Mrs. Starko's Daily Math Routines

Introduction:    

 I am currently teaching two very different kindergarten classes.  My morning class has 23 children in it.  There are more boys than girls, there are 8 girls.  I have some very young children who have never had a school experience before.  This resulted in some of the children having difficulties adjusting to the school environment.  I remember the first group time we had, I had to very gently turn about 15 bodies around to face me so that they could actually see what was going on.   We also have a student who is learning English as a second language.   The group has come together well when exploring a common interest in snakes. 

My PM class has 17 children in it.  There are 6 girls in this class.  They form a very compassionate group, who help each other out, as well as, support and share ideas with one another.  They were very school oriented from the start. 

Before I can describe the math events in the classroom I need to provide an over view of the philosophy behind my classroom environment and how the room contributes to the kind of learning I want to happen there. 

All subject matter be it language arts, math or science is integrated into all parts of our day.  The children's interests and activities are often used to guide curriculum.  The majority of the curriculum in not planned out by the month necessarily.  Instead, children's interests and ideas are incorporated into our curriculum to become a negotiated or emergent curriculum. 

While the skill content of the math area can mapped out somewhat, the learning connections and opportunities can be influenced again by the children at hand.  Topics are introduced, worked on, revisited and reflected upon often.  Skills are often taught as needed to help the children accomplish work they are doing involving a project.  For example, last year the children were running a dig site out of our classroom dinosaur museum. They wanted to open a store and sell tickets to the dig site.  They already knew how to record numbers to 100, count by two's and by 10's.  When this counting was extended to the toonies, and ten dollar bills they were very excited.  They then demanded to learn how to count by 5's and 25's to accommodate the quarters and $5.00 bills.

There is a math area that expands and contracts or moves when necessary to accommodate ongoing activities.  The tables are set up in such a way as to encourage group, or social learning.  I want the children sharing, planning, working together, so I expect them to talk and help one another.  Whenever possible I want the children to be actively involved and have to produce their own work.  In other words, relationships are important, encouraged and supported.

I always try to begin with the oral first.  Songs, poems, rhymes, actions first, then the visual symbol behind what we are doing.  It makes for a much smoother transition.  Addition, subtraction, multiplication and division are taught through action and story.  Then number sentences are introduced for + , -,  =, x, etc. 

Math must be connected to their lives or interests in some way.  Numbers and processes have to become real to the children.  They need to make connections from the skills they learn, to their application of them, in situations that are real for them , that solve their problems or  help them realize an intent. 

I believe in the potential of the children.  They are capable and full of possibilities.  I trust that they will learn, make connections and be motivated to try as they become actively involved in their learning.  This trust means I must listen, many more times  than I talk.  I must observe and try to  understand what and  how they are thinking.  I must also provide scaffolding to the next levels and encourage them to stretch, while working along side of them as we co-construct our learning field.  I believe in the construction model of learning.

September:

I do begin each September in much the same way as far as math skills go.  I begin with shapes.  I combine this with the idea of drawing lines and introducing a wide variety of drawing materials to help the children produce them.   They are also introduced to our junk collection and making collages.   

We began with a home, school connection first.  The children collected a variety of natural objects that they brought into the classroom to share.

We did math when we sorted and classified these materials and shared stories with one another.  Natural shapes were easiest to compare and start talking about.  This then led to our look at the circle, square, circle, triangle and oval. 

Shel Silverstein has a wonderful poem entitled shapes that outline the shapes and help the children to learn them.  Hap Palmer has a song on his cassette entitled Circle, Triangle and Square, that also helps with the names of the shapes.

Silverstein's poem:                         Shapes

A square was sitting quietly beside his rectangular shack.                              When a triangle came down kerplop and struck him in the back.                           "I must go to the hospital," cried the wounded square.
So a passing rolling circle picked him up and took him there. 

Now,  my class wanted to include the oval in this and we came up with:

Where Dr. Oval stitched him up with care.

We act out this poem over and over and over again, they love it.  Then we share it with the school.  We go on scavenger hunts and we finally try to create these shapes, and even to cut them out.  This is where we learn about corners, and parallel lines.    We then put many shapes together in a collage and we create a real picture from them, complete with a story.  We return to shapes and categorize them later.  3 D shapes enter the sand and water table to allow for measures of quantity.  We notice shapes in everything, our doors, clocks, etc.  We draw them with skinny felts, thick ones, in paint making designs like the great artists, Miro, Kandinsky, and Picasso.  We work with oil pastels, and water colour pencils.  We literally explore using shapes as a base. 

