If you have been listening for a while, you know my wheelhouse is early elementary math,
but recently I've been working a lot with third grade math specifically in early multiplication,
so arrays, equal groups, and I thought that I would share some of the stuff that I have been
working on and maybe it'll be helpful to you too. Specifically when it comes to working with
students who may have a hard time grasping or understanding ideas of multiplication and with
language learners. Hello and welcome to Making Number Sense Make Sense, a podcast for elementary
teachers, specifically early elementary teachers, looking to really make an impact in the number
sense of their students. Something that I feel that can be really challenging when working with
arrays is just the vocabulary of a row and a column. It's kind of hard concept to understand
and especially since row is a homonym, like you can have a row of seats but you can also row your
boat. And if you are a language learner and you're starting to learn English, what would be the way
that you would think of that word most commonly? A row of items or like row your boat, especially
if it's a song that they're hearing a lot younger kids, it can be kind of tricky. Same thing for a
column, it's just like what does this word mean that's equal representations. So I think that's
something that you can really kind of focus on like which ways the rows go and which ways the
columns go. That and also that you can have two arrays that have the same product, that have the
same expression or equation can also be kind of tricky. I feel like the way or a way to really
support students and understanding that is hands-on and something that I notice as kids get
older is they start to do kind of math centers less. And sometimes I wonder about that because
when working with younger kids, center time is their absolute favorite time. Now there has been
back and forth of centers, like if students are not doing it correctly then what are they really
learning? But I think especially if you're working with like second grade, third grade, the opportunity
to work with different mathematical concepts in that way and just kind of have the opportunity
to play with the math can be really helpful in making the concepts feel more tangible and more
like things that are accessible to them versus so abstract. So I came up with some center ideas that
are kind of similar to what I've created or used in the past with younger kids and just kind of
switched the subject and have the similar concepts. So we're not reinventing the wheel,
we're just making it work for the grades that we're at. So the first one is roll an array treasure
hunt. So using dice which I love, using a hundreds chart mat which I also love, it doesn't have the
actual numbers on it but basically students would roll two die and then that would be the numbers
that they're multiplying together. They would have to draw an array on their work mat that would be
the product of the two numbers that they rolled. And now the way you kind of take it up here is
there's three different versions of this game. In the first one there are coins all over the map,
so what their goal is is to make sure that their arrays can cover as many coins as possible
and then at the end the person who has the most coins in their arrays is the winner. The second
version is roll an array but collect the treasure and so this one has coins but it also has gems,
it has treasure chests and they have different values. So your kids are going to be really
creative and thinking about okay how can I put my array, do I need to make it the long way, do I need
to make it horizontal, do I need to make it vertical, that it can cover the most space so I can get the
points for the treasure or I can get the points for the gem. And again this kind of is helpful
for the concept of an array can be vertical or horizontal and still represent the same thing
because they're really trying to figure out how to make that work for them. And the last one is
roll an array and avoid the traps. So in this one they're trying to avoid different spots on the
mat instead of trying to cover them. So again they're going to have to be creative with how they
fit their arrays to not lose all of their gems or all of their points if they hit one of the traps.
So that was roll an array treasure hunt three ways. The next is spin multiply and find the expression.
In this game they have a spinner that has an array for each kind of set of number facts. So it's like
two by two, two by three, two by four, two by five and so the students would spin and then on either
side the expressions are written both ways. So it might say two times three and also three times two.
So then your students would color in and your kids would mark off if they got that array and see if
they can get it again. So that again forces them to think about the arrays being vertical or horizontal
or two expressions can represent the same array. The next one is array pick build and cover. So
students pick up an expression card and represent it on the work mat. So for this one they have a
large space to work with so you will need a lot of manipulatives for this to make it work. So they'd
pick an expression say they had five times six and then they would actually build an array that shows
five rows and six columns five times six and then cover the product on the work mat until they can
cover all of them. So it helps students work on their math facts, helps them kind of build arrays
and really get that hands-on experience with building them for a purpose. The next game is
more about multiplication facts than arrays but it still kind of works in the same wheelhouse in
the same family. Empty the board multiplication or multiplication facts they would have either one die
or two dice and if they had two dice they would add those together and that's the number that
they're going to multiply by the target number. So for example if they rolled a two and a six
that would be eight. If the board they're working on is the nine facts multiplication board then
they would multiply eight by nine and then remove one cube from where the product is. So the setup
of this game is they have their mat with their target number on it so they're working on nines
facts or they're working on five facts and they would put a cube in each space that's available
and on the bottom it has the product of these multiplication facts. So they roll the die to
get the number that they're multiplying the target number by and then they would take off a cube if
they rolled that number that makes that product and they would continue until their board is empty.
So again they're getting a lot of practice with multiplication especially in a kind of target
number but in a different way than just doing drills or flashcards. And if doing all 12 numbers
is a bit intimidating you can also just start with one die and multiply your target number by one
through six before moving to one through 12. And next is an array thinking task. Now if you have
tried the escaping ants task that's more of an equal groups task than an array task but I have
seen students without prompting even kindergarten students without me showing them how to create
an array created an array on their own to represent what they were doing. So that's a great way to
kind of bridge equal groups repeated addition and multiplication together. Or if you're
looking for something a little more challenging you can work on this bake sale array task. So
basically in this task the students are baking cookies for a bake sale and they have to figure
out how many trays they'll need to have enough for the bake sale. So that task has an unknown
factor included into it to make it a little more challenging but still has you know thin slicing
questions as well as check your understanding questions as well as the opportunity to create
their meaningful notes. So there's lots of versions of notes that they can use. One that has their
that's broken up into quadrants so in their first quadrant and be kind of a fill in the blank.
Their second quadrant can be kind of a worked example that they write or there's versions that
have a worked example already there. And then the other two is where they can choose to write down
things that they think will be important for them to remember. And in the last one they can kind of
look around to see what other students were doing and see if there's a different strategy that they
really like that another student used. Using notes in the older grades so third grade fourth grade
even second grade really can be helpful for them to solidify their learning and understanding. I
wouldn't necessarily do notes for kinder at the beginning of the year but probably midway through
they can start to kind of create their own notes or their own rememberings. So I hope that that
gave you some ideas about working with arrays and early multiplication with your students.
Let me know if you give any of them a try and I will talk to you next time.