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Step-by-step practice: Maths · Level 4Chapter 1 · Counting and place value to 10000
Level 4 · Chapter 1

Counting and place value to 10000

By the end of this chapter you will be able to

  • Count on and back in hundreds, thousands and fifties
  • Say the value of each digit in a four-digit number
  • Partition a number in more than one way
  • Read and write four-digit numbers in figures and words
  • Say 1000 more and 1000 less than any number

You should already know

  • Counting and place value to 1000 (Level 3, chapter 2)
  • Counting in tens and hundreds (Level 3, chapter 1)

Where this leads

  • Comparing, ordering and rounding four-digit numbers (chapter 2)

Step-by-step practice: maths (Level 4). Small steps, repeated until fluent. Content: Count in steps of 50, 100 and 1000 from any number, forwards and backwards (PV1), Recognise the place value of each digit in a four-digit number (PV2), Read and write numbers to 10000 in figures and in words (PV5), Count in 1000s and find 1000 more or less than a given number (Year 4 paraphrase).

Exercise P  Do you remember?

Non-calculator
1
FCount on in tens from 340. What number do you reach after 4 counts?
2
FWhat is 100 more than 645?
3
FWrite 507 in words.
4
FWhich is greater, 412 or 421?
5
FWhat is 2 + 2 + 2 + 2?
1.1

Counting in hundreds

Level 4
Count on and back in steps of 100 from any number to 10000
Video lesson: Counting in hundredsComing soon

Counting in hundreds means each number is 100 more than the one before. Only the hundreds digit goes up by 1 each time, until the hundreds go past 9. Then the thousands digit goes up by 1.

Counting back in hundreds means each number is 100 less than the one before.

Key ideas

  • Counting on in hundreds adds 100 each time.
  • Counting back in hundreds takes away 100 each time.
  • Find the step first, then count in that step.
Worked example 1.1.1
Count on in hundreds from 2350. What number do you reach after 3 counts?

Method. Count in steps of the same size, one step at a time.

  1. Start at the first number. It is where we begin.
    2350
  2. Add 100 each time. Each count moves by the same step.
    2350 + 100 = 2450
  3. Add 100 each time. Each count moves by the same step.
    2450 + 100 = 2550
  4. Add 100 each time. Each count moves by the same step.
    2550 + 100 = 2650
  5. Write the answer. This is the last number we reached.
    2650

Check. Count the steps back: 2650 - 300 = 2350.

Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.

Worked example 1.1.2
Count back in hundreds from 4100. What number do you reach after 2 counts?

Method. Count in steps of the same size, one step at a time.

  1. Start at the first number. It is where we begin.
    4100
  2. Take 100 each time. Each count moves by the same step.
    4100 - 100 = 4000
  3. Take 100 each time. Each count moves by the same step.
    4000 - 100 = 3900
  4. Write the answer. This is the last number we reached.
    3900

Check. Count the steps back: 3900 + 200 = 4100.

Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.

Worked example 1.1.3
Fill in the missing number in this count: 6200, 6300, ___, 6500

Method. Find the step between the numbers, then count on to fill the gap.

  1. Find the step. The numbers go up by the same amount each time.
    6300 - 6200 = 100
  2. Count on from 6300. Add the step to the number before the gap.
    6300 + 100 = 6400
  3. Write the missing number. It fits the pattern.
    6400

Check. Check: 6400 + 100 = 6500, the next number.

Watch out. Look at the numbers either side of the gap.

Watch out

Watch out. 2950 + 100 is 3050, not 2960. The hundreds go past 9, so the thousands digit goes up.

Exam tip

Grown-up tip. Ask the child to say the step out loud as they go: “2350, 2450, 2550.” Aim to count in hundreds from any number in under 10 seconds.

