Like many teachers, I began our school year looking at place value concepts. Place value is so foundational to a child's understanding of maths that it always seems like the obvious place to start.

​Prior to this year, I've always taught in infants (K-2), so place value concepts focused mostly on 0-100, stretching to 1000 when I taught P3 (2nd grade/Year 2). I had a few children in P3 who were ready to go to 10,000, but for the most part, the class needed to focus on developing fluency with smaller numbers. To develop deep understanding of place value (like any maths concept), children need to follow the concrete - representational - abstract progression. So - cue getting out lots of cubes, counters, base 10 materials, etc during my infant years.

​But this year, I've moved to P5, so I needed to teach place value to 10,000 and 100,000 for some of my class. This is much more difficult to do at the concrete level - even having bought a class room set of Base 10 materials before I started teaching, I still only have 3 thousand cubes. And even if I hoard all the thousand cubes in the entire school (not that I even considered doing that!), I still could only model working with 10,000 for my class - I couldn't give each child a set of Base 10 materials that would allow them practise building these numbers themselves. What to do?

​As you can see from the above picture - I decided to make sets of Base 10 cards for my class. Granted, it's representational, rather than concrete - but that's still better than working only with the abstract concepts. I have made 12 sets of these cards (20 of each Base 10 value), so the children can use them with partners (I have 23 children in my class at the moment). I made an additional set for my magnetic white board by simply adding magnetic tape to the back of each card (several of the girls in my class take it on themselves to organise any cards I've used at the end of each maths lesson, so they stay relatively neat!).

I use these cards to give kids a visual representation of any 'number talk' equation I'm asking them to solve. This allows them to see that when you have 5 hundreds and you take away 3 hundreds, you have 2 hundreds left, etc. Having the visual available can help take some of the mystery out of working with larger numbers.

​Making the sets took a bit of time at the beginning of the year, but it's all easily guillotine-able, so it isn't as bad as it looks! And once the sets are made, you have them - so far, my sets seem to be holding up pretty well. Having 1 set between 2 children can seem like a lot, especially if you have a larger class. However, if you have your class work in groups, you could probably get away with making fewer sets.

​If you think these would be helpful in your own class, you can get the file by clicking on either picture.

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!

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!