Part of my morning routine for the past few years has been counting the days in school with my little ones. We've then borrowed the American '100 days of school' celebration idea and as an infant department, had a 'maths morning' in which we celebrated all things '100'.

​This blog post gives a good overview of how I used this routine with younger children. It is wonderful for building number sense. If you are interested, you can click on the '100 days of school templates' picture above and download everything you need to make this simple routine part of your school morning as well.

I'm teaching Primary 5 (equivalent of 4th grade in the States or Year 4 in England) this year, however, so if I wanted to keep this routine, I needed to vary it a bit so that it was a productive use of class time. I love the routine (and you always have kiddos who benefit from reinforcement of simple place value concepts, even in P5), so at the beginning of the year, I thought about how I could extend this idea to develop my class's mathematical thinking.

At the moment, there are 2 main ways I'm using my 'count the days' ten frames.

First, we are consolidating our ability to get to the next multiple of 100 quickly and accurately. We all know how important it is for children to know their number bonds to 10. But getting to the next multiple of 100 is an equally important skill - and children often find it tricky.

​In the 'Counting the Days' set up to the left, we need 98 more days to get to 100. When we left school last Friday to start our 2 week October break (which is one of the reasons I'm finally finding the time to add a blog post), we had counted 37 days in school, which means we need 63 more days to get to 100.

​This daily practice getting to the next 100 is important. While many in my class understand how to do this, we still have more-frequent-than-I-would-like mistakes where the 'tens' add up to 100 because we forget that the digits in the units place also add to 10, making the last group of 10 that we need. Seeing the dots laid out on the 10 frames gives the kids a visual reminder that we need 9 tens in the tens place, because our final group of 10 will come from adding the units together.​

We are also using our 'Count the Days' routine to start thinking about and visualising decimal numbers. Our maths slot is right before lunch most days - once we reach lunchtime, we have completed half of our school day. So when I remember (which isn't every day!), we add half a dot just before lunch to represent the half day we have completed. We then write the total number of school days as both a mixed AND  decimal number. So if we have been in school for 36 1/2 days, that is also 36.5 days (and we read that as 36 and 5 tenths days, rather than 36 point 5 days).

​When we looked at place value at the beginning of the year, we talked about the first decimal place to the right of the decimal point, and how that showed us how many 'tenths' of one thing we had. We've also discussed how, in order to talk about part of a school day as a decimal, we have to divide one day up into 10 equal parts - and at our lunch break, 5 of those equal parts have passed, and we have 5 parts left. This is an idea that I reinforce most days when we add our 1/2 day. Repetition within a context that makes sense is great for developing number sense!

To give the kids a visual representation of the idea of 'tenths' of one day, I've made up the following fractional cards (below), which I've cut out, laminated and put on a scrapbooking ring (click on the picture below to get your own set). There are squares representing each tenth. I've made these into A3 size cards, but you can size them up or down as needed, as the file is a Powerpoint document and editable.

​If you are also counting the days of school with your class and have different ways you use this routine to extend their mathematical understanding, I'd love to hear your ideas in the comments!

Well - we're back from a last minute holiday to Northern Ireland (arrived home late last night), and I have a fair amount to do before I'm ready for our in-service day tomorrow, and pupils arriving on Tuesday (eek!). But since it's been a week, I wanted to write a short post about a different approach to Number of the Day that I'm planning to try out this year.

Last year, 'Number of the Day' was a mental maths routine for my Primary 1 (kindergarten) class. It will still be a mental maths routine on some days this year, but I want to introduce 'Maths Journaling' into our maths block, and I'm hoping to incorporate our Number of the Day routine into that.

I really like the idea of Maths Journaling - getting kids to write about their mathematical thinking. The K-5 Math Teaching Resources website has a great explanation of what Maths Journaling is.

In their journals, we want children to be thinking mathematically, in an open ended way. Many of the 'Number of the Day' cards ask closed questions, but for getting started with Maths Journaling, with a new class who has never done it before, that's OK with me. :-) Once we have established our oral 'Number of the Day' routine, it will hopefully be fairly straightforward to transfer that into written form in our journals.