 

September:
When beginning classes in September there are two very important words in the classroom that I emphasize.  The first is relationships as that is what is being developed and the second is exploration.  Exploration in the math area means there are:

-number puzzles the children can play with
-wooden numbers and pegs that fit into them  (0 - 10)
-vinyl mats with holes that the pegs fit into ( 0 - 10)
- metal board with magnetic pieces all having to do with the sea
- shapes and cards that the children can create pictures using the shapes, using triangles, squares,                                                                                                
hexagons, trapezoids, etc.
- geo- boards with rubber bands to create many shape designs on  
- scale to balance and objects to put into it.  Actually, this year this was in our sunflower seed table
- colored cellophane shapes on the light table for exploration, and natural shapes
- individual magnetic/write and wipe (dry erase ) boards from Staples with magnetic numbers and number cards to write with - 3 on the table.  I have enough for 7 children and am working my way to 10.
- shapes and color shapes for sorting and classifying.  Name my group activities.  These are done in the morning when the children come in and put their name tags in the pocket charts.  I will have a shape or object to classify and they will bring it to the carpet and decide which group to put it in and they will also have to tell me my rule, or why they put it where they do.  

We explore the room, the centres and talk a lot about shapes we are seeing beginning in this first month of school and into October.

Along with this I build into the program the oral part of number.  We begin with rhymes like:

5 Fat Sausages Sizzling in the pan.  Sizzle, sizzle, sizzle, sizzle, sizzle, sizzle, pop. Until we get to 0.

5 Fat Peas in a pea-pod pressed.  One grew , two grew and so did all the rest. They and grew and they grew and they did not stop, until one day they all went pop.  

One elephant went out to play, on a spider's web one day.  She had such enormous fun, that she called on another elephant to come (Lois and Bram song).

We do a lot of oral counting at this time any chance we get.  Before I introduce the numbers I want them them to hear the numbers over and over again.  

Then toward the end of September I begin to introduce the number characters as if they were guests coming into the classroom.  I give them one or two at a time.  Inie Graham gave me the following list of number names, I use these and turn them into a book that goes home in December.  I like them because the numbers are introduced by the writing of them.  I prefer having the children construct the numbers in this way, playing with them in a sense by creating them.  
0  - zero the hero.
1 - one is fun.
2 - around and back on a railway track.
3- around a tree, around a tree, that's the way we make a three.
4 - down and across, and down once more, that's the way to make a four.
5 - down the street and around the corner, oops I forgot my hat.
6 - make a loop, add a hoop.
7 - across the sky and down from heaven, that's the way to make a seven.
8 - make an S and don't be late, go back up and shut the gate.
9-  make a hoop, add a line, that's the way to make a nine.
10 -  one is fun and zero the hero make 10 and now my book comes to an end.

Each of the verses is easily learned and help the children remember how to construct the number.  If a child needs a number we refer to them by saying, three, that's around a tree, around a tree, and the child can usually construct the number from there.

I usually work my way to 5 and really practice those to mastery by Halloween. I make sure the children are picking this up in centres or small groups.  

-  number puzzles to 5 with shapes that punch out and have to be put back together.  Card games and more number songs that we record.

By October we have added:

Songs,
3 Crows sat upon a wall, sat upon a wall, sat upon a wall.  3 Crows sat upon a wall on a cold and  frosty morning.  One crow flew away.  2 crows sat upon a wall, etc. We do this with our fingers.

Charlotte Diamond's  5 Little Sparrows sitting on the wire.  We act this out in  two ways.  One I have a glove with the little sparrow felt pieces that go onto it, and we also act this out using children, who sing their sparrow parts.

5 Little Pumpkins -  Raffi version.  We like the wind part and we act this out all the time before and after Halloween.

This is where we begin to play with 3 D shapes as well and we start to use the spacial transformation terms, like before, in front of, in between, behind, above, below.  We do this with shapes and each other orally in groups or acted out.  3 D shapes are at the sand and water tables and we note shapes of our small blocks and their relationship to each other.  The half blocks, half circles, etc.

Ordinal numbers comes in here too.  We talk about the 1st bird and go over their singing part, the 2nd pumpkin, the 3rd pumpkin says ...  and I ask them who is the 1st pumpkin, 4th pumpkin/bird, etc. We go over this a lot.  

Now, I need to explain how I begin at this time talking about the idea of plus and minus or take away stories.  When we do our number poems, rhymes and songs, we act them out with our fingers, or bodies etc.  Then I ask the children are we taking away something, or adding/ putting groups together.  We use terms like how many  are left?   How many altogether?   By this time most of the children can tell me whether or not I have a plus or take away story.   Later on I will introduce the plus and take away signs and then show them the number sentences they are already giving me with later poems and stories.   What I am doing now is laying the oral foundation for addition and subtraction.  I am teaching the movement of adding to and taking away with their bodies and hands.  They can feel and see what these actions do.  This is very important as they can truly understand the process this way.  Pretty soon in their own stories during writer's workshop, especially the eating stories the children will begin to tell me, "This is a take away story, Mrs. Starko".    

