GoalShow numbers with place value models, write them in expanded form, compare them, and make the smallest 6-digit number.
New words
expanded form · a number written as a sum of the values of its digitsgreater than (>) · bigger than; the open side of the sign faces the bigger numberless than (<) · smaller thanhundred thousands · the sixth place from the right
Explanation
A number can be shown with blocks: big squares for thousands, flats for hundreds, rods for tens and small cubes for ones. The model of 2,346 has 2 thousands, 3 hundreds, 4 tens and 6 ones. The expanded form adds the value of each digit: 2,346 = 2,000 + 300 + 40 + 6. To compare two numbers, start at the left. The number with the bigger digit in the highest different place is greater, so 5,642 > 5,624, because the tens are different and 4 tens are more than 2 tens. Six-digit numbers have two more places on the left: ten thousands and hundred thousands. For example, 604,073 = 600,000 + 4,000 + 70 + 3.
Worked examples
The blocks show 3 thousands, 5 hundreds, 0 tens and 8 ones, which is 3,508. In expanded form: 3,508 = 3,000 + 500 + 8. We can leave out the zero tens.
Number
Thousands
Hundreds
Tens
Ones
5,642
5
6
4
2
5,624
5
6
2
4
Compare 5,642 and 5,624 on the mat. The thousands are the same, 5. The hundreds are the same, 6. The tens are different: 4 tens are more than 2 tens. So 5,642 > 5,624, or 5,624 < 5,642.
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones
Discard
2
0
3
4
5
7
9
Rahma has seven cards: 4, 0, 7, 2, 9, 5, 3 and six boxes. For the smallest number she leaves out the biggest card, 9. The first digit cannot be 0, so she starts with the smallest other digit, 2. Then 0, 3, 4, 5, 7. The smallest number is 203,457.
Class activity
Number detectives. Write a six-digit number on a card, such as 530,218, without showing it. Give your partner clues: the digit in the thousands place, whether the number is greater than 500,000, and so on. Your partner builds the number with digit cards. Then both of you write it in expanded form.
Practice
1
Write the number shown by the blocks.
4,125 (4 thousands, 1 hundred, 2 tens, 5 ones).
2
Write 7,090 in expanded form.
7,000 + 90.
3
Write > or < in the blank: 8,413 ___ 8,431.
8,413 < 8,431, because 1 ten is less than 3 tens.
4
Write 352,160 in expanded form.
300,000 + 50,000 + 2,000 + 100 + 60.
5
The seven cards are 3, 8, 0, 6, 1, 5 and 7. Make the smallest 6-digit number from six of them.
103,567. Leave out the 8, and start with 1, because 0 cannot go first.
