when we look at fractions especially when we look at junior often we like to start with
a book from grade three so these are pictures from uh hockey homework i believe
yep hockey homework from a grade three little book so when we get into mathology.ca you'll see that
you um everyone has access to kindergarten to grade six materials and
starting with a little book from grade three for a grade four class or even sometimes grade five is really helpful
because we can see that students can be very confident in seeing
things so let's just take a quick look at some of these pictures and lise what are some fractions
that you might think some of your students might see in there um
definitely the ones that the girls holding up so the the quarter ones with the the circles
the thirds they would get and then some of them would try and make fractions out of
like the blue and the paint or the blue and the yellow seats um
and the two-thirds and the well the ones that are actually written they would know as well
yeah and they would be looking at um things like the seats like in a set some
of them would be uh looking at the shapes and and partitioning them out into fractions as
well so this has a story but it also has a variety of ways of looking at fractions the way you want
students to start thinking about linear models set models lots of different ways of looking at
fractions so when we look at fractions whether they're
in mathology or whether it sparks ideas outside so this was um
oh we didn't get the date on that one it says 18 hours ago it wasn't 18 hours from today but i think it was around
march we might have been uh are you in ontario lease
i am yeah so we might have been at home at that point too and there's a lot of action going on
twitter and asking uh what do you hear see and use at home with fractions and
these are some uh things that some of the students came up with so whether it's actually using mathology or
sparking ideas from mythology there's lots of great things for students to work with
and one of the benefits of mathology k-9 it's actually built on a learning
progression learning progression is a set of 13 big ideas
and again the benefit as educators i don't have to study this little booklet of 13 big ideas
but rather as i work through the activities with my students i come to know what this learning
progression looks like so for example starting in grade four that's where they start to
compare and order whole numbers moving into that idea of fractions all the way to
the right hand side where this is grade six where they compare order and locate
positive rational numbers using flexible strategies so we can see that it becomes
much more complex as the grades go up and basically whether a student is
physically in grade four or they may be in grade six but at that level it helps a teacher move
the student along that continuum it doesn't matter what grade they're in so let's take a look at a few of the
activities and see how this learning progression actually builds from that idea of where they are
in grade four all the way up to where they are in grade six
so let's take a look at one of these activities and just if you can take a minute to
just read over the activity
and so if you were going to order fractions from least to greatest um where might you
start would you start with asha and put that on the line would you start with malik
and put that on the line if you think about some of your students keep in mind let's say one of your
students where might they start to put them on the number line
they would start with number one they would start with malik and why why do you think some of your
students would start with malik because they know that the one is the
the least is the lowest number and they would also recognize that all the denominators are
the same so that they know that they're when they're comparing they're comparing
the same thing yeah they're comparing all those things that belong within a unit
of 10 and so then they can easily say i'm looking at the top number basically
to determine 1 10 is smaller than 5 tenths would some of them start with 5 10 and
know that that is half of that number line or would they really kind of start at one or the other
end they'd most likely start one or the other end
my ones that are are quick and fast they just want to be efficient and get it done
um and they would just go in in order in sequence the ones that would have no clue how to
do this would just pick them randomly anyways
yeah they might just start with asha because ash is on the left and go and and plunk them in nearly willy but
using a strategy of like um that idea of starting when the
one-tenth is great because that gives you an estimate of how much space to two-tenths then that gives you how
much more space you have to move over to get to five-tenths and so it's it is a really good strategy
for them to build and so some might build that way some might know that five tenths is one half and be
able to partition it's easier to partition a smaller line than a bigger line
and so they might be able to do that more equitable and
so there's a variety of strategies to working with this but again some are more efficient than
others and you clearly articulated some would just be willy-nilly some would think aha
i'll start with one tenth and that will give me a better idea some would start with five tenths and no
i can partition five spots equally easier than i can partition 10 spots equally with my eye
right yeah and so um as they move from grade four they
start using different tools one is the number line tool but one uh is a fraction strip tool
and so for this activity if i can pull it up here i'm oops that's not going to help i need
to copy it here this is one of the virtual tools that is in mathology.ca
available to teachers and i just put it in the chat if you want to click on it
and so now when they come to comparing numbers with the same numerators that idea of using the number