By the end of this month I want the majority of the children to have a firm grip on quantity of number to 5 and be able to produce those numbers during their play time.  During writer's workshop then we have fun working with and producing numbers and stories.  They should also be able to name and draw the 5 shapes we looked at.  A few will have trouble with rectangle and triangle but by the end of November all the children have usually mastered these.

Friday, Jan. 18, 2002

1st group time:  review math concepts working on orally.

- pattern of actions is done.  Clap, clap, clap, touch the floor, touch the floor.  My helpers for the day must convert this into a repeating pattern using unifix cubes for now. 

- deck of large cards.  Two help up at a time, they say 10 is greater than 7 and I put the cards on the right or left side of me.  Children on the right side get the group if it is greater, children on the left side if I happen to have the larger card on the left.  They play this with dice and cards during center time.

- counting on orally first...   get it going 0, 12345  get it going from 7...  8,9, 10, 11 then from dominoes.  We look at one side which has 6 say and then the other.  I ask them how many all together?   We start with 6 and count on the bottom for our answer.  We then repeat the problem 6+3 = 9.  We do not write anything at this time.

Review counting by 10's

Began work with counting by 2's on Monday of January 15th.  I have a tricky question for you this morning/PM.  Watch carefully.  One bicycle goes whizzing by, how many wheels do you spy?   

2 bicycles go whizzing by how many wheels do you spy?  4 
3 bicycles go whizzing by how many wheels do you spy?6
4 bicycles go whizzing by how many wheels do you spy?8 
5 bicycles go whizzing by how many wheels do you spy? 10

Today we quickly review this and then we do something new.

I go clap, clap, clap, slap, slap, slap  One and two and here we go. (With my fingers using both hands, I hold up first my two index fingers, then middle fingers, then ring fingers etc.)  2, 4, 6, 8, 10 counting by two's out loud.  The children count with me now.  Then I go on to our new rhyme.

      10 Fat Sausages

10 fat sausages frying in the pan     
One went pop and the other went bang.
(I say 4 plus 4 as I have now put both thumbs down)  children say 8 and we count to make sure.

8 fat sausages frying in the pan, one went pop, and the other went bang (little fingers go down).

3 plus 3 equals  6 fat sausages frying in the pan, one went pop and the other went bang.  Keep going to 0. 

I then ask the children if this is a plus or minus story.  They tell me without hesitation that this is a minus story. 

This ends our math review and the following story comes from my morning class, which I hope illustrates how observation and collaboration help to further skill learning.

Today the helpers go to make patterns, only I get requests from 4 other children who want to work both independently and together to create repeating patterns as well.  They begin to work on these while the other children are moving to chosen areas for centre time.  After working with  a group and paint, I return to the carpet and R stops me.  He hands me his unifix cube pattern blocks.  I notice immediately that he has not quite got the concept of a repeating pattern for in actual fact he hands me a cube of black, black, brown, red, yellow, blue, green, yellow, red and a number top, he proudly proclaims as the stop sign or period.

I congratulate him on his work and then I pose a question to get him to explain his idea and maybe see the discrepancy in his design.  He begins to explain his pattern is touch my nose, touch my nose, clap my hands.  Touch my nose, touch my nose, clap my hands.  That is a great pattern I tell him and  then I ask him to show me that part on his stick.  He begins to say black, black, brown and then stops.  He sees the problem and looks at me and says, wait.  I ask him if he would like to change something.  He begins to dig for the black and brown cubes and reconstructs the rest of his chain, again remembering to put on his stop sign.  He has solved a discrepancy from his intended pattern of nose and hands and the design, he had originally created.  By having to revisit and explain his idea, he was able to take the step from design to repeating pattern. 

     In this case R was ready to take this step.  Another student may not have seen the discrepancy and this would just say to me that more practice would come in other forms for this one.  Because the children are now opting to make patterns and requesting to do so, I have added this centre to my others.  I have placed strips of paper, junk materials, and glue in the math area.  There are also beads, with yarn to make repeating necklaces with. 

The children will be creating patterns together using these materials and then sharing their efforts.  We have decided to call repeating patterns that, and the other , like R's first attempt, designs.  Observation and conversations are so important in designing curriculum at this age.  

To encourage numbers from 10 to 20  the new Leap Frog battery run number games is out with the cards and the black and white dice mentioned above.

