GoalSolve place value puzzles, including puzzles with too many hundreds or tens, and compare numbers by their digits.
New words
place value · what a digit is worth because of its place in a numberexpanded form · a number written as the sum of the values of its digitsregroup · to rename 10 of one unit as 1 of the next unit, such as 10 tens as 1 hundred
Explanation
A place value puzzle describes a number by its parts. Write each part as a number and add them. A number with 4 thousands, 3 hundreds, 8 tens and 2 ones is 4,000 + 300 + 80 + 2 = 4,382. Sometimes a part is too big for its place. For 14 hundreds + 12 tens + 5 ones, write 1,400 + 120 + 5 = 1,525. To compare numbers, count the digits first. 9 is the biggest digit, but a number with more digits is bigger. So 1,002 is bigger than 899, because 1,002 has 4 digits and 899 has only 3.
Thousands
Hundreds
Tens
Ones
4
3
8
2
Worked examples
Thousands
Hundreds
Tens
Ones
7
2
0
6
The number has 7 thousands, 2 hundreds, 0 tens and 6 ones. The zero tens keep the place, so the number is 7,000 + 200 + 6 = 7,206.
Part
Amount
Value
hundreds
13
1,300
tens
14
140
ones
7
7
The puzzle is 13 hundreds + 14 tens + 7 ones. 13 hundreds is 1,300 and 14 tens is 140. The number is 1,300 + 140 + 7 = 1,447.
Number
Digits
899
3
1,002
4
Marwan says 899 is bigger than 1,002, because 8 and 9 are big digits. Count the digits: 899 has 3 digits and 1,002 has 4 digits. So 1,002 is bigger.
Class activity
Make your own puzzle. Write a place value puzzle with thousands, hundreds, tens and ones, for example one with a zero or with too many hundreds. Write the answer on the back of the card. Swap cards with a partner and solve each other's puzzles. Check the answers together.
Practice
1
A number has 3 thousands, 5 hundreds, 8 tens and 1 one. What is the number?
3,000 + 500 + 80 + 1 = 3,581.
2
What number is 15 hundreds + 3 tens + 2 ones?
1,500 + 30 + 2 = 1,532.
3
Write in standard form: 400 + 70,000 + 6,000 + 8.
Put each part in its place: 70,000 + 6,000 + 400 + 8 = 76,408.
4
Write 8,205 in expanded form.
8,000 + 200 + 5. There are 0 tens, so no tens part.
5
Nour writes 7 hundreds + 14 tens as 714. What is her mistake? What is the right number?
14 tens is 140, not 14. The number is 700 + 140 = 840.
