Chapter 4 of 6

All 6 chapters
  1. 1Hundreds, tens and ones, readunderstood
  2. 2Thousands, readunderstood
  3. 3Counting on in big steps, readunderstood
  4. 4Comparing and ordering, readunderstood
  5. 5Rounding and estimating, readunderstood
  6. 6Up to a million, and lakhs, readunderstood

M2.1.4 Chapter 4

Comparing and ordering

The nines look so big. Is 999 bigger than 1 000?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Compare two numbers up to 10 000 using < and >
  • Put five numbers in order from smallest to largest

Amina has 999 seeds. Kofi has 1 000 seeds. Who has more?

To compare two numbers is to say which one is bigger.

First take two numbers with the same count of digits. Watch where they first differ.

Draw it first

Compare 3 472 and 3 508

  1. Two place value charts, one above the other. The top chart shows 3 472 and the bottom chart shows 3 508. The headings are thousands, hundreds, tens and ones. Step 1 asks: which is bigger? Step 2 boxes the thousands column and says: thousands: 3 and 3, the same. Step 3 boxes the hundreds column and says: hundreds: 4 is less than 5. Step 4 writes 3 472 < 3 508.thousandshundredstensones3472thousandshundredstensones3508which is bigger?

    1 Write the numbers one above the other. Line up the places.

  2. Two place value charts, one above the other. The top chart shows 3 472 and the bottom chart shows 3 508. The headings are thousands, hundreds, tens and ones. Step 1 asks: which is bigger? Step 2 boxes the thousands column and says: thousands: 3 and 3, the same. Step 3 boxes the hundreds column and says: hundreds: 4 is less than 5. Step 4 writes 3 472 < 3 508.thousandshundredstensones3472thousandshundredstensones3508thousands: 3 and 3, the same

    2 Start at the left. The thousands are 3 and 3. They match, so move right.

  3. Two place value charts, one above the other. The top chart shows 3 472 and the bottom chart shows 3 508. The headings are thousands, hundreds, tens and ones. Step 1 asks: which is bigger? Step 2 boxes the thousands column and says: thousands: 3 and 3, the same. Step 3 boxes the hundreds column and says: hundreds: 4 is less than 5. Step 4 writes 3 472 < 3 508.thousandshundredstensones3472thousandshundredstensones3508hundreds: 4 is less than 5

    3 The hundreds are 4 and 5. They differ. 4 is less than 5.

  4. Two place value charts, one above the other. The top chart shows 3 472 and the bottom chart shows 3 508. The headings are thousands, hundreds, tens and ones. Step 1 asks: which is bigger? Step 2 boxes the thousands column and says: thousands: 3 and 3, the same. Step 3 boxes the hundreds column and says: hundreds: 4 is less than 5. Step 4 writes 3 472 < 3 508.thousandshundredstensones3472thousandshundredstensones35083 472 < 3 508

    4 So 3 472 is less than 3 508. Write 3 472 < 3 508.

The first digit that differs decides. Stop there. The other digits do not matter.

Now think about numbers with different digit counts. Look at 999 and 1 000.

Two place value charts, one above the other, with the headings thousands, hundreds, tens and ones. The top chart shows 999, with the thousands box empty. The bottom chart shows 1 000.thousandshundredstensones999thousandshundredstensones1000
1 000 has four digits. 999 has three. The number with more digits is bigger.

More digits means bigger, when no number starts with a zero.

987 starts with a 9, but 4 205 is bigger.

Two signs say which is bigger. The sign < means less than. The sign > means greater than.

Two rows. The top row shows 3 < 5, with the word point under the 3 and the words open side under the 5. The bottom row shows 5 > 3, with the words open side under the 5 and the word point under the 3.3point<5open side5open side>3point
The open side faces the bigger number. The point faces the smaller one.

3 < 5 reads: 3 is less than 5. And 5 > 3 reads: 5 is greater than 3.