Exercise 1A  Practice: counting in hundreds

Non-calculator
1
FCount on in hundreds from 3009. What number do you reach after 5 counts?
2
FCount back in hundreds from 1290. What number do you reach after 2 counts?
3
FCount on in hundreds from 2082. What number do you reach after 5 counts?
4
FCount back in hundreds from 1910. What number do you reach after 4 counts?
5
FCount on in hundreds from 1478. What number do you reach after 4 counts?
6
FCount on in hundreds from 7174. What number do you reach after 3 counts?
7
FCount on in hundreds from 8726. What number do you reach after 5 counts?
8
FFill in the missing number in this count: 4864, 4964, ___, 5164
9
FCount on in hundreds from 7878. What number do you reach after 5 counts?
10
FCount back in hundreds from 7424. What number do you reach after 5 counts?
11
FCount back in hundreds from 9961. What number do you reach after 3 counts?
12
FCount back in hundreds from 4069. What number do you reach after 2 counts?
13
FCount on in hundreds from 8581. What number do you reach after 5 counts?
14
FFill in the missing number in this count: 4771, ___, 4971, 5071
15
FCount back in hundreds from 4363. What number do you reach after 2 counts?
16
FFill in the missing number in this count: 7133, ___, 7333, 7433
1.2

Counting in thousands; 1000 more and 1000 less

Level 4
Count on and back in steps of 1000, Say 1000 more and 1000 less than any number to 10000
Video lesson: Counting in thousands; 1000 more and 1000 lessComing soon

Adding 1000 changes only the thousands digit: it goes up by 1. Taking away 1000 changes the thousands digit: it goes down by 1.

The hundreds, tens and ones stay the same.

Key ideas

  • 1000 more: the thousands digit goes up by 1.
  • 1000 less: the thousands digit goes down by 1.
  • The other digits do not change.
Worked example 1.2.1
What is 1000 more than 4826?

Method. Change the thousands digit by one; the other digits stay the same.

  1. Look at the thousands digit. Only the thousands digit changes.
    4826 has 4 thousands
  2. Add one thousand. The thousands digit goes up by 1.
    4 + 1 = 5 thousands
  3. Write the answer. The hundreds, tens and ones stay the same.
    5826

Check. Check: 5826 - 4826 = 1000.

Watch out. Do not change the hundreds, tens or ones.

Worked example 1.2.2
What is 1000 less than 7060?

Method. Change the thousands digit by one; the other digits stay the same.

  1. Look at the thousands digit. Only the thousands digit changes.
    7060 has 7 thousands
  2. Take away one thousand. The thousands digit goes down by 1.
    7 - 1 = 6 thousands
  3. Write the answer. The hundreds, tens and ones stay the same.
    6060

Check. Check: 6060 + 1000 = 7060.

Watch out. The 0 in the hundreds place stays a 0.

Worked example 1.2.3
Count on in thousands from 2415. What number do you reach after 3 counts?

Method. Count in steps of the same size, one step at a time.

  1. Start at the first number. It is where we begin.
    2415
  2. Add 1000 each time. Each count moves by the same step.
    2415 + 1000 = 3415
  3. Add 1000 each time. Each count moves by the same step.
    3415 + 1000 = 4415
  4. Add 1000 each time. Each count moves by the same step.
    4415 + 1000 = 5415
  5. Write the answer. This is the last number we reached.
    5415

Check. Count the steps back: 5415 - 3000 = 2415.

Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.

Watch out

Watch out. 1000 more than 4826 is 5826, not 4836. Change the thousands, not the tens.

Exam tip

Grown-up tip. Point to the thousands digit before each answer. Ask: “Which digit changes, and by how much?”

Exercise 1B  Practice: counting in thousands

Non-calculator
1
FCount on in thousands from 3334. What number do you reach after 4 counts?
2
FCount on in thousands from 1128. What number do you reach after 4 counts?
3
FWhat is 1000 less than 3054?
4
FCount on in thousands from 1867. What number do you reach after 4 counts?
5
FCount on in thousands from 4441. What number do you reach after 2 counts?
6
FCount on in thousands from 3427. What number do you reach after 5 counts?
7
FCount on in thousands from 1370. What number do you reach after 2 counts?
8
FCount on in thousands from 1436. What number do you reach after 2 counts?
9
FWhat is 1000 less than 3745?
10
FWhat is 1000 more than 1910?
11
FCount on in thousands from 5514. What number do you reach after 4 counts?
12
FCount back in thousands from 9613. What number do you reach after 5 counts?
13
FCount on in thousands from 3901. What number do you reach after 5 counts?
14
FCount back in thousands from 4738. What number do you reach after 2 counts?
15
FCount back in thousands from 7752. What number do you reach after 5 counts?
16
FWhat is 1000 more than 4496?
1.3

Counting in fifties

Level 4
Count on and back in steps of 50 from any multiple of 50 to 10000
Video lesson: Counting in fiftiesComing soon

Fifty is half of a hundred. Counting in fifties gives 50, 100, 150, 200 and so on.

