Place Value progression, 3rd step
The purpose of the activity
In this activity, the learners extend their understanding of the place value of digits in a whole number by adding and subtracting 1, 10, 100 and 1,000 from a given four-digit whole number.
The teaching points
The places increase by a factor of 10 (1, 10, 100, 1,000).
There are challenges in dealing with the digit 9.
The learners understand the use of 0 as a place holder.
The learners can rename thousands as hundreds, hundreds as tens and tens as ones.
Discuss with the learners relevant or authentic situations where the understanding of wholenumber place value is necessary. For example, stocktaking, car sales with trade-in deals.
Two dice for each pair of learners (wooden dice with blank faces are available from educational supply shops). One dice in each pair has the symbol for adding on three of its faces and subtracting on the other three (+, +, +, –, –, –). The other dice has the numbers 1, 10, 10, 100, 100 and 1,000 on its six faces.
The guided teaching and learning sequence
1. Write a four-digit number (not including the digits 0 or 9) on the board, for example, 3,467.
2. Ask a volunteer learner to roll the two dice.
3. Demonstrate how to write the resulting problem beside the four-digit number. (For example, if the dice show + and 100, record “3,467 + 100 = ?”)
4. Ask the learners what the answer would be, have them explain their thinking and record “3,467 + 100 = 3,567”.
5. Have another learner roll the dice again and repeat the process a few times, always using the previous answer as the new four-digit number to add to or subtract from. For example, since 3,467 + 100 = 3,567 was the first equation, the next might be 3,567 – 1000 = 2,567 and the following one might be 2,567 – 10 = 2557.
6. Repeat the whole activity with a different starting number.
7. Once the learners are familiar with the process, ask them to do the activity by themselves in pairs (selecting numbers that do not include the digits 0 and 9) and to share their results with another pair.
When the learners are using this process confidently and successfully, ask them to consider numbers that include the digits 9 and 0.
8. Write a problem with a number that includes the digit 9 on the board, for example, 4,975 + 100 = ? Ask the learners what the answer is and have them explain their thinking. Listen for and reinforce the idea that 10 hundreds is the same as 1 thousand so that when a place holding the digit 9 is increased by 1, the next (higher) place (on the left) also increases by 1.
9. Repeat with other numbers, for example 3,091 + 10 = ?, 4,309 + 1 = ?
10. Write a problem with a number including the digit 0 on the board, for example, 4,056 – 100 = ?
Discuss the difference between 4,056 and 456 and the use of 0 as a place holder.
11. Ask the learners what the answer is and have them explain their thinking. Listen for and reinforce the idea that 4 thousand can be renamed as 40 hundred and that 40 hundred and 56 take away one hundred is 39 hundred and 56.
12. Repeat with other numbers, for example, 4,605 – 10.
Give the learners a set of numbers coupled with answers and ask them to work out what the dice must have rolled to come up with these answers.
For example, if the original number was 4,582, what must the dice have rolled in order to get:
4,482? ( – and 100)
5,482? ( + and 1,000)
5,481? ( – and 1).