Individual magnetic boards are there with erase pens and magnetic numbers to write and play with.  We are getting very close to introducing the + and - and = signs.  The leap frog game board is the most popular.  Children are always here using it.  I bought mine at Toys R Us for about 40.00 dollars.

During centre time we are measuring swords, daggers, and shields and drawing these on cardboard and then cutting them out.  We use a tape measure and talk about length.  IN the PM class we have weighed and measured bones in a dinosaur dig.  We label these as 6 cm and the weight as 3 kubz.

Jan. 22, 2002

Our math section of our morning was a very homey gathering this morning. We began by counting all the way to 25 in portions. Let's go from 7, let's count from 10, 15, etc. We counted by 10's and I asked the children if I wanted to write any number that begins with sixty _, what would my number begin with? They answered 6. We did examples for eighty, fourty, ninety, and they answered these. Some filled in the correct number. Now they can do this as a group, collaborative effort, but not individually yet. 

Therefore I keep the work oral and supported by the group until we are ready to do this. Next step, they will write big numbers.

Something unexpected and fun for us came up as we were counting by 2's. We began a cheer. 2, 4, 6, 8, who do we appreciate? Then we would give a student's name and cheer for them. Of course everyone had to have a turn and boy did we practice counting to 8 by 2's. It was fun. 

We read a scholastic book entitled Patterns. It presents a repeating pattern using a variety of animals on a two page spread and the children have to tell what would come next. Our pattern today was touch my shoulder 4 times and 1 clap. They had no trouble putting these together.

Popular Math Centres today:

-Pooh math CD was popular today as the children were doing the calendar one where they write the numbers.
-a variety of pattern centres are out, what the children chose to do was to create necklaces. They began stringing colored macaroni onto yarn in repeating patterns. We shared these at our second group time. Even the boys made them and the girls added bracelets.

A MATH VIGNETTE: Building Towers

January 24


Literacy events take over today. A short session.

- counting by 2's with 10 Fat Sausages
-reread Scholastic pattern book
-pattern for today given to children two claps, three touch the floors. Today is my last day for being in charge of the pattern. Now the morning helpers will take over.
-counting by 10's


Centre time:

- children continue to make towers and buildings
-children enjoy working with beads to make pattern necklaces, today they also begin to create junk material patterns, they all have repeating colours so far. It is easier for them to represent their own movement pattern than to randomly come up with a pattern. They also enjoy working with each other lending and receiving support.

2nd group time:
-sharing pattern necklaces with one another
-singing our 1,1, 1, song And when you're one, one, one, show me your thumb, thumb, thumb. And when you're 2, 2, 2, tap with your shoe, shoe, shoe. And when you're 3, 3, 3 bend with your knee, knee, knee, and when you're four, four, four, stamp on the floor. And when you're 5, 5, 5 you do the jive, jive, jive, and when you're 6, 6, 6, you do but nix, nix, nix etc. We have actions for all of them. I have not had a year where the children did not want to do this over and over again. 

It is impossible to get an accurate vision of this class from just the math portion of our day. To give you more depth I would just like to describe some of the other events happening in the class. 

The children have been into the word habitat since October. First, they created snake habitats and now dinosaur ones. After creating  nonpermanent habitats the children want a more permanent version. We are now creating dioramas using shoe boxes and junk for their clay dinosaurs. The children are working mostly on their own except for the glue gun.

Meanwhile we are sending our egg banks home today after designing them. These we made out of paper maché. We want to collect money for the endangered animals in our world, this coming from our snake interest.

I was working with a group of four children on dinosaur prints, using brayers and Styrofoam plates for the stencil. Again, the children were creating habitats. They first drew a picture of a dinosaur and gave it a story. And then they recreated their picture to print more than one copy. 

Still drying is the large volcano four children made two days ago, with a parent. We had been talking and reading about them and an opportunity came up with our left over wall paper paste from the balloon banks. 

Some children are still creating snowmen from junk and did an experiment with water, to see if they could make snow. They discussed their ideas on how snow is made. Others were feeding each other in the house corner, acting out dinosaur family stories in the sand, and there were northern
animals in the snow/water table. This is an example, of our kind of day.  Skills are just the tools that are given to the children to help the above happen. To help them realize their dreams. They are not the end in themselves.

Jan. 24 2002

Math Vignettes:
Today we had a rehearsal for tonight's performance so we really did not do much in the morning class except to make some very good repeating patterns. 
In the PM our day was broken by gym and library. With a poem that we read together and a birthday to celebrate that was all we were able to do in group time. However, math stories did abound today. I spotted several. I suppose they would not fit in a math text as such, nor would they come with objectives to be quantified. I offer them here as small math vignettes or little stories.

