We are exploring place value, too. (2nd grade, 2nd -language learners)
I gave students 2 numbers: 24 and 42
- How are they similar (Answers: They both have tens and ones; they both have the digits 2 and 4; they both are two-digit numbers etc)
- How are they different? (Answers: One is greater than the other.)
(Me) Hm, stop a little. How do you know that since they have so many things in common?
(Kid) Well, 42 IS greater than 24.
(Me) It might be. Can you prove that?
(Kid) Well... It has four tens and the other has just two tens.
(Me) How do you know it has four tens? Both numbers have a 4 and a 2.
(Kid, puzzled) Um...because it is at the beginning?
(Me) Aha. So what helped you figure that out?
(Another kid) The place, the place!
Wow, what a relief. PLACE VALUE as a concept.
But that is not enough. Jigsaw groups (each group receives a question, write the answer in a specific color, then swaps question with another group when I clap hands) to further develop thinking:
1- Explain what "place value" is to a 5-year-old. (Got 'em! It is tough to explain your thinking or understanding in a simple,clear manner).
2. What does place value help us do in math? (Answers: We can compare, order numbers, add or subtract them etc.)
3. What is the connection between place value in math and real life? (Answers: We can take the right bus - 62 not 26!, we can measure correctly, we can compare quantities etc.)
4. What if we mixed up the place value? (A long list of troubles the kids wrote).
Well, that is our thinking. Plus practice in stations and spontaneous questions (mostly related to "cool" numbers such as 0, 10, 100, 111 etc.)