Transcript Year 7 Level 4 Probing Questions Version A

What do
you think?
Using Probing Questions in
Mathematics lessons
Year 7
Level 4
Assessment Criteria
Click on a link to Jump to the Assessment
Criteria you are looking for.
Assessment Criteria for Year 7 Level 4
• Using and applying mathematics to
solve problems
• Numbers and the number system
• Calculations
• Shape, space and measures
• Handling data
Using and applying mathematics to solve
problems
• Solve word problems and investigate in a
range of contexts: number, algebra,
shape, space and measures, and handling
data.
I wonder how
many addition
signs I should
put in?
Put some addition
signs between digits
987654321 to get a
total of 99?
I’m going to try to put
addition signs between
every number!
9+8+7+6+5+4+3+2+1
I wonder if it’s
going to be odd
or even?
What’s an
integer?
If you begin with a
one digit integer,
multiply by 3, add 8,
divide by 2 and
subtract 6, you
will get the integer
back. What’s the
number?
Is it going to be
more than 10?
I think I can
work
backwards!
How many
sides does a
pentagon
have?
What does
“regular”
mean?
If every vertex of a
regular pentagon is
connected to every
other vertex, how
many triangles
are formed?
What’s a
vertex again?
I think I’ll
draw it first!
I wonder how many
combinations of double
scoop cones you could
get?
Does having the
same flavour
twice count?
Ice Cream Flavours
Vanilla
Maple
Chocolate
Rum Raison
Strawberry
Toffee
How do those
guys think up
those
questions?
Numbers and The Number System
• Multiply & divide any positive integer up to 10 000
by 10 or 100 and understand the effect.
• Compare and order a mixed set of numbers or
measurements with up to three decimal places.
• Recognise and use multiples and factors and
primes; use simple tests of divisibility.
• Multiply a fraction by an integer.
• Understand percentage as the number of parts in
every 100 and find simple percentages of small
whole-number quantities.
Why’s that,
then?
Hey, Look!
30 ÷ 10 gives the
same answer as
300 ÷ 100.
I wonder if it
works for
multiplying
too?
I bet I can find
some other
ones as well!
I think 3.146 is a
number that is
between these?
3.14
What if these
numbers are
pounds and
pence?
I think 3.146
is closer to
3.14
and 3.15
How do you guys know
this?
Doesn’t every
number have
an infinite
number of
factors?
You must have
made a mistake,
because every
number has an
even number of
factors
I found a number
that has 3
factors!
I bet your number is a
prime number.
Could your
number end in
a 5?
Don’t you need a
calculator for
that?
I can find any
number bigger
than 500 that is
divisible by 3!
Tell me your number
and I’ll tell you if it’s
also divisible by 6!
I can tell if you can find
1
of other amounts.
8
£72
Could you
1 find
3
of it?
I can find
1
of that!
8
One eighth of 72…
Hmm. Where’s the
button for “of”?
I need an easy
way to work out
VAT.
Finding 10% is
easy!
Was £240
Now 20%
Off
To find 20% all you
have to do is divide
by 20!
Calculations
• Calculate mentally a difference such as 8006 2993.
• Recall multiplication facts to 10 x 10 and derive
associated division facts.
• Add and subtract decimals using written
methods.
• Use written methods to calculate HTU x U and
HTU ÷ U.
• Check whether a result is the right order of
magnitude.
I think I can do it easily
without a calculator.
8006 – 2993?
This is really hard! I
think I need a
calculator.
How can you tell if
there’s a short way of
doing it in your head?
I wonder if you
could use facts
from other
timestables?
I forgot my 8
timestables. How
can I work them
out?
Did you know that 4
X 7 = 28? That could
help.
I can see you made at
least one mistake.
There!
That should
do it!
How did she know
there was
something wrong?
What numbers did you
multiply to get the 7?
I think I got this
right. I wonder how
I could check to
see if it’s correct?
I like the grid method
of doing multiplying.
Would you like to see
it?
I think I have
enough
money for 8.
I think 8 will
cost more
than £4.
Shape, Space and Measures
• Recognise and visualise the
transformation and symmetry of 2-D
shapes including reflection in given mirror
lines, and line symmetry.
• Read and interpret scales on a range of
measuring equipment.
• Understand area measured in square
centimetres (cm2).
• Read and plot coordinates in the first
quadrant.
I don’t have a
mirror – could I
use tracing
paper?
I can reflect any
object in a line of
symmetry if I have
a mirror
Let me see you do this
one – it’s really hard!
I don’t need any
equipment at all!
What’s the first
thing I should
look for?
How can I decide
what each division
is?
I can’t decide. Is
the area of the
front cover 100
cm2, 600 cm2 or
6000 cm2?
What other shapes
could be measured in
square centimetres?
Why do you think it’s
any of them at all?
I wonder why
are there two
numbers?
How do I read
the scales?
We’re supposed to
put an “X” on the
point (2, 5).
Which way is the first
number again?
Handling data
• Solve a problem by representing,
extracting and interpreting data in
tables, graphs and charts.
• Calculate statistics for small sets of
discrete data:
– find the mode, median and range;
– calculate the mean in simple cases.
I wonder what kind
of questions the
teacher is going to
ask about this
stuff?
This looks really hard.
I think these
questions will be
easy!
I can think of 5
numbers that have
a mode of 10
How are
they
working
these out?
Mean
Median
Mode
Range
I can think of five
numbers that have a
mode of 10 and a
range of 8.
I can think of five numbers
that have a range of 8 and a
mean of 6.
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