Packets  /  Place Value and Number Sense
Grades 2-4Elementary

Place Value and Number Sense

Master place value from ones to millions: read and write big numbers, use expanded form, compare and order, round to any place, and estimate answers with confidence.

1Place Value: Ones, Tens, Hundreds

Key idea: Every digit's value depends on its PLACE: the 5 in 57 is worth 50, but the 5 in 75 is worth only 5.
  1. Write the number and label each place from right to left: ones, tens, hundreds.
  2. The rightmost digit is always the ones place.
  3. A digit's VALUE is the digit times its place: the 3 in 300s means 3 x 100 = 300.
  4. Read big digits first: 4,385 is four thousand three hundred eighty-five.
Worked example
In 726, what is the value of each digit?
6 is in the ones place: 6. 2 is in the tens place: 2 x 10 = 20. 7 is in the hundreds place: 7 x 100 = 700.
Worked example
What number has 5 hundreds, 3 tens, and 8 ones?
5 x 100 = 500, 3 x 10 = 30, 8 x 1 = 8. Add them: 500 + 30 + 8 = 538.
Watch out: Do not confuse the DIGIT with its VALUE. The digit is 7, but in 753 its value is 700!

2Beyond Thousands: Up to Millions

Key idea: Numbers are grouped in families of three: ones, thousands, millions. Each family has ones, tens, hundreds inside it.
  1. After hundreds come thousands (1,000), ten-thousands (10,000), hundred-thousands (100,000).
  2. Then millions: 1,000,000 has 6 zeros.
  3. Read each group of three like a small number, then say the family name: 2,347,891 = 2 million, 347 thousand, 891.
  4. 1 million = 1,000 thousands = 10 hundred-thousands.
Worked example
Read 5,206,340 aloud.
Split into families: 5 | 206 | 340. Say: five million, two hundred six thousand, three hundred forty.
Worked example
What is the value of the 4 in 4,512,000?
The 4 is in the millions place, so its value is 4 x 1,000,000 = 4,000,000.
Watch out: Saying 'two millions' is wrong — it is 'two MILLION' (no s) when a number comes before it.

3Reading and Writing Big Numbers

Key idea: Standard form (numbers) and word form (words) are the same number in different clothes — learn to translate both ways.
  1. To read: break into groups of three from the right, read each group, add the family name (thousand, million).
  2. Zero groups still count as a place: 20,045 is 'twenty thousand, forty-five'.
  3. To write from words: write each family's three digits, using zeros as placeholders for missing parts.
  4. Say the number out loud when you check your work.
Worked example
Write 'three hundred forty-five thousand, six hundred two' in standard form.
345 thousand = 345,000. Then add 602: 345,000 + 602 = 345,602.
Worked example
Write 12,008 in words.
Families: 12 | 008. 'Twelve thousand eight.' The two zeros hold the hundreds and tens places.
Watch out: Never skip zeros! 12,008 is NOT 12,800 — each zero is a placeholder holding its place.

4Expanded Form

Key idea: Expanded form breaks a number into the value of each digit added together, showing exactly what each place is worth.
  1. Find the place and value of each digit.
  2. Write each value with plus signs between them.
  3. Digits that are zero add nothing — you can skip them.
  4. Check: add your expanded parts back up — they must equal the original number.
Worked example
Write 4,567 in expanded form.
4 thousands = 4,000; 5 hundreds = 500; 6 tens = 60; 7 ones = 7. So 4,000 + 500 + 60 + 7.
Worked example
Write 30,042 in expanded form.
3 ten-thousands = 30,000; 0 thousands = skip; 0 hundreds = skip; 4 tens = 40; 2 ones = 2. So 30,000 + 40 + 2.
Watch out: In 3,507 the zero hundreds add 0, so the expanded form is 3,000 + 500 + 7 — not 3,000 + 500 + 0 + 7.

5Comparing Numbers

Key idea: Compare numbers from the LEFT, starting with the biggest place. The first place where the digits differ decides the winner.
  1. Line up the numbers. The one with MORE digits is bigger (no leading zeros).
  2. If both have the same digits, compare from the leftmost digit.
  3. Stop at the first place where the digits differ — the bigger digit wins.
  4. Use < (less than), > (greater than), or = (equal to). The open mouth always eats the bigger number.
Worked example
Which sign fits: 4,567 ___ 4,765?
Same thousands (4 = 4). Hundreds: 5 vs 7 — 5 is smaller. So 4,567 < 4,765.
Worked example
Which is bigger: 98,765 or 102,000?
102,000 has 6 digits, 98,765 has 5. More digits wins: 102,000 > 98,765.
Watch out: More digits is not about the first digit! 99,999 (5 digits) is smaller than 100,000 (6 digits).

6Ordering Numbers

Key idea: Ordering is comparing all the numbers at once: least to greatest goes up like stairs, greatest to least goes down.
  1. First sort by digit count: fewer digits = smaller number.
  2. For numbers with the same digit count, compare from the leftmost digit.
  3. Place the smallest (or largest) first and cross it off your list.
  4. Re-read your final order to check every pair.
Worked example
Order least to greatest: 3,204; 3,042; 3,240.
All have 4 digits and start with 3,2. Hundreds: 2, 0, 2. The 0 is smallest: 3,042 first. Then 3,204 vs 3,240: tens 0 < 4, so 3,204 < 3,240. Order: 3,042; 3,204; 3,240.
Worked example
Order greatest to least: 45,000; 54,000; 40,500.
Ten-thousands: 4, 5, 4. 54,000 is biggest. Then 45,000 vs 40,500: thousands 5 > 0. Order: 54,000; 45,000; 40,500.
Watch out: 3,042 and 3,204 look alike but are different — a digit out of place changes the whole number. Read every digit!

7Rounding to Any Place

Key idea: Rounding finds the nearest 'clean' number. Underline the target place, then peek at the digit to its right: 5 or more, round up.
  1. Find and underline the digit in the place you are rounding to.
  2. Look at the digit just to its RIGHT (the boss digit).
  3. If the boss is 5, 6, 7, 8, or 9, round UP (add 1 to the underlined digit). If it is 4 or less, keep it the same.
  4. Change every digit to the right of the underlined place to zero.
Worked example
Round 4,567 to the nearest hundred.
Target is the 5 (hundreds). Boss to the right is 6, which is 5 or more, so round up: 5 becomes 6. Digits after turn to zeros: 4,600.
Worked example
Round 2,349,000 to the nearest million.
Target is the 2 (millions). Boss is 3 (hundred-thousands), which is less than 5, so keep 2. Result: 2,000,000.
Watch out: Rounding UP a 9 causes a carry: 4,951 rounded to the nearest hundred is 5,000, not 4,900!

8Estimating Sums and Differences

Key idea: Estimating means rounding FIRST, then doing the easy math — perfect for checking whether an exact answer is reasonable.
  1. Decide the place to round to (the biggest place in the problem is a good start).
  2. Round every number in the problem to that place.
  3. Do the easy addition or subtraction with the rounded numbers.
  4. Label it an estimate — it will be close, but not exact.
Worked example
Estimate 398 + 212 to the nearest hundred.
398 rounds to 400, 212 rounds to 200. 400 + 200 = 600. Estimate: about 600.
Worked example
Estimate 7,812 – 2,908 to the nearest thousand.
7,812 rounds to 8,000, 2,908 rounds to 3,000. 8,000 – 3,000 = 5,000. Estimate: about 5,000.
Watch out: An estimate is NOT the exact answer! Use it to check your work: if your exact answer is far from the estimate, recheck.
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60-Second Challenge

How many place value and number sense problems can you solve in 60 seconds?