Chapter 3 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

M2.1.3 Chapter 3

Counting on in big steps

I count on in 100s from 3 950. What number comes next?

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

  • Count on and back in 10s, 100s and 1 000s
  • Mark 3 700 on a number line from 0 to 10 000

Counting in big steps is quick. You jump by 10, 100 or 1 000.

To count on is to add the same step again and again. To count back is to take the step away each time.

Count on in 10s from 40: 50, 60, 70. Only the tens digit changes.

Count on in 100s from 300: 400, 500, 600. Only the hundreds digit changes.

Count on in 1 000s from 3 000. Say 4 000, 5 000, 6 000. Only the thousands digit changes.

Take care when a place reaches 10. It moves up to the next place.

Two place value charts. The top chart is labelled 990 and has columns hundreds, tens and ones. Then the words add 10. The bottom chart is labelled 1 000 and has columns thousands, hundreds, tens and ones.990hundredstensones990add 101 000thousandshundredstensones1000
99 tens and 1 more ten make 100 tens. 100 tens is 1 000.

The same thing happens in bigger numbers. 3 950 + 100 = 4 050.

Two place value charts with the headings thousands, hundreds, tens and ones. The top chart is labelled 3 950 and shows 3, 9, 5 and 0. Then the words add 100. The bottom chart is labelled 4 050 and shows 4, 0, 5 and 0.3 950thousandshundredstensones3950add 1004 050thousandshundredstensones4050
9 hundreds and 1 more hundred make 10 hundreds. That is 1 more thousand.

It happens going back too. 1 005 − 10 = 995.

Two place value charts with the headings thousands, hundreds, tens and ones. The top chart is labelled 1 005 and shows 1, 0, 0 and 5. Then the words take away 10. The bottom chart is labelled 995, with the thousands box empty, and shows 9, 9 and 5.1 005thousandshundredstensones1005take away 10995thousandshundredstensones995
1 005 is 100 tens and 5 ones. Take away 1 ten and 99 tens are left.

And at the top: 9 000 + 1 000 = 10 000.

Worked example

Count on in 100s from 6 950. Write the next four numbers.

  1. 6 950 + 100. The hundreds go from 9 to 10.
  2. 10 hundreds make 1 thousand. 6 thousands become 7 thousands.
  3. The hundreds place is now 0. So 6 950 + 100 = 7 050.
  4. Keep adding 100: 7 150, 7 250, 7 350.

Answer: 7 050, 7 150, 7 250, 7 350

Worked example

Count back in 10s from 1 005. Write the next three numbers.

  1. 1 005 is 100 tens and 5 ones.
  2. Take away 1 ten. That leaves 99 tens and 5 ones.
  3. 99 tens and 5 ones is 995.
  4. Keep taking away 10: 985, 975.

Answer: 995, 985, 975

See it three ways

With things

Tie sticks in bundles of 10. Put 4 bundles in a row. Add one bundle at a time and say the total.

As a picture

Seven rods, each one a bundle of 10 sticks, with the label 40, 50, 60, 70.40, 50, 60, 70

In symbols

40 + 10 = 50. 50 + 10 = 60. 60 + 10 = 70. The same works with 100s and 1 000s.

A number line is a line with numbers in order along it. Big numbers fit on one.

Now mark 3 700 on a line from 0 to 10 000. Watch.

Draw it first

Mark 3 700 on a line from 0 to 10 000

  1. A number line from 0 to 10 000 with a long mark at every 1 000 and a short mark at every 500. Step 1 labels 0, 5 000 and 10 000. Step 2 shades the stretch from 3 000 to 4 000 and labels it 3 000 to 4 000. Step 3 puts a point a little past the middle of that stretch, labelled 3 700.05 00010 000

    1 Draw a line. Put 0 at one end and 10 000 at the other. Mark every 1 000.

  2. A number line from 0 to 10 000 with a long mark at every 1 000 and a short mark at every 500. Step 1 labels 0, 5 000 and 10 000. Step 2 shades the stretch from 3 000 to 4 000 and labels it 3 000 to 4 000. Step 3 puts a point a little past the middle of that stretch, labelled 3 700.05 00010 0003 000 to 4 000