Each hundred has two fifties in it: the number ends in 50 or 00.

Key ideas

  • Each fifty ends in 50 or 00.
  • Fifty is half of a hundred.
  • Count in steps of 50 to find the answer.
Worked example 1.3.1
Fill in the missing number in this count: 1850, 1900, ___, 2000

Method. Find the step between the numbers, then count on to fill the gap.

  1. Find the step. The numbers go up by 50 each time.
    1900 - 1850 = 50
  2. Count on from 1900. Add 50 to get the missing number.
    1900 + 50 = 1950
  3. Write the missing number. It fits the pattern.
    1950

Check. Check: 1950 + 50 = 2000.

Watch out. Fifties go up in steps of 50, so the ones and tens count in fifties.

Worked example 1.3.2
Count on in fifties from 3250. What number do you reach after 4 counts?

Method. Count in steps of the same size, one step at a time.

  1. Start at the first number. It is where we begin.
    3250
  2. Add 50 each time. Each count moves by the same step.
    3250 + 50 = 3300
  3. Add 50 each time. Each count moves by the same step.
    3300 + 50 = 3350
  4. Add 50 each time. Each count moves by the same step.
    3350 + 50 = 3400
  5. Add 50 each time. Each count moves by the same step.
    3400 + 50 = 3450
  6. Write the answer. This is the last number we reached.
    3450

Check. Count the steps back: 3450 - 200 = 3250.

Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.

Worked example 1.3.3
Count back in fifties from 6000. What number do you reach after 3 counts?

Method. Count in steps of the same size, one step at a time.

  1. Start at the first number. It is where we begin.
    6000
  2. Take 50 each time. Each count moves by the same step.
    6000 - 50 = 5950
  3. Take 50 each time. Each count moves by the same step.
    5950 - 50 = 5900
  4. Take 50 each time. Each count moves by the same step.
    5900 - 50 = 5850
  5. Write the answer. This is the last number we reached.
    5850

Check. Count the steps back: 5850 + 150 = 6000.

Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.

Watch out

Watch out. After 1950 comes 2000, not 1960. Fifties always end in 00 or 50.

Exam tip

Grown-up tip. Ask the child to count in fifties from a multiple of 50, such as 3250, then say the next number before you do.

Exercise 1C  Practice: counting in fifties

Non-calculator
1
FCount on in fifties from 2000. What number do you reach after 4 counts?
2
FCount on in fifties from 4200. What number do you reach after 3 counts?
3
FCount on in fifties from 2950. What number do you reach after 3 counts?
4
FCount back in fifties from 6350. What number do you reach after 3 counts?
5
FCount back in fifties from 7250. What number do you reach after 3 counts?
6
FCount back in fifties from 4650. What number do you reach after 2 counts?
7
FCount on in fifties from 4000. What number do you reach after 3 counts?
8
FFill in the missing number in this count: 6500, 6550, ___, 6650
9
FCount on in fifties from 3700. What number do you reach after 5 counts?
10
FCount on in fifties from 8000. What number do you reach after 2 counts?
11
FFill in the missing number in this count: 5900, ___, 6000, 6050
12
FCount back in fifties from 2400. What number do you reach after 5 counts?
13
FFill in the missing number in this count: 7350, 7400, ___, 7500
14
FCount back in fifties from 8900. What number do you reach after 2 counts?
15
FCount back in fifties from 5850. What number do you reach after 4 counts?
16
FFill in the missing number in this count: 8300, ___, 8400, 8450
1.4

Place value in four-digit numbers

Level 4
Recognise the place value of each digit: thousands, hundreds, tens and ones
Video lesson: Place value in four-digit numbersComing soon

A four-digit number has four columns: thousands, hundreds, tens and ones. The value of a digit depends on its column.