See it three ways

With things

Write 4 621 and 4 598 on paper, one digit per box. Line up the places. Check from the left.

As a picture

Two place value charts, one above the other. The top chart shows 4 621 and the bottom chart shows 4 598. The headings are thousands, hundreds, tens and ones. The hundreds column is boxed in both charts.thousandshundredstensones4621thousandshundredstensones4598

In symbols

4 621 > 4 598. The thousands match. The hundreds decide: 6 is more than 5.

4 598 has bigger digits at the end. They do not matter. The hundreds already decided.

Worked example

Order these numbers, smallest first. 4 250, 987, 4 205, 5 031, 1 000.

  1. Count the digits. 987 has three. The others have four. So 987 is smallest.
  2. Look at the thousands digit. 1 000 has 1. 4 250 and 4 205 have 4. 5 031 has 5.
  3. So 1 000 comes next, and 5 031 comes last.
  4. 4 250 and 4 205 match in the thousands and hundreds. The tens are 5 and 0. So 4 205 comes first.

Answer: 987, 1 000, 4 205, 4 250, 5 031

Try it

Put number cards in order

You need: five small bits of paper, a pencil.

  1. Write one number on each bit of paper. Use 4 250, 873, 4 205, 1 090 and 9 999.
  2. Mix the cards up on the table.
  3. Find the card with the fewest digits. Put it on the left.
  4. Compare the others from the left. Put the smaller card first each time.
  5. Read the cards aloud, from smallest to largest.

What you will see: The card with the fewest digits comes first. When digit counts match, the first different digit decides.

If you cannot try it, this is what happens.
Five cards in a row: 873, 1 090, 4 205, 4 250 and 9 999. The word smallest is under the first card and the word largest is under the last card.8731 0904 2054 2509 999smallestlargest

A wrong idea many people have

999 is bigger than 1 000, because nines are big digits.

Why it feels right: A 9 is the biggest digit. A number of nines feels huge.

The test that breaks it: Count up from 997. You say 998, 999, then 1 000. Counting up always gives a bigger number. So 1 000 is more than 999.

What is true: Count the digits first. More digits means a bigger number. 1 000 has four digits and 999 has three.

Key words

compare
to say which of two numbers is bigger.
less than
smaller than. The sign < means less than.
greater than
bigger than. The sign > means greater than.

Back to your guess

The answer is B: 1 000 is bigger, because it has more digits.

1 000 has four digits. 999 has three. A number with more digits is bigger. 1 000 is just one more than 999.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Which sign goes in the gap? 6 308 __ 6 380

    Two place value charts, one above the other. The top chart shows 6 308 and the bottom chart shows 6 380. The headings are thousands, hundreds, tens and ones.thousandshundredstensones6308thousandshundredstensones6380
    Tap your answer.

    1. Not this one. Look for the first digit that differs. The tens are 0 and 8. 0 is less than 8, so 6 308 is the smaller number. Try another.

    2. Not this one. The digits are the same, but they sit in different places. The tens are 0 and 8. Go to M2.1.1. Try another.

    3. Yes, that is right. The thousands and hundreds match. The tens are 0 and 8. 0 is less than 8, so 6 308 < 6 380.

    See the answer

    <

    The thousands and hundreds match. The tens are 0 and 8. 0 is less than 8, so 6 308 < 6 380.

    • If you chose A: Look for the first digit that differs. The tens are 0 and 8. 0 is less than 8, so 6 308 is the smaller number.
    • If you chose B: The digits are the same, but they sit in different places. The tens are 0 and 8. Go to M2.1.1.

  2. Which is bigger, 9 999 or 10 000?

    Tap your answer.

    1. Not this one. Four 9s look big, but 10 000 has five digits. More digits means a bigger number. Go to M2.1.3. Try another.

    2. Not this one. 9 999 + 1 = 10 000, so 10 000 is one more. Try another.

    3. Yes, that is right. 10 000 has five digits and 9 999 has four. More digits means a bigger number.

    See the answer

    10 000

    10 000 has five digits and 9 999 has four. More digits means a bigger number.

