A Few Simple but Effective Games and Routines for Preschool and Kindergarten Children

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I have had the privilege of spending some time with some very sweet kindergarten children this week who have not had a great deal of school experiences and are not comfortable with recognizing or writing numerals to 6 or even recognizing small quantities without counting by ones.  I am working with them on a few simple games with a few simple materials that will hep students instantly recognize small quantities (subitize) and recognize numerals.

These games and routines would also work very well with pre-school students as they are preparing to enter Kindergarten.

Match numerals and dot dice

This is a great game for kids to play on their own or with a partner if they are ready for partner work

I start by giving kids the first 6 cards in my numbers to 120 place value deck.  I hand them to them in a random pile and ask them to spread them out and put them in counting order.  This helps kids practice orienting the cards so the numerals are all facing the right way and lets me see which kids can put the numbers in order without counting the place value pieces by ones and which kids still need to count to figure out what the numeral says.  

Once kids have the base 10 cards in order, I give them a dot die and have them roll it.  (I really do take time here to teach how to roll a die if this is the first time they are using them!!!) If they roll a 6, they get to flip over the card with the numeral six on it.   

They continue playing by rolling a die and turning over the corresponding card until all the cards are turned over.  If they roll a 2 and the 2 card has already been turned over, they just move onto the next roll.  This can take longer than it might seem because one number very often stubbornly refuses to come up on the die.  If the game is going on and they keep rolling, I make sure they are still saying the number they rolled and often make them do something like show me that many fingers.

I change this game up just a little to practice going the other way from numerals to picture representations.  I simply use a 1-6 numeral die and a set of dot cards from 1-6 that I made using index cards and dot stickers.  The procedure is the same.  Kids roll the dice and turn over the corresponding card.

Another variation of the game where student rolls a numeral dice and turns over the matching picture.  

I also use these dot cards that I made as flash cards and flash a picture at them and ask them to tell me or show me on their fingers how many they saw.

What early numeracy activities do you use with students who are just starting to think about number?

Want to read about the next activity I did with students to extend this one?  Check out THIS POST!

Here is a sneak peak at the picture of the activity

Want to know more about what is going on here?  Check out this post!

Estimating and Counting Routines Part 4

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New to my estimating and counting routines series?  Click here to start from part 1!

I did this estimating and counting routine with a group of second graders who need a bit more practice with some early numeracy ideas.  I also knew that they would be beginning to work on counting by 25's in class as they got into their money unit and wanted to give these 5 kids a head start on this idea.

To do this counting and estimating routine, I used my bucket of buttons.  Kids love using these for math because they are super engaging and you can keep adding to your set as you find unique buttons.  I have even had kids bring in more buttons to add to the collection.  I also read them The Button Box when we first start using the buttons. 

I dumped out what I estimate to be more than 125 but less than 200 buttons.  It took me some practice to be able to do this because the tiny buttons can make it tricky!

After dumping out these buttons, I gave kids about 20 seconds to look at the collection and make an estimate about how many buttons they thought were there.

I then pulled 10 buttons aside and asked kids to think about if this is 10, how many are there alltogether.

After doing this, I let kids adjust their estimate if they wanted to.

Here is a look at each student's initial estimate and their adjusted estimate.  As you can see most students increased their estimate after seeing what a pile of 10 looked like but one kid actually decreased their estimate. 

I then asked the kids to think about how many we could each take from the pile without running out.  They looked very unsure so I did some further prompting. 

"Is there enough for us to each take 10?"

"Yes!"

"Is there enough for us to each take 20?"

"Yes!" (I thought this was funny since none of them estimated the quantity was over 100 yet they were sure that we could each take 20.  Six of us at the table X 20 each = 120. 

"Is there enough for us to each take 30?"

(mixed words of uncertainty)

"So if there is enough for us each to take 20 but you are not sure there is enough for us to each take 30, how many should we each take?"

"20"

"25"

"yeah 25 sounds good"

Hmmm.... let's see, one of my goals for this lesson was to introduce the idea of counting by 25's and here I have a few students suggesting that we each take 25.  BRILLIANT! 

We decided to each take 25.  We briefly talked about how to take about 25 into our own area and then quickly count and confirm how many were actually there.  We also talked about taking turns and not grabbing.  Then I turned them lose to each take 25.

