in if x = – 2?
Calculations
• Use standard column procedures for
multiplication and division of integers
and decimals, including by decimals
such as 0.6 and 0.06; understand
where to position the point by
considering equivalent calculations
I know you’re
wrong without
even doing it!
Hey, Look!
37 X 64 is 2366.
Well I think
she’s about
right!
If she’s wrong,
how do you work
it out without a
calculator?
I can work out a
calculation that
gives 23.68!
Hey, Look!
64 X 37 is 2368.
I wonder if there are
other calculations
that give 2368?
Can you work out a
dividing calculation
that gives 3.7?
Algebra
• Simplify or transform linear expressions by
collecting like terms; multiply a single term
over a bracket.
• Substitute integers into simple formulae.
I can think of lots of
expressions that
give the same
answer as this!
4p + 3q - 2
What do you look
for when you have
an expression to
simplify?
Do any of your
expressions
include brackets?
There! I’m done!
4(a + 2) = 4a + 2
3(p – 4) = 3p - 7
-2(5 – m) = -10 – 2m
I need some tips
when you have to
remove brackets.
I think you made
some mistakes!
I can think of
other expressions
that give 6 – 8x
I know what’s
behind the
Post It notes!
10
2x) = 6 – 8x
4(1
I wonder if something like
this could make 6 – 8x?
10
4(1
2x)
If I make x = 2,
I can tell which
cards match.
Would it
make sense
if x = -3?
Would they
still match if
I made x =
5?
I think that when x = –1, y
will equal –7.
y = 5x - 2
The way these guys talk
gets me all confused!
“When x equals something
then y equals something”
WHAT!!??!
I can think of
another formula
that give y = –7
when x = –1.
Shape, Space and Measures
• Transform 2-D shapes by simple combinations
of rotations, reflections and translations, on
paper and using ICT; identify all the symmetries
of 2-D shapes.
• Use units of measurement to estimate, calculate
and solve problems in everyday contexts
involving length, area, volume, capacity, mass,
time, angle and bearings; know rough metric
equivalents of imperial measures in daily use
(feet, miles, pounds, pints, gallons).
I can
transform tile
A2 using
reflection then
a rotation.
What information do
you need to rotate an
object?
How can I
transform the
First Pattern to
the Second
Pattern?
I wonder what stays
the same and what
is different when
you reflect objects?
I can make up
some hard
questions about
these containers!
I know that 1
cm3 of water
weights 1 gram.
I wonder how
much all this
water weighs?
How do you
change
millilitres to
Litres?
I think I know about
how many pints this is.
Handling data
• Estimate probabilities from experimental
data; understand that:
– if an experiment is repeated there may be,
and usually will be, different outcomes;
– increasing the number of times an experiment
is repeated generally leads to better estimates
of probability. .
I think all these
dice are unfair.
I don’t think you
can tell which one is
fair and which one
isn’t fair.
Here are the
results of my
experiments
I don’t even
understand
this table!
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