I took NaN's advice about poker chips for place value in March, and I've been really pleased with them. I wrote a little bit of detail about my first experience using them (with my 6-year-old daughter), not quite publicly, and I looked it up again a few days ago because I'm about to introduce them to a relative. I'll paste it below.
I've been using some handmade "poker chips," each of them is a square inch that I cut out of red or orange or blue construction paper.
I gave her a light load of worksheets this morning, and told her that when she finished we would play a game with little paper squares I had made. These red squares are 1, and these orange squares are 10. "Then the blue squares must be 100!" Yes.
These won't be her only "model" for three-place numbers, she already has experience with pirate numbers (from BA), plastic cubic centimeters that stick together, the number line, the numerals themselves. But I had reviewed some questions over the last week like "451 is the same as 3 hundreds, __ tens and 1 one" and they weren't effortless.
One way the cardstock squares are worse than plastic poker chips: when you give someone a stack of 8 or 9 of them it takes a little bit of dexterity to separate and count them.
Anyway I set it up like this. She has a blank sheet of paper and pencil, and I slide some orange and red squares to her. "I want you to write down the value of these squares that I gave you, as a two-digit number." She didn't need any explanation, she counted the two orange squares as "ten, twenty", looked at the six red squares, and wrote 26.
"Now here are some more. Don't mix them together yet. How many did I give you in this group?" and she wrote 29.
When I asked her to add them together, she did it in her head by saying "forty fifteen." That's a joke that she likes that I don't always discourage. "That's kind of a good answer as a joke, but you have to remember that 15 isn't a digit. What do you really mean by 'forty fifteen'?" She knows to answer 40 + 15.
"Good, you can remember 40+15 for a minute. Before we talk more about it I want you to write "problem 1" on your paper, and then write 26+29 since that's the problem you're doing." I let her guess a little about the letters in 'problem' before spelling it for her. Then she wrote 26 + 29 = ▢. I hadn't asked her to write the equals sign or the box, and didn't mind that she did.
"OK what was 26+29 again?" 40 + 15, which is 55. "Good. Now, you still have 4 orange squares on your side of the table, and 15 red squares on your side of the table. Is there a way we can make that look more like 55, without changing the value?"
This stumped her, she couldn't guess what I wanted her to say. "Here's a rule for the game. A red square is 1 and an orange square is 10, so whenever you like you can trade me a 10 red squares for 1 orange square. Let's try that now." She counted out ten of her red squares, slid them to me and I handed her one orange square.
"Now, how many tens do you have? How many ones do you have?" She shouted back, I think excited because she had put together what we were doing, "Fifty-five!"
Next problem. "OK, write problem 2 on your paper. No, don't hand those back to me, this time you're going to start with those 55. How many do you have there, five oranges and five reds? Can you write that as a two-digit number." She wrote "PROBLeM 2," underlined it, and wrote 55 underneath.
"Here are some more for you." I gave her 1 blue square and 1 orange square. She knew I had given her 110, I had her write down 55+110, and she knew that was 165. I didn't make her prove it to me by counting her squares.
"OK, now write Problem 3. You can keep those 165. Now I want you to tell me: what's 165 minus seven. Can you use your paper squares to find out?" She fussed with her squares for a little bit and then asked me "can I have two more reds?" I told her no, I don't want to change the value of the number you're starting with. "But you can give me one orange square and I'll give you back ten red squares. That won't change the value and it will help you."
After the trade she was reluctant to give up the seven red squares she was taking away to the "bank." I told her it was fine, she could keep them on her side of the table, she just had to get them out of the way of the squares she ended up with. "When you subtract you take seven away from the number you start out with, so take those away, put them over there, and don't count them when you tell me what you end up with."
She didn't count at first, she was pretty sure she had 148. I asked her why, she said "because 10 minus 2 is 8." Well, that's true and it's a good observation for your problem but let's look at how many orange squares you have, remember you started out with six and you only traded one of them to me, I think you have five. "I'll write 158."
I thought that was the right place to stop for the day.