Kids working on taking 25 buttons

One student's collection of 25 buttons

Once we each had 25 buttons, we needed to figure out how many buttons we had altogether.  I started and we worked on counting around the circle.  Having the buttons as a visual model was VERY helpful as kids thought about putting fives together to make tens.  One particular student was very stuck and needed to use a 100 bead string to help her.  After using it she was able to connect what she did back to the piles of beads. 

After counting by 25's around the circle a few times we recorded the numbers on the board and looked for patterns in the numbers.  A great way to get kids to practice counting by 25's multiple times is to have them check and see if it matters what person starts the counting.  Of course they quickly realize it doesn't matter at all but in the meantime they get some extra practice. 

After we each had 25 buttons, there was a small pile remaining in the middle.  A student suggested we count them by 2's (which is another important second grade skill!)

A student lined up the remaining beads and counted them by 2's.  I had another student do it after to check her work, and of course give one more student some practice with this skill!

All we had left was to figure out 150 + 18.  I recorded this equation on the board and gave kids a few minutes to think about it and asked them to give me the ready signal when they knew the answer.  I then had kids turn and talk to a partner about what they thought the answer was and how they knew they were right.  We then talked about different strategies kids used to figure it out.  The most popular strategies were counting on by 1's and  the idea of adding the 10 and then the 8 ones.  This was a great time to discuss efficiencies of strategies and the difference between counting and thinking strategies. 

Stay tuned for more in my counting and estimating series. 

Ready to read more?  Check out part 1, part 2 or part 3!

My Favorite Apps: Line 'em up and Count on It

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Line 'em Up

A great and FREE app that I find myself using over and over again with K-2 students is Line 'em up.  It is a great way to work with students on ordering sequential numbers under 200.  The options pages allows you to vary things such as the number of cards that need to be put in order, the starting number and the range of numbers (from 0-200).  You can also further customize it by changing the way the tiles are displayed.  

Here is a great set for working on bridging the decade and century marks.  The display is currently set to one pile so kids have to place the card they are given before they get another.  After a student has put all of the cards in order, I have them read the numbers from least to greatest and then in most cases also from greatest to least.

Here is an easier set that starts at 24.  They go as easy as starting at 0 (which is where most of my K kids are functioning this time of year!)  Again I have kids read the numbers from least to greatest and if they are ready also from greatest to least. 

Here is a more challenging set that I use with first and second graders (and sometimes older students in need of intervention!)  The option this time is set to spread out and students can pick and choose cards as they see fit. 

This app is yet another way to practice comparing and ordering numbers.  If your students struggle with this app, you may want to start with my 0-120 place value cards where your students will benefit from visual models of base 10 pieces. 

Want to read more about this?  Check out this post!

If your students get really good at comparing and ordering numbers under 200, you may want to move them towards ordering numbers under 1000.  Check out this post to learn more about how I do this with my students!

Count on It

This is another great free app that is great to differentiate for grades K-3.  It has an abacus that is similar to The Number Rack App I talked about last week but not as easy to differentiate so I find myself using other aspects of this app more. 

My favorite feature of this app is called quick add and it is a great way to work on fluency with adding 2 or more numbers.  You can also choose 1 ten frame and I often do this to have K kids work on instantly recognizing quantities.  You can also adjust the number of seconds students get to perform the calculation. 

A look at adding 2 ten frames.  Notice the way the student might think about adding 8 and 5 by pulling the 5 out of the 8 and seeing 10 and 3 more. 

A way to use this app for kids at a higher level.  I love how this pushes kids to think in groups of ten.

Looking for more ways to expose your students to 10 frames?  Check out this post!

These apps are both developed by classroom focused software

What are your favorite math apps?

Multi-Digit Addition and Subtraction and the Common Core Part 2

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If you missed part 1 of this series where I look at subtracting 2 and 3 digit numbers click here to check it out!

Over the next week and half, I will be seeing a class of third graders 3 separate times for about 40 minutes each.  In this time, my goal is to help move them from subtracting from 100 to subtracting from 1000.  I will be taking lots of pictures and sharing how I use problem strings to move kids forward in their thinking about place value and their own development of strategies for multi-digit subtraction.   

