Introducing Place Value in Class 2

The following is a rough outline of how I might introduce place value in the classroom. It begins, as all good learning does, with a story:

Day 1:

Let me tell you about when I used to work on a farm. We used to grow all sorts of vegetables and fruit. We sow seed in spring and tend the young crops all summer and then in the autumn we would harvest the vegetables.

Now sometimes when we dug up the root vegetables they would be damp and muddy, so we would need to lay them somewhere to dry. Well for the potatoes we had a drying rack:

PV

And as we harvested the potatoes we would put them on the rack. The first day I harvested two potatoes:

PV1

The second day I harvested three potatoes:

PV2

So how many potatoes did I have all together? – that’s right, five potatoes.

Well, the next day I harvested four potatoes:

PV3

So how many potatoes did I have all together? – that’s right, nine potatoes.

And the next day was not a good day for harvesting. I only found one potato:

PV4

So how many potatoes did I have all together? – that’s right, ten potatoes. But there was a problem. I had no more room on my rack. Well, not to worry because when I had 10 potatoes, I could fill up a bag to take to market as we often sold bags of ten potatoes.

PV5

And I could hang my sack on a hook on the wall.

PV6

And carry on harvesting potatoes as before. Well the next day was a good day and I harvested nine potatoes all at once. So where can I put my nine potatoes? On the rack!

PV7

Great, so next day I harvest just one potato again.

PV8

Where does it go? No room on the rack. OK, so I have enough for another bag, great:

PV9

And I can put my bag on a hook:

PV10

OK, so now, how many bags of potatoes do I have? Two. How many potatoes are in each bag? Ten. So how many potatoes do I have all together? Twenty. OK, so I have 2 bags of 10 on my hooks. I have twenty all together.

Well the next day was a super harvest day and I dug up 12 potatoes!

PV11

What am I going to do with all these potatoes? They won’t all fit on my rack.

PV12

Ah, so I can use a bag. How many can I fit in a bag? Ten. OK lets put 10 in a bag.

PV13

So I can put the bag of 10 potatoes on my hook and the spare potatoes can go on my rack

PV14

Now how many potatoes do I have all together? I have three bags of potatoes on my rack. How many potatoes in each bag? 10. Ok, so three bags of 10 makes … 30. And I got two spare ones. So I have 32 all together.

At this point we can play around with different numbers, I can present different amounts of potatoes and bags of potatoes and ask the children to tell me how many potatoes we have all together, or I can say a number and ask the children how many bags and spares I will need. I can even bring in a little bit of mental addition at this point saying, OK, If I have 63 potatoes and then I harvest 4 more, what will I end up with? How many bags and how many spares?

Stage 1: Demo from front: Using large manipulatives, I could if I was enterprising use real potatoes etc, but maybe magnetic manipulatives on a board would suffice – A visualiser and projector would work if tech was an option.

Stage 2 I would have the children play with their own manipulatives as well, so I could print out a sheet of a rack and hooks to give them each with counters and cards for potatoes and sacks. They could work in pairs initially.

Stage 3: Children can draw this in their main lesson books.

Once I felt the majority were confident with this method I would move onto the hundreds:

Day 2:

Begin with a recall about the story, ask the children to tell me how we arranged the potatoes etc.

Then show them this and ask them how many potatoes I have, 99:

PV15

And ask what would happen if I dug up one more potato? I would have 100 potatoes!

PV16

Well, it can’t go in my rack because that is full. But I can fill a bag because I have 10 loose potatoes.

PV17

But where to put the bag? I have no more hooks for bags of potatoes. How many bags of 10 potatoes do we have? 10. 10 bags of 10 makes 100.

Well, sometimes, we sell sacks of potatoes to shops, so I can put my 10 bags of potatoes into a big sack to sell to the greengrocer:

PV18

At this point we can have another play with numbers up to 999, again moving from a whole class demonstration at the front to paired work and then individual manipulation, call and response for number recognition, asking “how many?” from an array and then asking “what would XXX look like?”.

Potential extension would be the crate of 10 sacks to sell to the wholesaler.

Children can draw this representation of the potato rack and bags and sacks in their main lesson book.

Day 3:

Recall. Numbers and images up to 999.

Introducing vertical addition

By extending the story and keeping it visual, we can introduce addition:

I had collected so many potatoes and my friend had collected so many, how many do we have altogether?

PV19

I would begin with sums which do not require any carrying to begin with. We will naturally at this stage begin to need names for the columns so the names, 1s, 10s, 100s and perhaps 1000s (represented by a crate) will arise.

Again I would like to move from whole class demonstration to paired and then individual work with manipulatives with the children drawing one or more representation of addition in this way in their books.

Day 4:

Recall simple addition.

The introduction of sums which require carrying

PV20

Whole class demo – Paired manipulation – individual representation in main lesson books

Day 5:

Recall addition.

Subtraction. Beginning with differences which don’t require any ‘borrowing’. Having considered this, I would not represent the subtrahend with images, but with the number as this would distinguish it from the images for addition. It also would not work in relation to the story, because the customer does not turn up with a quantity to be matched by the vendor, but turns up with a request:

Mrs O’Riley just wants 2 potatoes for her dinner:

PV21

Or Mr Walsh is entertaining guests and wants 12 potatoes etc:

PV22

Whole class – paired – individual

Day 6:

Recall simple subtraction.

Subtraction 2: ‘borrowing’. With the explanation that if a customer wants to buy 16 potatoes when I have 24, I will need to open up a bag for the customer:

PV23

PV24

PV25

Whole class – paired – individual

Day 7:

Recall addition and subtraction.

After a week or more working with these images, the children will, on the whole be ready to move onto the more abstract forms of written column addition and subtraction. I would keep all the problems contextual so that the children are using the mathematical tools to represent and model real life problems, rather than just practicing isolated algorithms.

 

Day 8, 9 and 10:

Extend and deepen the exploration of column addition and column subtraction with a variety of problems to solve, investigations and/or games such as dice games, exploring consecutive number addition and games involving making certain totals etc. The NRich website has plenty of material to keep a class busy for three days exploring addition and subtraction.

 

Addendum

 

After consideration and with a helpful comment from Kieran Mackle (@Kieran_M_Ed) I decided I would arrange the rack on the right, with 9 potatoes in a 2-2-2-1 formation rather than a straight line as this would make counting/seeing how many loose potatoes I have much easier.

Also, the schedule of days represented here may well be too fast and I would certainly consider slowing down the process more with more practice of the key skills and concepts before moving on.

3 comments

  1. Great post Brendan. Teaching a basic concept from first principles is always hard and I think you’ve nailed it with the story. (The images didn’t display on my phone but the narrative was so clear that I had the perfect mental image.)

    I like the way it slow builds up, the use of manipulatives and your atomisation of questions, particularly around the 10 and 100 “barriers”.

    I have a personal agenda around subtraction. I don’t think it’s introduced early or routinely enough. So in days 1, 2 and 3 of your story, I would include scenarios where some potatoes or bags are being taken *off* the rack (dad needed 3 for cooking, 2 were mouldy, 5 were used to feed the pigs). Again, as you did with addition, playing around 10s and 100s barriers.

    As I said, great post.
    If I’m ever in a situation again where I have to introduce place value I’ll use this.

    Liked by 1 person

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s