Marian Small
June 2017
What could inquiry in math look like?
It could be inquiry into the world using
math.
It could be purely math inquiry.
We will look at both at primary and
junior levels.
People talk about things called giant
steps and things called baby steps.
How “big” or “long” do you think a giant
step or baby step is?
How many baby steps would make a
giant step?
This leads to students realizing that a
measurement value is big for one of two
reasons (or both).
The unit used is small AND/OR the object
being measured is big.
Kids could investigate:
Sizes of different animal’s footprints vs
pawprints
“ratio” of hand size to foot size for people
and various animals
The relationships between various
measurement units and how knowing
about one unit allows you to predict
results with another unit
What are typical hair lengths (in cm) for
various age, cultures?
What is long hair in those cultures at
those ages?
If a traffic jam was reported and it said
that 100 cars were at a standstill, what
distance would that cover?
How long must parking spaces be? How
about the width of the “lanes” between
them?
How wide do streets need to be to allow
parking on one side and two-way traffic,
parking on both sides and one-way
traffic, etc.?
How much paper does a school typically
go through in a year?
How can you find out?
How big a space (in cubic metres or
cubic kilometres) would you need to hold
ALL the people in PEI?
How much sand is usually needed to fill a
sand area at a public park?
How much faster is it to fly than drive to
….?
How many sections are in a typical
grapefruit?
What is the range?
How big is an Ipad screen compared to a
cell phone screen? A TV screen? A laptop
screen?
What about an Ipad mini?
How many windows does a typical
skycraper have?
How could you predict without being
there and counting every window?
How much slower is traffic during rush
hour?
We can pose all kinds of things kids
could inquire about in math.
Some might come to you as you watch
them play, but some will be more
deliberately selected to bring some
ideas to kids’ attention.
Kids in K might be playing on a walk=on
number line.
You could ask them for different ways to
get to, e.g. 10.
Or you could pose a problem like this:
You were standing on the number line at
5.
You went forward some and then back
some and you ended up at 7.
How far forward and back MIGHT you
have gone?
What if you did it twice (same forward
and back combination twice)?
If you started at 5 and ended at 11, what
might you have done?
You notice kids are playing with square
tiles making designs.
You could take it to this problem.
 You made a design that had ALMOST half
red tiles.
What could it look like?
OR
You had some red tiles.
You had one more blue tile than red.
You had two more greens than blues.
How many tiles could you have used?
Choose a number of counters, but more
than 20.
 Can you make 3 equal piles with it?
 Can you make 2 piles, one double the
size of the other?
 Can you make 3 piles, one double the
size of another?
Students make some structures with
linking cubes.
You have them put them out and then ask
how to rebuild every structure so it is
upside down
OR so it has only one face the same as it
used to look and all the others different.
You might investigate what a structure
could look like if the top looked like this:
You might fold a piece of paper in half or
fourths or eighths and hole punch and
predict what you will see when you open
it.
Kids might be adding and subtracting
numbers and you might ask any of these
questions:
You choose two numbers.
The answer when you add is twice as
much as the answer when you subtract.
What could they be?
What do you notice?
You choose two numbers.
You add a number to another one. The
answer is about triple the smaller
number.
What numbers might you have added?
What do you notice?
You choose two numbers.
The answer when you add is 10 more
than the answer when you subtract.
What could the numbers be?
You can add 3 numbers in a row and get
the number 74.
You can add 4 numbers in a row and get
the number 74.
You can add 5 numbers in a row and get
the number 75.
1. It is possible to show the number 534
with 21 base ten blocks.
2. It is possible to show the number 121
with 13 base ten blocks.
3. It is possible to show the number 1048
with 23 base ten blocks.
You multiply two numbers and the tens
digit is 1 more than the ones digit.
What numbers might you have
multiplied?
You might notice that 2/3 > 1/5 and that 2
and 3 are closer together than 1 and 5.
So the inquiry focuses on--- If the
numerator and denominator are closer
together, is the fraction always greater?
You might wonder if when you add 5 to a
numerator and 5 to a denominator, the
fraction gets bigger or smaller or stays
the same.
You might wonder– can the numerator
and denominator of a fraction equivalent
to 2/5 be 100 apart?
90 apart?
Is it possible to show the same amount of
money with 8 coins as with 20 coins?
How?
If you paid for something with a $20 bill
and you get 1 bill and 4 coins back, how
much might it have cost?
If you cut a rectangle on a line of
symmetry and only use half the
rectangle, what fraction of the old
perimeter can the new perimeter be?
A rectangle has a perimeter 3 times its
length.
What could the length and width be?
Graham Fletcher examples
https://gfletchy.com/paper-cut/
https://gfletchy.com/graham-cracker/
What kind of inquiries can you put
together while I’m still here to support
you?
www.onetwoinfinity.ca
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