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.

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!