With P1s, I usually only used 4 cards per day (sometimes 5 or 6), but with P3s, I might eventually use more (we'll see how it goes). But if, as an example, I had the above 7 cards up (taking out the '100 less' for now!), I would ask children to draw the following simple grid in their journals (we can probably get some fraction thinking out of that!):

I know many of the 'Number of the Day' routines you find on-line have photocopied sheets with a variety of number tasks, similar to the ones you see on my cards above. But I'm always looking for ways to use journals, rather than photocopies - it makes my life easier (I have less copying and less filing to do) and it's more eco-friendly.



Additionally, it's much easier to see the progression in what the children are doing, as everything is naturally in date order in a journal (once you train your class to NOT skip pages!). Using a journal rather than a static photocopied sheet also lets you more easily change the maths skills you want to focus on and practice that day. Rather than making up and photocopying a separate sheet of paper, with different skills to practice, you can just change the cards you have up on your Number of the Day board.

After drawing the grid, the children would then fill in the answers for each card, beginning with the cards at the top. If this is already an established oral routine, then hopefully it will transfer into journals fairly easily (although that is never guaranteed, of course). The finished page would look something like this:

Once the 'Number of the Day' journaling is established, I plan to add in more of the 'open ended' journal questions. So on a separate page, the class might be asked to write and illustrate an answer to a question like:

Sally had 25 chocolate bars, she gave some to a friend and kept some for herself. How many did she give away and how many did she have left?

This kind of question is asking children to decompose 25, of course - which is a task they will be familiar with from the 'Addition' and 'Subtraction' sheets in our mental maths routine.

I'll let you know how it goes once school is back, and we get this up and running!

Above, you see the 'Addition' and 'Subtraction' sheets I've created in my Number of the Day pack (see my post below for a bit more information about it, as well as some screen shots of pages from the pack). Last year, I just used plain laminated sheets of paper, but I wanted it to look a bit nicer this year! But the important thing isn't how they look, really - it is how they are used. So this is what we did...

After we completed 4-6 of the 'Number of the Day' task cards (see my previous post if you'd like to download these cards to use in your own class, or you can just click on the pictures above), my kiddos and I used these Addition and Subtraction sheets to come up with all of the addition sums for our 'Number'. So, if our number was 9 (as in the picture), the kids would first give me all of the sums that added up to 9.

I really liked this routine, as I think it developed and strengthened a variety of maths skills and knowledge. At the most basic level, the class was getting daily practice with their number bonds to 10. However, this routine also developed their understanding of how numbers work, so that they were beginning to be able to think strategically about how to solve maths problems.

When the first child gave me 4+5, I'd then ask the next child to 'flip' the addends for me - so they would tell me that if 4+5 = 9, then 5+4 = 9 too. They knew (and it was reinforced frequently) that it didn't matter which number you started with when you added - you always got the same answer. This helped a lot when it came to sums like 4+10...they knew they didn't have to start with the 4, just because it came first!

This routine also developed 'part-part-whole' thinking. Instead of being given 2 numbers and being asked to add them together, the kids were being given the answer. They then had to split it into 2 different groups. Knowing that numbers can be split up in many different ways is such an important skill for developing a variety of mental maths strategies. With this daily routine, the kids were getting lots of practice splitting our Daily Number up in many different ways.

After we found all of the adding sums, we moved to Subtraction. Using the same number (9, in the picture above), the kids gave me all of the subtraction sums that start with the number 9. Again, at a basic level, we were practicing our subtraction bonds to 10. But I think the value of this goes beyond that.

I always did Subtraction AFTER Addition, so that the kids could use the addition sums to help with the subtraction equations. We talked often about how addition and subtraction were opposites - if we start with 4 and add 5 to get up to 9, if we take that 5 away again, we're back at 4. I often used my Learning Resources Base 10 materials to model this on our magnetic white board.  

We also 'flipped' our subtraction sums. So when the first child gave me 9 - 6 = 3, I'd ask the next child to give me the matching equation: 9 - 3 = 6. Again, I usually modelled at least one of these using the Base 10 materials - kids need to 'see' what we are doing when we are adding and taking away.