line those strategies sometimes are a lot more difficult to know in your
head where these actually belong but by using the digital tool or by using
the math mat it's helpful for students to do
and so if i have the digital tool up i'm wondering please
now now where might your students start who would they start with
they would start with the tense they would go with the tense and so yeah because
the oh what they oh sorry i didn't i wasn't looking at your next question yeah yeah the new ones now with the new
one they would probably go with the eighths and then they would try and find um
equivalent fractions for the other ones yeah so the benefit of a tool like this is
i can go pick two eights and drag it out
and now i can pick it doesn't really matter which one i pick because oh they don't have to okay i
thought that they could only choose one no so we can compare them right because
they have to order from least to greatest so let's say let's say i pick two fifths next let's
do two fifths and i'm going to line them up at the left-hand side that's the only trick they need to know
right let's do two halves uh okay have i got two eighths i don't
have two fourths two-fourths i'm just going to plunk it up there
for now and then do i i've got too many screens open here two sixes let's just do one more two six
and so now i have to order them from lease to grace great so it's easy to do so there's my
least i can just visually look at them and start to understand visually
before i have to do computations to figure this out that i know that 2 8 are smaller than
2 6. and so using this over a number line
is probably a better strategy just because it's so easy to visually see and then
a a tool like this actually allows them to color in these particular
fractions and label them so this is a copy of a mathematic
which comes applicable in print so it's either for grade 3 4 or
5 6 and they come in a spiral bound um wipe
wipe wipe offable um set of a variety of tools like this and so
students can use them one-on-one or they can be working with pairs and use them like the digital tool but
now they can just have them right in their hands and start playing around with it and so this is just one of the tools
that's in that spiral bound kit or when we go into mathology.ca this could also be printed out for
students if that's needed so we get but it can they manipulate can
manipulate it online too right in that link that you sent me yeah so there's the whole set of digital tools
that is available to students
and as we get into grade 5 they start thinking about different ways
again like folding fractions and being able to compare and order
those fractions just by folding them and finding equivalent fractions so just by folding
into halves into fourths just to find equivalent fractions fold it again and it's easy to see
and easy to manipulate what those equivalent fractions are because these
are equivalent fractions that are easily doubled
and so the activities in themselves tactfully and visually allow students to
get a really good sense of the like the magnitude of these numbers how
big how small they are which ones are bigger which ones are smaller when we think about it that's how we started in kindergarten in
grade one with whole numbers so this is doing the same thing with fractions and giving kids similar
experiences for them to integrate that real idea of fractions
before they have to do computations with them and they don't have an idea in their head or they don't have a vision in their head
of how much that actually is and so as we go further into grade five
they start comparing with different denominators so here's another activity again this is asking for a number line
now that they've had all those experiences that yes they've got different
denominators different numerators here and here is where it's talking about use any materials you want to help so kids
would have access to the digital tools they'd have access to their math mats and they'd flip to the page or the tool
that is really going to help them best at this point because they've had experience with a lot of them
already and so you know moving forward there's things
like the number line where again they can start comparing now with different
denominators and be able to use that number line efficiently because they have a vision
of how much three sixes they know automatically it's half then they can partition off the other
things and they could start with a similar strategy in thinking about 7
8 is almost 1 or at the other end they might want to start with that number
that it's almost zero so now they've got some additional benchmarks that might help
them along the way because they're familiar with tools they're familiar with the number line
and can use it with i would say getting into more complex fractions
than one-fourth and one-half yeah right and now
for sure as grade five moves on in ontario they're starting to compare fractions greater than one
and again here it suggests use any materials you want to help but already grade four well from grade three grade
four and into grade five they've had the opportunity to use a variety of materials and they would be adaptive
being and efficient at being able to pick what is best going to help them because if they don't know these
fractions offhand like they know that 20 is bigger than 10
because they've had so much practice with it but they haven't had that much practice with numbers like this so they
need those tools to help them really visualize the the magnitude or the quantity of it
and then going into grade six here's an example of using things around the home using
a grid a hundreds grid that is a logical way to compare fractions decimals and
percents as you're working with numbers like that and again helping them to really conceptualize
using things they know groups of a hundred to really think
about how does that relate to fractions and to decimals and so this is where they get into those