    2 Find 3 000 and 4 000. The number 3 700 is in this stretch.

  3. A number line from 0 to 10 000 with a long mark at every 1 000 and a short mark at every 500. Step 1 labels 0, 5 000 and 10 000. Step 2 shades the stretch from 3 000 to 4 000 and labels it 3 000 to 4 000. Step 3 puts a point a little past the middle of that stretch, labelled 3 700.05 00010 0003 000 to 4 0003 700

    3 The middle of the stretch is 3 500. Put your point a little past it.

Try it

Lay out a number line

You need: 11 small stones or bottle tops, 1 bean, a pencil and some scraps of paper.

  1. Put 11 stones in a straight row. Leave the same gap between each stone.
  2. Write 0 on a scrap of paper. Put it under the first stone.
  3. Write 5 000 under the sixth stone. Write 10 000 under the last.
  4. Each stone is 1 000 more than the one before it. Put the bean where 3 700 goes.

What you will see: The bean sits between the fourth and fifth stones. It is a little past the middle.

If you cannot try it, this is what happens.
Eleven stones in a row, spaced the same. The labels under them are 0, 5 000 and 10 000. A bean above the row sits between the fourth and fifth stone, labelled 3 700.3 70005 00010 000

A wrong idea many people have

Counting on in tens only changes the tens digit. So 990 + 10 is 9 100.

Why it feels right: It works for 340 + 10 = 350. The tens digit goes up by 1.

The test that breaks it: Show 990 as 9 flats and 9 rods. Add one rod. Now there are 10 rods. Tie them into a flat. Now there are 10 flats, which make 1 thousand.

What is true: 990 + 10 = 1 000. When a place gets to 10, it moves up. 9 100 is far too big.

Key words

count on
add the same step again and again.
count back
take the same step away again and again.
number line
a line with numbers in order along it.

Back to your guess

The answer is B: 4 050

3 950 + 100 = 4 050. The hundreds place reaches 10. It moves up and makes one more thousand.

Check yourself

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

  1. Count on in 100s from 8 950. What number comes next?

    Tap your answer.

    1. Not this one. You added 10. A step of 100 changes the hundreds place. Try another.

    2. Yes, that is right. 9 hundreds and 1 more hundred is 10 hundreds. That makes one more thousand. 8 950 + 100 = 9 050.

    3. Not this one. You added 1 000. A step of 100 is smaller. Try another.

    See the answer

    9 050

    9 hundreds and 1 more hundred is 10 hundreds. That makes one more thousand. 8 950 + 100 = 9 050.

    • If you chose A: You added 10. A step of 100 changes the hundreds place.
    • If you chose C: You added 1 000. A step of 100 is smaller.

  2. Count on in 10s from 970. Write the next three numbers.

    See the answer

    980, 990, 1 000

    970 + 10 = 980. 980 + 10 = 990. 990 + 10 fills the tens place to 10. That moves up and makes 1 000.

  3. Count back in 10s from 2 000. Write the next three numbers.

    See the answer

    1 990, 1 980, 1 970

    2 000 is 200 tens. Take away 1 ten and you have 199 tens. That is 1 990. Then 1 980 and 1 970.

  4. Fill the gap: 7 000, 8 000, 9 000, __

    Tap your answer.

    1. Yes, that is right. 9 thousands and 1 more thousand make 10 thousands. We write 10 000.

    2. Not this one. You added 100. This line goes up in 1 000s. Try another.

    3. Not this one. 9 000 and 1 000 more make 10 thousands. That is 10 000, with five digits. Try another.

    See the answer

    10 000

    9 thousands and 1 more thousand make 10 thousands. We write 10 000.

    • If you chose B: You added 100. This line goes up in 1 000s.
    • If you chose C: 9 000 and 1 000 more make 10 thousands. That is 10 000, with five digits.

