Chapter 1 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

M2.1.1 Chapter 1

Hundreds, tens and ones

The 5 in 538 is not worth 5. So what is it worth?

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

  • Show a number up to 999 as hundreds, tens and ones
  • Say what each digit in 538 is worth
  • Use 0 to hold an empty place, as in 305

You have a pile of 538 beans. Counting them one by one takes ages.

A faster way is to make groups. 10 ones make 1 ten. 10 tens make 1 hundred.

A bundle of 10 sticks is a ten. Tie 10 bundles together and you have a hundred.

Three base ten blocks. A small square labelled 1 one. A rod of 10 squares labelled 1 ten. A flat of 100 squares labelled 1 hundred.1 one1 ten1 hundred
A flat is 10 rods side by side. 10 rows of 10 squares is 100.

Now build 538 with blocks. Watch.

Draw it first

Build 538 from hundreds, tens and ones

  1. Blocks for 538. Step 1 shows 5 flats, labelled 5 hundreds = 500. Step 2 adds 3 rods, labelled 3 tens = 30. Step 3 adds 8 small squares, labelled 8 ones = 8. Step 4 adds the sum 500 + 30 + 8 = 538.5 hundreds = 500

    1 Show 5 hundreds. Each flat is 100, so this is 500.

  2. Blocks for 538. Step 1 shows 5 flats, labelled 5 hundreds = 500. Step 2 adds 3 rods, labelled 3 tens = 30. Step 3 adds 8 small squares, labelled 8 ones = 8. Step 4 adds the sum 500 + 30 + 8 = 538.5 hundreds = 5003 tens = 30

    2 Add 3 tens. Each rod is 10, so this is 30.

  3. Blocks for 538. Step 1 shows 5 flats, labelled 5 hundreds = 500. Step 2 adds 3 rods, labelled 3 tens = 30. Step 3 adds 8 small squares, labelled 8 ones = 8. Step 4 adds the sum 500 + 30 + 8 = 538.5 hundreds = 5003 tens = 308 ones = 8

    3 Add 8 ones. Each small square is 1, so this is 8.

  4. Blocks for 538. Step 1 shows 5 flats, labelled 5 hundreds = 500. Step 2 adds 3 rods, labelled 3 tens = 30. Step 3 adds 8 small squares, labelled 8 ones = 8. Step 4 adds the sum 500 + 30 + 8 = 538.5 hundreds = 5003 tens = 308 ones = 8500 + 30 + 8 = 538

    4 Add them up. 500 + 30 + 8 = 538.

The symbols 0 to 9 are digits. 538 has three digits.

Each digit has a place. The place tells you what the digit is worth. This is place value.

A place value chart with three columns: hundreds, tens and ones. The digits are 5, 3 and 8.hundredstensones538
The 5 is in the hundreds place. The 3 is in the tens place. The 8 is in the ones place.

So the 5 is worth 500. The 3 is worth 30. The 8 is worth 8.

Worked example

What is the 3 worth in 538?

  1. 538 is 5 hundreds, 3 tens and 8 ones.
  2. The 3 is in the tens place.
  3. 3 tens is 3 × 10 = 30.

Answer: 30

Worked example

Write 3 hundreds and 4 ones as a number.

  1. 3 hundreds is 300.
  2. There are no tens, so put 0 in the tens place.
  3. 4 ones is 4. Now 300 + 0 + 4 = 304.

Answer: 304

See it three ways

With things

A farmer packs beans. A big sack holds 100. A small bag holds 10. For 124 beans she uses 1 big sack. She adds 2 small bags and 4 loose beans.

As a picture

Blocks for 124 with the label 124 = 100 + 20 + 4. One flat for 100, two rods for 20 and four small squares for 4.124 = 100 + 20 + 4

In symbols

124 = 100 + 20 + 4. That is 1 hundred, 2 tens and 4 ones.

Try it

Draw a number in blocks

You need: a pencil, a sheet of paper, or an old page.

  1. Draw a big square for 100. Draw a long line for 10. Draw a dot for 1.
  2. Draw 237 like this. Make 2 big squares, 3 long lines and 7 dots.
  3. Ask a friend to read your drawing and say the number.
  4. Now your friend draws a number. You read it.

What you will see: The drawing shows how many hundreds, tens and ones there are. Add them up to find the number.

If you cannot try it, this is what happens.
Blocks for 237 with the label 237 = 200 + 30 + 7. There are 2 flats, 3 rods and 7 small squares.237 = 200 + 30 + 7
A place value chart with three columns: hundreds, tens and ones. The digits are 3, 0 and 4.hundredstensones304
Three hundred and four. There are 3 hundreds, no tens and 4 ones.

What if you leave the 0 out of 305? Look at the two charts.

Two place value charts with the headings hundreds, tens and ones. The top chart is labelled 35 and has the digits 3 and 5, with the hundreds box empty. The bottom chart is labelled 305 and has the digits 3, 0 and 5.35hundredstensones35305hundredstensones305
Without the 0, the 3 slides to the tens place. It is worth 30, not 300.

A wrong idea many people have

You write a number the way you say it. "Three hundred and four" is 3004.

Why it feels right: You say 300, then 4. So it seems you write 300 and then 4.

The test that breaks it: Build three hundred and four with blocks. You need 3 flats, no rods and 4 ones. Put them in the chart. The digits are 3, 0 and 4.

What is true: The number is 304. The 0 holds the tens place, where there are none.

Key words

digit
one of the symbols 0 to 9.
place value
what a digit is worth, because of the place it sits in.
hundred
10 tens, or 100 ones.

Back to your guess

The answer is B: It is worth 5 hundreds, which is 500.