flexible strategies so along the way in mathology to help
move students doesn't matter what grade they're in there is an assessment support with every lesson
that moves from the top left for this concept so this is the concept of exploring
fractions decimals and percents in grade six they might just start with partitioning
and partitioning and partitioning but they know that they actually have to get to really flexibly connecting
across those number systems of fractions decimals and percents but there's all these steps in between
and if we can help students move along those steps it's helpful and the next step button give us some
ideas of how to actually do that or what to prompt the students to actually move them along that
continuum so there's support in the actual activity built intentionally
and then there's support for educators and teachers as you're working with students
what is the student displaying to me and how might i help them move forward
in addition to so looking at those next steps that keep in mind as i'm planning for
the next day these are really great next steps as we move forward with our fraction
learning okay so we're going to get into mathology.ca
and i'm going to show you just the functionalities of quickly you know how you can search
it works the same way as kindergarten to grade three
i'll show you what's available for grade four to six kind of what's coming and
how that assessment tracker actually works so let's just get into mathology.ca here
i'll just do a quick i say quick but um it's never quick with
mathology. because there's so much in there so let's just
i headed up but let's just pull it up again i can close this one sorry about all
this jumping here but we'll get in
here we go i like the digital tools for junior because i find when we're in class they don't want to
use the manipulatives because they don't want their friends to see them using it so i really like the digital ones
because no one can see them using it then yeah and and sometimes as we move more towards
using digital or using manipulatives to represent and share share
their thinking as opposed to using the manipulative to solve the problem it changes the
perspective of the junior kids so i've i've had years in education's been a long time since i
taught grade six though um yeah i've more recently done the primary grades and so
when when we look at it and we say okay um can this pair uh
share your thinking of how you got to where you got to so instead of them just talking if they
could show me with the tile cubes or show the group with something then the other kids in the class are
like i get it right so it's when we we almost and then the students are using
it to do their thinking but it's for the purpose to actually share with other
kids it's easier for them to share their thinking when they've got something for the other kids to look at
as opposed to just talking about and moving numbers around on a chart sheet right um and then they sometimes
get into it so virtual tools are always a winner and i'll show you in a minute how we can get
there so the whole g dot ca is meant you can just search and find an activity if you
wanted if you're working on something i can just search there it brings me to
what i call my magic sorter and i'm just going to um
fine tune i'm just going to go to uh grade four i'm going to go to number
and i've got 13 results but i just want an activity and so i've got eight
results for fractions in grade four that generally are listed in the number
you would in the order you would generally teach it so that's one way of searching another
way of searching is let's say i'm thinking about a particular piece in the curriculum
i'm going to go to grade 4 again and i'm going to go to number and number sense and i'm still working
on those fractions maybe we're fairly early in fractions just representing fractions
and again there is my results for looking that way i can just
quickly go back to the home page and i can search by the learning progression as well by those big ideas
but one of the best ways to actually find what's available for your grade is to go up here to the top right to the
plan click all plans and what will happen is you'll see
three buckets kind of three squares in the bottom square are shared plans
which when you're new will be empty because you wouldn't have you're able to share plans between
colleagues but you might not have done that yet and in the middle bucket are sample plans so let's just go
to a grade 4 sample plan way currently it is being built as we speak so there
are some units in here for august back to school they will have all the units in here for the whole
curriculum the whole curriculum will be covered with these units so let's just take a look at a fraction
unit generally for grade four five six they
will start with a readiness task which is basically a simple task you can do with students
it's based on the previous year's expectations so you can kind of find out where they are with some of the big
ideas infractions as they move forward to grade five and decide you know do i need to dip back
to maybe a couple lessons in grade three for this week before i dive into two
weeks of grade four fractions it gives you that sense of kind of where they're at
and then here's the unit infractions and we can see just by the topics in grade four
they move from easy or early concepts on to more complex so we start
by counting unit fractions and then it's ending more in exploring
equivalent fractions and then the last activity is always usually some sort of consolidation type
activity so um let's take a look at i think i was going
to take a look at a different uh a different grade one than this one
but what grade do you want to look at for an activity grade four grade five grade six uh let's do six
okay so let's go back and let's do grade six
and i'm going to go fractions fractions decimals percents and integers so we can take a look