In 4826 the 4 is worth 4000, the 8 is worth 800, the 2 is worth 20 and the 6 is worth 6.

Key ideas

  • Thousands, hundreds, tens and ones.
  • The value of a digit = the digit × the place value.
  • Place values: 1000, 100, 10 and 1.
Worked example 1.4.1
What is the value of the digit in the hundreds place of 4826?

Method. The value of a digit depends on its place. Multiply the digit by the place value.

  1. Find the digit in the hundreds place. Read the digit in that column.
    8 is in the hundreds place
  2. Multiply the digit by its place value. Each hundred is worth 100.
    8 × 100 = 800
  3. Write the value. This is what the digit is worth in this number.
    800

Check. Check: 800 is eight hundreds.

Watch out. Say what the digit is worth, such as 800 not 8.

Worked example 1.4.2
What digit is in the tens place of 5271?
ThousandsHundredsTensOnes

Method. Read the number from the right, column by column.

  1. Count from the right to the tens column. Ones are on the right, then tens.
    5271: ones 1, tens 7
  2. Read the digit in the tens column. It is the digit that stands in that place.
    the tens digit is 7
  3. Write the digit. Write only the digit.
    7

Check. Check: 70 is the value of the 7 in the tens place.

Watch out. Count the columns from the right, not from the left.

Worked example 1.4.3
How many thousands are there in 9034?

Method. The thousands digit tells how many thousands.

  1. Look at the thousands digit. It is the first digit in 9034.
    9034: thousands digit is 9
  2. Read the number of thousands. Nine thousands.
    9 thousands
  3. Write the answer. This is how many thousands there are.
    9

Check. Check: 9000 is 9 thousands.

Watch out. The number of thousands is not the same as the whole number.

Watch out

Watch out. The 2 in 5271 is worth 200 (hundreds), not 2. The digit and its value are different.

Exam tip

Grown-up tip. Ask: “What is the value of the digit, not just the digit?” Get the child to say the place value as a number.

Exercise 1D  Practice: place value

Non-calculator
1
FWhat digit is in the ones place of 1822?
ThousandsHundredsTensOnes
2
FWhat digit is in the ones place of 1961?
ThousandsHundredsTensOnes
3
FWhat is the value of the digit in the ones place of 4774?
4
FWhat is the value of the digit in the thousands place of 6415?
5
FWhat is the value of the digit in the tens place of 2817?
6
FWhat digit is in the hundreds place of 4608?
ThousandsHundredsTensOnes
7
FWhat digit is in the thousands place of 1428?
ThousandsHundredsTensOnes
8
FWhat is the value of the digit in the ones place of 9657?
9
FWhat digit is in the hundreds place of 3131?
ThousandsHundredsTensOnes
10
FWhat is the value of the digit in the ones place of 7764?
11
FWhat digit is in the ones place of 8865?
ThousandsHundredsTensOnes
12
FWhat is the value of the digit in the thousands place of 9150?
13
FWhat digit is in the thousands place of 7505?
ThousandsHundredsTensOnes
14
FWhat is the value of the digit in the tens place of 1456?
15
FWhat is the value of the digit in the ones place of 5321?
16
FWhat is the value of the digit in the thousands place of 5807?
1.5

Partitioning, reading and writing numbers

Level 4
Partition a number in more than one way, Read and write numbers to 10000 in figures and in words
Video lesson: Partitioning, reading and writing numbersComing soon

Partitioning means splitting a number into its parts: 4826 = 4000 + 800 + 20 + 6.

In words, the thousands come first, then the hundreds, then the tens and ones. Use and before the tens and ones.

Keep a zero in any empty column: 4006 has no hundreds and no tens.

Key ideas

  • Partition: split the number into thousands, hundreds, tens and ones.
  • Use and before the last two digits in words.
  • Empty columns need a zero in figures.
Worked example 1.5.1
Fill in the gap: 4000 + 800 + ___ + 6 = 4826

Method. Find the parts we know, then subtract them from the whole.

  1. Add the parts we know. These are the parts in the sum.
    4000 + 800 + 6 = 4806
  2. Take this from the number to find the missing part. 4826 minus 4806 is the gap.
    4826 - 4806 = 20
  3. Write the missing part. It is the value of the tens column.
    20

Check. Check: 4000 + 800 + 20 + 6 = 4826.