Where a digit sits tells you what it is worth. The 5 is in the hundreds place, so it is worth 500.

Check yourself

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

  1. What is the 7 worth in 372?

    Tap your answer.

    1. Not this one. That is the digit, not what it is worth. The 7 is in the tens place. Try another.

    2. Yes, that is right. 372 is 3 hundreds, 7 tens and 2 ones. 7 tens is 70.

    3. Not this one. 700 is 7 hundreds. In 372 the 3 is in the hundreds place. Try another.

    See the answer

    70

    372 is 3 hundreds, 7 tens and 2 ones. 7 tens is 70.

    • If you chose A: That is the digit, not what it is worth. The 7 is in the tens place.
    • If you chose C: 700 is 7 hundreds. In 372 the 3 is in the hundreds place.

  2. Write 6 hundreds, 2 tens and 9 ones as a number.

    See the answer

    629

    600 + 20 + 9 = 629.

  3. Write 407 as hundreds, tens and ones.

    See the answer

    4 hundreds, 0 tens and 7 ones

    The 4 is in the hundreds place. The 7 is in the ones place. The 0 means no tens.

  4. Which number do these blocks show?

    Blocks showing some flats, some rods and some small squares. The labels are flats, rods and ones.flatsrodsones
    Tap your answer.

    1. Yes, that is right. 2 flats is 200. 5 rods is 50. 3 small squares is 3. 200 + 50 + 3 = 253.

    2. Not this one. You may have swapped the tens and the ones. Rods are tens. Squares are ones. Try another.

    3. Not this one. You may have started with the 5 rods. Flats come first, and there are 2 flats. Try another.

    4. Not this one. That adds up how many blocks there are. A flat, a rod and a square are worth different amounts. Try another.

    See the answer

    253

    2 flats is 200. 5 rods is 50. 3 small squares is 3. 200 + 50 + 3 = 253.

    • If you chose B: You may have swapped the tens and the ones. Rods are tens. Squares are ones.
    • If you chose C: You may have started with the 5 rods. Flats come first, and there are 2 flats.
    • If you chose D: That adds up how many blocks there are. A flat, a rod and a square are worth different amounts.

  5. Kofi writes three hundred and eight as 3008. What is the right number?

    See the answer

    308

    3 hundreds, 0 tens and 8 ones is 308. The 3 is in the hundreds place. The number has only three digits.

  6. In which number is the 4 worth 40?

    Tap your answer.

    1. Yes, that is right. 248 is 2 hundreds, 4 tens and 8 ones. 4 tens is 40.

    2. Not this one. In 482 the 4 is in the hundreds place. It is worth 400. Try another.

    3. Not this one. In 824 the 4 is in the ones place. It is worth 4. Try another.

    See the answer

    248

    248 is 2 hundreds, 4 tens and 8 ones. 4 tens is 40.

    • If you chose B: In 482 the 4 is in the hundreds place. It is worth 400.
    • If you chose C: In 824 the 4 is in the ones place. It is worth 4.

  7. Which number do these blocks show?

    Blocks showing some flats and some small squares, and no rods. The labels are flats and ones.flatsones
    Tap your answer.

    1. Not this one. There are no rods, so the tens place needs a 0. Without it the 2 is worth 20. Try another.

    2. Not this one. The squares are ones, not tens. Put the 6 in the ones place. Try another.

    3. Yes, that is right. There are 2 flats, no rods and 6 squares. That is 2 hundreds, 0 tens and 6 ones. 200 + 0 + 6 = 206.

    See the answer

    206

    There are 2 flats, no rods and 6 squares. That is 2 hundreds, 0 tens and 6 ones. 200 + 0 + 6 = 206.

    • If you chose A: There are no rods, so the tens place needs a 0. Without it the 2 is worth 20.
    • If you chose B: The squares are ones, not tens. Put the 6 in the ones place.

  8. Ana says six hundred and five. Which number is it?

    Tap your answer.

    1. Not this one. That is six thousand and five. Six hundred and five has only three digits. Try another.

    2. Not this one. You may have left out the 0. Then the 6 is worth 60, not 600. Try another.

    3. Not this one. The 5 is 5 ones, not 5 tens. The 0 holds the tens place. Try another.

    4. Yes, that is right. 6 hundreds, 0 tens and 5 ones. 600 + 0 + 5 = 605.

    See the answer

    605

    6 hundreds, 0 tens and 5 ones. 600 + 0 + 5 = 605.

    • If you chose A: That is six thousand and five. Six hundred and five has only three digits.
    • If you chose B: You may have left out the 0. Then the 6 is worth 60, not 600.
    • If you chose C: The 5 is 5 ones, not 5 tens. The 0 holds the tens place.

  9. How is 614 made of hundreds, tens and ones?

    Tap your answer.

    1. Not this one. That swaps the tens and the ones. In 614 the 1 is in the tens place. Try another.

    2. Yes, that is right. The 6 is in the hundreds place. The 1 is in the tens place. The 4 is in the ones place.

    3. Not this one. That swaps the hundreds and the tens. The 6 is in the hundreds place. Try another.

    See the answer

    6 hundreds, 1 ten and 4 ones

    The 6 is in the hundreds place. The 1 is in the tens place. The 4 is in the ones place.

    • If you chose A: That swaps the tens and the ones. In 614 the 1 is in the tens place.
    • If you chose C: That swaps the hundreds and the tens. The 6 is in the hundreds place.

Keep it

Copy this into your exercise book.

10 ones make a ten. 10 tens make a hundred. In 538 the 5 is worth 500. The 3 is worth 30. The 8 is worth 8.

Draw: 5 big squares, 3 long lines and 8 dots. Write 500 + 30 + 8 = 538 beside them.

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.