Day 1
I started day 1 with a string of problems related to subtracting from 100.  The first few were subtracting just tens and the next few subtracting just ones.  I have done a great deal of work with this group as second and third graders with combinations of 100.  I started at this level to be sure kids were building on their prior knowledge and to make even the lowest students feel like this was something they could do. 

The first problem string.  At this point in the year with these third graders this went very quickly without much discussion.  My students were showing me they were ready quickly and fluently.  If I was doing this same string at this point in the year with first or second graders, I would expect a great deal of discussion around these problems and strategies for finding answers.   I expect third grade and up to be fluent with these ideas. 

I quickly moved onto a second string of problems.  These were subtracting tens and ones from 100.  We had a bit more discussion about how kids knew they were right.  The two most common strategies in this class are subtracting tens and then ones or adding up.

The second set of problems.  I expect third graders to be fluent with these problems as well.  Check out this post on how work with kids towards achieving fluency at this level. 

After making sure kids were thinking about previous subtraction strategies they had developed, I upped the ante and we looked at a problem string that was all about subtracting from 1000.

Our 1000 take away problem string.  Notice I start with just subtracting hundreds and then just tens before I start combining them. 

Our first problem was 1000-200.  Some kids required a lot more think time than I was expecting to come up with the answer to this so we had a great deal of discussion about how various kids knew the answer.  I really liked that one student connected it to what he knew about 10 - 2 = 8.  He said, "I know 1000 is 10 hundreds and if you take 2 hundreds away from that then it is 8 hundreds."  I had him write this using words and numbers like this on the board

10 hundreds - 2 hundreds = 8 hundreds

Another kid wanted to come up to the board and added this:

100 - 20 = 80
10 tens - 2 tens = 8 tens

WOW!!  I loved this idea so I had to add my own to it

10 - 2 = 8
10 ones - 2 ones = 8 ones

This discussion REALLY helped kids get the big idea and further reinforced how important it is for kids to be fluent with combinations of 10.

Moving onto the next problem, we tried 1000-500.  The kids were much faster with this and were easily able to connect it to the last discussion so I decided to move on to subtracting some tens.

We looked at 1000 - 80.  Students were fairly fast to get this idea and several students talked about how they looked at 1000 as 900 + 100 and took the 80 out of the 100 part leaving 900 + 20 left.  Students were so quick with this idea, I decided to jump right to subtracting hundreds and tens.

We tried 1000-180.  Most students subtracted the 100 first and then the 80.  There were a few students who had some errors in their thinking such as thinking about 1000-100=900 and then subtracting 80 from 900 and coming up with 980.  Other students were quick to see and correct these mistakes.

We tried another problem subtracting tens and ones 1000-350.  Fifty is a really friendly number for kids and all students were able to agree on the correct answer for this.

I ordinarily would build up a bit more to my ultimate goal of subtracting a 3 digit number where none of the digits is zero but I was running short on time.  This entire lesson had been very teacher driven with lots of partner and whole group discussion and I was afraid I was losing the students' focus and they were due to leave for P.E. in about 6 minutes.  I decided to go for it and see how they would do with 1000-738.  This would give me a good idea of where kids were with their strategies and who could extend their previous understanding to a more challenging problem. 

Students had about 4 minutes to think about this problem and as they were finishing up, I had them whisper the answer to me which is one of my favorite formative assessment strategies.  About half of the class got it correct and another fourth of the class was off by either 10 or 100.  The final fourth of the class was either way off or unable to come up with a solution in the time given.  This quick check in as students were lining up gave me good ideas about where to start the next lesson and who to target my instruction at. 

Make sure you are following my blog so you will get to see what happened in the next lesson!  On the right hand side of the top of the page there are many different ways you can follow my blog and stay up to date on my latest posts!

Want to read more?
Here is a post about fourth graders subtracting money amounts
Here is a post about multi-digit subtraction in second grade
Here is a post about extending fact strategies into multi-digit subtraction in grades 2 and 3

Monday Math Literature Volume 13

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Want to start at the beginning of my Monday Math Literature series?  Click here to start from the first post.

A great K-2 topic to introduce or reinforce with math literature is the idea of odd and even.  Here are the two books I use to discuss this idea with kids!

