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!

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!