As I move to Primary 3 this coming year, I'll need to modify this a bit, of course, as the kids will be working with larger numbers. If our number is 23, for example, I don't think ALL of the addition and subtraction sums for 23 will fit onto our sheet! But I think that having children come up with 4-5 addition sums (and flipping them), along with 4-5 subtraction sums (and their matching equations), will continue to be an efficient way to help my class develop number sense. I'll let you know how it goes - as I try it out with my class, I'm sure I'll need to adapt my current plans to meet the learning needs I find!

In the States, the idea is that you count the first 100 days of school. On the 100th day there is a big celebration, with lots of activities based on 100.

Our infant department did '100 days of school' this year, and I'm pretty sure everyone enjoyed our 'celebration' (who doesn't like to make chocolate wheeto necklaces with 100 cheerios?). But in Primary 1, we carried on counting - this picture is from yesterday, when we hit Day 177. 

In this simple addition to our morning routine, place value and reading numbers to 100 and beyond is reinforced every single day. I like using the ten frames to keep track, as we use them often during maths rotations.

Little ones need repetition so much - especially for tricky maths concepts like place value. Luckily, they also LOVE repetition, so even though I am mightily tired of counting beyond 100, they are still tuned in!

As part of our mental maths, and before we get to dot cards, my class and I count how many days we've been in school that year. This is a fabulous idea I've borrowed from the American teaching blogs I follow.

We don't just add a dot to our ten frame and change the number on our counting wall, though. I have magnetic Base 10 materials that we use to make the number from the previous day, and then add 1 to it. When we have the time, 4 kiddos get to be involved in this process (one to make 177, another to add 1 to it and finish the equation, one to add another dot to our counting wall and one to change the counting wall number).

I'd love to hear how you develop number sense in your classroom. And any ideas on how I can use and/or adapt this routine for older children would be very much appreciated!

As the year ends, I've been thinking a lot about how I teach number sense in maths. As I've been in Primary 1 (kindergarten) this year, that is my main job in numeracy. I want my kiddos to go up to Primary 2 with a solid understanding of early numbers and how you can combine and take apart numbers in different ways.

One of the resources I've loved this year (and which I think has made a positive difference to the numeracy learning in my class) is dot cards. I first heard about dot cards on Math Coach's Corner, and I bought her dot card set on Teachers Pay Teachers to get started.

Primary ones need lots of experiences counting concrete objects. But you also want them to start being able to subitise - to see groups of objects as a group, rather than having to count each one individually. Dot cards are a great way to develop this skill in a fun way.

As you can see from the side of one of my cupboards below, there are dot card rings available for kids to use in my class. I keep some rings out for the kids and some with me, that I use during our mental maths time. The kids love playing 'teacher' with these rings, and quizzing each other on 'how many dots' they see.

As part of our mental maths at least 2-3 times a week, I use a routine similar to the one found in Number Talks: Grades K-5 - Helping Children Build Mental Math and Computation Strategies. Using one of the sets of cards, I flash a card for a few seconds. My kids love the challenge of figuring out 'how many' when I've told them that they only get to see the card for one second!

When they know how many dots are on the card, they put a 'thumbs up' on their chest (so I don't have hands waving in faces and distracting others who are still thinking). I then have several kiddos tell me 'how many dots' they saw. Once we have several answers (or, when everyone is on the ball, only one correct answer), I get the children to tell me 'how they saw their number'. Hopefully, kids will see groups of dots and be able to add those groups together - for example, in the dot card ring furthest to the left, I'm pleased when my kids can tell me they saw 4 + 3 = 7, although someone else might tell me they see 6 black dots + 1 white dot makes 7 - also great thinking.

I always write up the sums they tell me they see, so we can see how many different ways there are to 'see' the groups of dots. When kids tell me that they counted all of the dots, we write up 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7. Kids can see for themselves that counting gets the right answer, but that there are faster, more efficient ways to get there.

As I'll be moving to Primary 3 next year, I've been thinking about how to continue to use my dot cards to develop number sense in older kiddos. I suspect that some of my kids will benefit from some of the dot card sets I'm currently using with my almost-Primary 2s, while I'll need to have a think about how to develop subitising skills for older children who are working with larger numbers.