Story 1: The habitat

Story 2: Negotiating Measurement

In the last month there have been several explorations going on in the classroom.  As we have been looking at dinosaur size and weight activities have been set up alone with surveys and graphing experiences.  The children have also worked on cloud sculptures that were made out of wire.  It was in the construction of the 3 dimensional cloud that the children had to again
deal with spatial awareness and the vocabulary that goes with it. The children also drew a 2 dimensional representation of their clouds which was very interesting to watch.  They were given the suggestion of following a wire with one finger as they drew the direction changes with the other hand.  This seemed to help organize them a bit to the task.  They then had to add the extras that they put on to represent the snow or rain, lightening etc. that was in their cloud.

Work continues on the number story front.  The children were asked to draw a number story and write down their number sentence.  This is a difficult task for them.  We got some very interesting stories.  Some of the number sentences did not match the picture but when asking the child to tell me their story they could pick this out and change the numbers if needed.   It is in this construction of their work that the discrepancies and their current understanding of the topic can be demonstrated.  When discrepancies occur between what they thought they were showing and what they actually showed the children can problem solve solutions.  As they correct their first attempts they extend their learning further as they work toward independence.  The children will work in pairs each morning as the morning helpers construct a story and number sentence.  This will give them practice in thinking through and showing  the addition and subtraction process. 

For fun the children practice counting by 2's, 10's, writing numbers from 10 to 20 and then from  20 to 100.

Math activity centers continue only now frogs have been added on logs that the children can put on count and take away.  This is combined with our 5 green and freckled frog song and a poem Big Frog, Little Frog and a new project on the Frog.

Books:   Counting Angels and the National Geographic Animal Counting book that goes to 20 is now in use. 

The children have been exploring the idea of earth, wind and fire in the
classroom since January.  The idea of storm came up and that is what
intrigued them.  We did create a water sculpture and then out interest
changed direction and went into the idea of a snow storm.  Snow was put into the water table and we set about trying to make snow by freezing snow, freezing water and then doing some experiments with the snow, melting it and finding out how much water would form etc. 
From here we read many snow stories and snowman stories and did poems and rhymes.  When we noticed that the water in our cup had evaporated I asked the children to tell me what they thought happened to the water.  They created a water cycle and then we decided to create snowman using junk.

What does this have to do with math?  If one looks at any math concept you will notice how it is connected and surrounded by the stories that are
happening in the classroom.  This snowman was hard to create as it had to
stand up and not lie down on the table.  IT became a three dimensional being with a bottom, middle, top.  We had to connect things behind, in front, on the side, and make it symmetrical.  After accomplishing this task, we revisited the snowman and this time I asked the children to draw a two dimensional representation or memory of their snowman.  This forces them to draw what they see and to put the shapes together and represent each one. 

Following this I ask them to tell me how they constructed the snowman.  Here they use words like first, I did ..., second ..., etc.  This goes on the
side, above, behind, I chose this circle for the eye, etc.  I believe this
falls under the category spatial relationships, etc.  Of course each snowman comes with its own story too.  The children are now creating clouds with wire, again representing a theory in a 3 dimensional way.  Our wire sculptures give them another opportunity to review this kind of math
vocabulary.

Well it has been a while since I last posted my class's math events.  We are very busy right now doing many things in many different areas.  To make it easier to read I will attempt to separate the areas a bit when in actuality of course they are not separate.

In our morning group times we have been counting by 2's and 10's and working on numbers to for 10 to 20.  Added to this the group has been reading the numbers 10 , 20 , 30 , 40, etc.  as we count by 10's.  We will now begin to put these numbers into their patterns so that we can write pretty well any number to 100.  The reason behind this is that I find that I now have a dinosaur museum in the classroom.  In the museum you can buy food, tickets to the dig site, tent and overnight stay, slide show, fossil dig or bone creations.  We also have a store. 

There are four wallets each filled with plastic and paper money in Loonies, Toonies, dimes, nickels, quarters, five dollar bills and 10 dollar bills. The cash register is a real one and the children now know how to use it. The tickets sell for 1, 2, and 4 dollars.  They must buy and show their
tickets if they are in the area to take part in any of the activities.

Today we tied their knowledge of counting by 10's and 2's to the dimes, 10 dollar bills and the toonies.  They were very proud to see how they could count these bills and the toonies to 100 and 10 dollars respectively.  They also had no trouble pricing the events or merchandise.  They are learning about the cents sign and dollar sign now.  Making change is also coming up and we use a calculator for that to match the amounts.  This is a great way to teach money.  I can add some real money too, later.