at one of the beginning ones representing comparing and ordering we
can take a look so all the lessons are built the same it starts with an about
uh it talks a little bit about the content background that students should have prior experience
with of course our curriculum and then where it actually appears on that learning progression
and then to the right where the students are moving towards so as a teacher that gives me a general
big picture and then all the goodies are found here in the lesson
so all the materials are at the front at right at the top that you might need the um suggested virtual
tools are selected at the top so here is our fraction strips another one is
considered as relational rods that you might want to use and again these are suggested within
the main plan there's a whole folder i'll show you where that is and you might choose something else
they're all written in a three-part lesson with differentiated support suggestions
right there one of the great things about great three enough there is
student facing material in other words these working on it are all written in
student-friendly language so it's easy to project it's easy for kids to see and
any visuals that where my cursor is an arrow right now but now it's turned to a
hand they are all their own projectibles so they're great for math conversations
or in back to school for each lesson there
will be a basic powerpoint that will be compiled
for the lesson so it's the student facing pieces like the visuals like the um working on it like
a guiding question and they will be available in a powerpoint button usually some i
don't i think it's going to go near the working on it but i'm not quite sure where that button will appear as well as a direct share to teams in
google classrooms so that if you want to share that powerpoint with students it's easy to just click the button and
away it goes each of the lessons have really great
prompts of what is it in the math that you're actually looking for you know especially
as you know we move into more depth with fractions in ontario or if we move into a new grade it's
really helpful to me if i had to go to a junior grade again i'm like uh what is it that
they're supposed to really learn here's the activity but what are they supposed to get out of it and when they're working
what are some things i might need to prompt them to and so here's a few questions that i might just put on a sticky note and have
ready handy for my lesson if it has any visuals like math maths
and stuff like that usually they will be found here in the images this one doesn't have one
for this lesson but every lesson has an exit ticket meaning one simple question that you can
ask students and get a sense of where they're at and it always has an extra practice
sheet that again you can download in word and take out questions change any of the
contexts of the questions add context to the questions but at least the math and the numbers
are there you don't have to do any thinking about that and that is go ahead i like the way that
they put the knowledge in understanding the communication so that um the kids know too what they're
working on i like that yeah again it works really well for ontario um
and it works really well for educators to kind of see if they you know take a look at what
kids did the day before where might i need to spend more time
and where might i need to spend less time so this practice sheet actually has
six six different questions so the next day i might decide well we
just need to do a couple of application questions so on the next
practice one for the next lesson i'm going to take out all the others and just keep these these application
questions so it's it just provides a lot of ways for
teachers to make it their own for their their kids and make it really applicable to where
their kids are at and so once we take a look at that they
might have done some activities here with this one um they're using relational rods and
they're asking to [Music] compare does he need more wood
is it long enough to then start thinking about the assessment of
the students and so this is something if you've got an ipad it's easy to
drag and drop your students with things that you're seeing if you're taking notes on binder paper
sticky notes it might be something you come back to at the end of the day and take a look at three or four of your kids
and just track them where they were so again the this is basically a section
of that learning progression that we went through from four to six students are starting at the top
left where they're starting to count to determine improper fractions and mixed
numbers all the way to the bottom right where they really fl
really really are flexible in connecting all those quantities across the number
systems of fractions decimals percents and grade six integers yeah
so there's lots of space in between to help move kids along but we know once they land in that last bucket
they have reached uh ontario expectations usually it's the last bucket or the last two two boxes that
are there yeah um and then there's a last tab
in grade one to three this is populated already for grade four to six this last
top will be researched over this year and will be populated over the course of the
year so if you go there you won't find anything right now and
then at the bottom there are related lessons within a similar unit that you can just click on
or it's as simple as going back to your most recent plan
and finding your next lesson there oops so this is um oh it's it's defaulted to
a different grade but you can see on the left hand side how many units will be there in grade six when it gets
solid um in august there's going to be a lot more there
and so that is just generally how you can find things the planning tool is a great
um oh i didn't that's why i didn't do it um a great tool to have because if i want to load
up a grade 6 plan right now i can't do anything with it i can't move anything or
anything but if i say use the sample plan