Even Steven and Odd Todd

This is a Hello Math Reader and is a great book to use in literature circles or to have in kid's book boxes.  It is easy to read and very engaging.  Even Steven and Odd Todd are cousins and each like things their own way.  Steven likes everything to be in even numbers and Todd likes everything to be in odd numbers.  When they have to spend time together, things get tricky!

One student I worked with several years ago loved this book so much, he found Even Steven's Odd Game and put it on his Christmas list.  The game seemed to really help him with addition and subtraction facts.  There is something very catchy about the title!


A great picture book with very sweet illustrations that also talks about odd and even is

Splitting the Herd: A Corral of Odds and Evens

In this book Kirby and Emma are farmers that live next door to each other.  Emma's cows keep leaving her herd and getting mixed in with Kriby's cows.  Since the cows all look the same, they decide to split them up equally and one person will get the odd numbered cows and one will get the even numbered cows.  By the end of the story they get stuck trying to divide up 5 cows equally so they decide to get married and instead of dividing the cows, they start multiplying.  It is a very cute story and really gets at the odd, even pattern in our counting numbers.

What math literature books do you use to teach odd and even?

My Favorite Apps: The Number Rack and Math Slide

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If you have ever read one of my blog posts, you know how much I love bead sticks, bead strings, rekenreks and number racks.  It will come as no surprise to you that I love the Number Rack App which is currently available for free through the Math Learning Center.  The VERY best part is that it is an app for the iPad as well as being an app you can use through any PC and it also gets a lot of use on the SMART board!!!!

Like other rekenreks or number racks, it allows you to work on big ideas around numeracy, addition and subtraction.  You can go from one bead string up to 10 which makes it very versatile as I move between grades and ability levels.

You can also pull up and adjust a "screen" that allows you to shield part of the bead string and is excellent for working on combinations of 10, 20 or 100.

In this screen shot, I was working with a student on pairs that make 100

You can also access this amazing app and a great FREE resource on how to use rekenreks in the classroom directly through the MLC's website by clicking here.

Math Slide

Cost: Free for a limited number of games, $0.99 to upgrade to a full version for each type

There is a whole series of these math slide games and I (and my students!!!!) are obsessed with them.  The basic premises is that a picture, answer, or equation is shown in the middle of the screen and each player (between 1 and 4 players can play each time) tries to slide the corresponding answer or equation into the middle.  The person who does this correctly first has their answer or equation disappear and are one number closer to winning.  The first person who gets all their numbers or equations slid into the middle wins. 

Here are several different versions of math slide that I currently have on my iPad

Addition and Subtraction

Tens and Ones

Hundreds, Tens and Ones

Multiplication and Division 

As you can see... there is something for everyone offered for math slide and I have been using it grades K-6

What apps are your students' favorites? 

My Favorite Apps: The Subitize Tree and Ten Frame Fill

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This summer I got an iPad and resolved to use it with students this school year.  Today I would like to share with you one of my favorite math apps for K-2 students.

Subitize Tree 

Price $0.99 and worth every penny!

In this app, there is a picture of a large tree with a set of french doors.  The doors open up to reveal an object for a short period of time for students to subitize.  Then the doors close and the student has to touch the number that they saw when the door was open.  It is very easy to customize depending on the level your students are at.  You can easily change the amount of time the door stays open, the range of the numbers. 

There are also many different representations you can switch between.  There are dominoes, playing cards, random animals, dice, ten frames, hands, bead strings and 2 color counters.  

This is a great app to build number sense and additive reasoning.

Ten Frame Fill

Price: FREE

In this app, a ten frame gets filled up with some counters and you are asked to figure out how many more counters you need to make 10.  There are counters of another color that you can pick up and drag into place if you need to or you can simply touch the number across the bottom if you know the correct response.  The options page lets you chose which equations to display as well as how you want the 10 frame to fill.  

I have been using this app a lot in grade 1 over the last month. I like to sit with a kid and ask them how many they see and how many more they need to make 10.  We also talk abut the different equations we could write to represent the situation.  It has really helped my students work on subitizing, addition, subtraction and the all important combinations of 10.  

What are your favorite apps to use with primary students?

Here are a few more of my favorites for primary students!

Here are few penguin themed apps to work on addition facts!