    • If you chose A: Four 9s look big, but 10 000 has five digits. More digits means a bigger number. Go to M2.1.3.
    • If you chose B: 9 999 + 1 = 10 000, so 10 000 is one more.

  3. Put these in order, smallest first. 5 120, 987, 5 102, 2 999, 7 010.

    See the answer

    987, 2 999, 5 102, 5 120, 7 010

    987 has three digits, so it is first. Then compare the thousands: 2, 5, 5, 7. For 5 102 and 5 120, the tens decide. 0 is less than 2.

  4. Use the digits 4, 0, 7 and 2 once each. Make the biggest number you can.

    See the answer

    7 420

    Put the biggest digit in the biggest place. 7 goes in the thousands, then 4, 2 and 0.

  5. From an earlier chapter

    In 6 319, what is the digit 3 worth?

    See the answer

    300

    The 3 is in the hundreds place. 3 hundreds is 300.

  6. Which is the smallest? 7 305, 7 035 or 7 350.

    Three place value charts, one above the other. They show 7 305, 7 035 and 7 350. The headings are thousands, hundreds, tens and ones.thousandshundredstensones7305thousandshundredstensones7035thousandshundredstensones7350
    Tap your answer.

    1. Not this one. You may have looked at the last digit, 0. Start at the left. The hundreds decide. Try another.

    2. Yes, that is right. The thousands all match. The hundreds are 3, 0 and 3. 0 is the least, so 7 035 is the smallest.

    3. Not this one. It has 3 hundreds. 7 035 has 0 hundreds, so it is smaller. Try another.

    See the answer

    7 035

    The thousands all match. The hundreds are 3, 0 and 3. 0 is the least, so 7 035 is the smallest.

    • If you chose A: You may have looked at the last digit, 0. Start at the left. The hundreds decide.
    • If you chose C: It has 3 hundreds. 7 035 has 0 hundreds, so it is smaller.

  7. Order 4 250, 879, 4 205 and 1 090, smallest first. Which list is right?

    Tap your answer.

    1. Yes, that is right. 879 has three digits, so it is first. 1 090 has the least thousands. The tens decide for 4 205 and 4 250. 0 is less than 5.

    2. Not this one. You compared only the first digits. 879 has three digits, so it is the smallest. Try another.

    3. Not this one. Look at 4 250 and 4 205. The tens are 5 and 0. The smaller one comes first. Try another.

    See the answer

    879, 1 090, 4 205, 4 250

    879 has three digits, so it is first. 1 090 has the least thousands. The tens decide for 4 205 and 4 250. 0 is less than 5.

    • If you chose B: You compared only the first digits. 879 has three digits, so it is the smallest.
    • If you chose C: Look at 4 250 and 4 205. The tens are 5 and 0. The smaller one comes first.

  8. Which sentence is true?

    Tap your answer.

    1. Not this one. The open side of < faces 4 598. That says 4 598 is greater. Try another.

    2. Not this one. 4 598 has bigger last digits. They do not matter. The hundreds decide. 6 is more than 5, so 4 598 is smaller. Try another.

    3. Yes, that is right. The open side of the sign faces the bigger number. 4 621 is bigger, so it goes on the open side.

    See the answer

    4 621 > 4 598

    The open side of the sign faces the bigger number. 4 621 is bigger, so it goes on the open side.

    • If you chose A: The open side of < faces 4 598. That says 4 598 is greater.
    • If you chose B: 4 598 has bigger last digits. They do not matter. The hundreds decide. 6 is more than 5, so 4 598 is smaller.

Keep it

Copy this into your exercise book.

More digits means a bigger number. With the same count of digits, look from the left. The first digit that differs decides. 3 < 5 and 5 > 3. The open side faces the bigger number.

Draw: Two numbers, one above the other, with a sign between them. Circle the first digit that differs.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (675 KB). It opens on any phone.