what happens is now it actually becomes a tool i can use as a teacher
in that i might decide to do financial literacy
before i do fractions so i just might move it up in the year i might decide um i'm doing financial
literacy this is grade six but i want to put some number sense in there a lot of
districts are spiraling the curriculum and putting things together so i'm going to go into the number
strand and i'm going to look at the activities and i can take a look at the type of
lessons that are here the unit is always the first so these are number relationships
if i scroll down i've got fractions and decimals and i there's some financial literacy so
when it gets going there's going to be i don't know six or eight different number units but i might
want some work with bigger numbers in this unit i just click it and pop it in
and it becomes my plan i can even add in non-mathology lessons so if i've
got some google powerpoints or i've got youtube videos i just click this button on the bottom
add non-mathology lessons and they land right here in my sorter with an icon
and so this is a math game website i really liked and so i can put that and my url is
right there i can just click it and it's ready to go projectable up on the screen ready to play with the students
so this is a great tool to use and then if you want once you get it planned you
might want to print it out and you can just export it to a document and then you've got it printed
you might want to share it with a colleague it's just a great way
to work through that and then once that you're comfortable with the planning and using some of the activities and
readiness tasks there's the whole analytic tool that actually
compiles all the things that you've dragged and dropped from the lesson
and here's austin and it gives me a lot of information of where he's on track
where he might need attention clicking the green buttons allows me to look for more goals
i'm just saying i know i know this is my little too late
this is my grade two class that i had high hopes for to yeah yeah my son is a
die hard leafs fan and uh uh i haven't heard from him since he
gave us his picture of i'm already or he said we're all ready they have two dogs and so they had the
kerchiefs on he had his his big hockey jersey on but no no it wasn't to be this year but
he says not yet maybe next year so and it just allows this analytic tool kind of goes
on and on uh for a lot of ways and just really allows a lot of that tracking over time
and helping with report cards and all that kind of stuff
so as you can see there is a lot of great stuff in here and with the planning and
the analytic tool it just makes things a lot more efficient i just wish i had
this when i taught grade two it would have made my life so much
easier yeah yeah it's it's kind of like searching on
google or pinterest for stuff but you know it's related to your curriculum you know it's going
to be engaging you know the line masters are all there the digital tools are all there it is
just great so when we look at
the way it's actually working that yes these are different grades but
just by doing the activities with kids especially if the whole division is
working similarly we know that we're moving kids along this
this math ideas and big ideas so we've taken a look at um
there's the idea you can use readiness tasks at the beginning of a unit so that it's more about what does the student
know not what the student not know so that you as a teacher can plan accordingly or dip back
into the previous grade for a couple of lessons the interactive tools are at your fingertips
there's the print versions of the mathmats that are available for grade three to six and then of course
everything is in mathology.ca for four to six so um patty do you just want to quickly
talk about the next slide or two just um in case lisa's people she needs to send
information to oh certainly thanks kim so um with mathology.ca you have a
choice between a one-year license that has all grades in it from k to six
or a five-year license and uh right now when you purchase a one-year license is
175 and you have all those grades inside or a five-year license is 665.
depending on which one you choose um this spring you actually um get a lot more
uh discounts on the print components and then for four five and six the print components are those math nuts that you
saw in the lessons that um kim showed earlier tonight so yeah buy a one-year license uh 15
off of the math mats and if it's a five-year license it's 25 off and then
in addition when we work with districts we also provide um professional services in the terms of
webinars or ongoing coaching uh support
and we've got lots happening on twitter and uh you can just follow at mathology at
pearson mathology one and you can start seeing what teachers are using and how they're mixing and matching
things that they already have and know so we have that community we have a
facebook community that's kind of teachers helping teachers those that are currently working with mathology and
again they're posting information there and sharing their learning there and uh there is a
30-day trial if you uh currently don't have a subscription and want to take a look
you can just go to pearson mathology.ca and click up click on for the 30-day trial and it's
yours to use um one thing um i didn't
show but in the sample plans there is a grab and grow folder and so if you when you click that
on you will see a couple of the the lessons and things we highlighted today
from each of the junior grades 456 and also at the very top of that folder
you'll see the interactive tool folder that has all the interactive tools that you can just click on the url and share
with your students so the grab and go is kind of a neat thing if you want to do a 30-day trial
and try something in the next little while they're just ready to go
perfect and so just curious on you and any comments or questions you
might have