  5. Mei marks 2 400 on a line from 0 to 10 000. The line has a mark at every 1 000. Where does it go?

    A number line from 0 to 10 000 with a mark at every 1 000 and a short mark at every 500. The labels are 0, 5 000 and 10 000.05 00010 000
    Tap your answer.

    1. Yes, that is right. 2 400 is 2 thousands and 4 hundreds. It is past 2 000 but less than 2 500, the middle.

    2. Not this one. The middle of that stretch is 2 500. 2 400 is less than 2 500. Try another.

    3. Not this one. You may have looked at the 4 in 2 400. The 2 is in the thousands place. Go to M2.1.2. Try another.

    See the answer

    Between 2 000 and 3 000, before the middle.

    2 400 is 2 thousands and 4 hundreds. It is past 2 000 but less than 2 500, the middle.

    • If you chose B: The middle of that stretch is 2 500. 2 400 is less than 2 500.
    • If you chose C: You may have looked at the 4 in 2 400. The 2 is in the thousands place. Go to M2.1.2.

  6. From an earlier chapter

    Write eight thousand, four hundred and six in figures.

    See the answer

    8 406

    8 thousands, 4 hundreds, 0 tens and 6 ones. 8 000 + 400 + 6 = 8 406.

  7. Count on in 10s from 2 990. What number comes next?

    Tap your answer.

    1. Not this one. You added 100. A step of 10 only fills the tens place. Try another.

    2. Not this one. The two 9s became 0, but nothing moved up. That is less than 2 990. Try another.

    3. Yes, that is right. 2 990 is 299 tens. One more ten makes 300 tens. 300 tens is 3 000.

    See the answer

    3 000

    2 990 is 299 tens. One more ten makes 300 tens. 300 tens is 3 000.

    • If you chose A: You added 100. A step of 10 only fills the tens place.
    • If you chose B: The two 9s became 0, but nothing moved up. That is less than 2 990.

  8. Count back in 10s from 3 005. What number comes next?

    Tap your answer.

    1. Not this one. You took away 100. A step of 10 takes away 1 ten. Try another.

    2. Not this one. You took away the 5 ones. Take away 1 ten instead. Try another.

    3. Yes, that is right. 3 005 is 300 tens and 5 ones. Take away 1 ten and 299 tens and 5 ones are left. That is 2 995.

    See the answer

    2 995

    3 005 is 300 tens and 5 ones. Take away 1 ten and 299 tens and 5 ones are left. That is 2 995.

    • If you chose A: You took away 100. A step of 10 takes away 1 ten.
    • If you chose B: You took away the 5 ones. Take away 1 ten instead.

  9. Joseph marks 7 800 on the same line. Where does it go?

    A number line from 0 to 10 000 with a mark at every 1 000 and a short mark at every 500. The labels are 0, 5 000 and 10 000.05 00010 000
    Tap your answer.

    1. Not this one. You may have looked at the 8 in 7 800. The 7 is in the thousands place. Go to M2.1.2. Try another.

    2. Not this one. The middle of that stretch is 7 500. 7 800 is more than 7 500. Try another.

    3. Yes, that is right. 7 800 is 7 thousands and 8 hundreds. It is past the middle, 7 500, but less than 8 000.

    See the answer

    Between 7 000 and 8 000, after the middle.

    7 800 is 7 thousands and 8 hundreds. It is past the middle, 7 500, but less than 8 000.

    • If you chose A: You may have looked at the 8 in 7 800. The 7 is in the thousands place. Go to M2.1.2.
    • If you chose B: The middle of that stretch is 7 500. 7 800 is more than 7 500.

Keep it

Copy this into your exercise book.

Count on in 10s, 100s or 1 000s. A full place moves up: 990 + 10 = 1 000. 3 700 sits past the middle of 3 000 and 4 000.

Draw: A line from 0 to 10 000. Mark every 1 000. Put a point for 3 700 and label it.

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

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