Watch out. The gap is a value, not a digit: it is 20, not 2.

Worked example 1.5.2
Write 3604 in words.

Method. Read the number in parts: thousands, hundreds, then the last two digits.

  1. Say the thousands. Read the thousands digit first.
    three thousand
  2. Say the hundreds. Then read the hundreds.
    six hundred
  3. Say the tens and ones. Use and before the last two digits.
    and four
  4. Write the answer in words. Join the parts together.
    three thousand six hundred and four

Check. Check: 3000 + 600 + 4 = 3604.

Watch out. The zero tens digit still needs a place in the words: and four.

Worked example 1.5.3
Write "six thousand and nine" in figures.

Method. Put each part of the words into its place in the number.

  1. Find the thousands. Six thousand is the first part.
    6000
  2. Find the hundreds, tens and ones. There are no hundreds or tens, and nine ones.
    0 hundreds, 0 tens, 9 ones
  3. Add the parts together. Each part goes in its own column.
    6000 + 0 + 9 = 6009
  4. Write the number in figures. Keep a zero in the empty columns.
    6009

Check. Check: read 6009 back as six thousand and nine.

Watch out. Keep a zero in the hundreds and tens columns when they are empty.

Watch out

Watch out. Six thousand and nine is 6009, not 6090 or 609. Keep the zero in the hundreds and tens places.

Exam tip

Grown-up tip. Let the child write each number in words, then check it back by reading the words aloud from the figures.

Exercise 1E  Practice: partitioning, words and figures

Non-calculator
1
FFill in the gap: ___ + 400 + 30 + 5 = 3435
2
FWrite "three thousand two hundred and sixty-two" in figures.
3
FFill in the gap: 2000 + ___ = 2700
4
FFill in the gap: 2000 + 300 + ___ + 8 = 2398
5
FFill in the gap: 1000 + ___ + 9 = 1089
6
FWrite "two thousand seven hundred and five" in figures.
7
FFill in the gap: 2000 + 200 + ___ + 8 = 2278
8
FWrite "one thousand six hundred and ninety-three" in figures.
9
FWrite 1336 in words.
10
FFill in the gap: ___ + 400 + 70 = 5470
11
FFill in the gap: 1000 + ___ + 3 = 1083
12
FFill in the gap: 6000 + ___ + 90 = 6490
13
FWrite 5484 in words.
14
FFill in the gap: 8000 + 700 + ___ + 3 = 8753
15
FWrite 4830 in words.
16
FWrite 2707 in words.

Chapter summary

SkillMethod
Counting in hundredsAdd or take away 100 each time; the thousands digit changes when the hundreds pass 9
Counting in thousands1000 more or less changes only the thousands digit
Counting in fiftiesFifties end in 00 or 50; count in steps of 50
Place valueValue = digit × place value (1000, 100, 10 or 1)
Partitioning and wordsSplit into thousands, hundreds, tens and ones; use and before the tens and ones

Can you…?

  • I can count on and back in hundreds from any number to 10000
  • I can say 1000 more and 1000 less than any number
  • I can count in fifties from a multiple of 50
  • I can say the value of each digit in a four-digit number
  • I can partition a four-digit number in more than one way
  • I can read and write four-digit numbers in figures and in words

Key terms

thousands
the first column on the left of a four-digit number
place value
what a digit is worth because of its column
partition
split a number into parts, such as 4000 + 800 + 20 + 6
digit
one of the symbols 0 to 9 that make a number

Exercise 1Z  Check-up

Non-calculator
1
Fill in the missing number in this count: 7422, 7522, ___, 7722
2
Fill in the gap: ___ + 500 + 90 + 5 = 1595
3
Count back in thousands from 5951. What number do you reach after 4 counts?
4
Fill in the gap: 3000 + 500 + ___ + 5 = 3595
5
What digit is in the thousands place of 4882?
ThousandsHundredsTensOnes
6
Count on in fifties from 7100. What number do you reach after 3 counts?
7
Count back in hundreds from 4531. What number do you reach after 3 counts?
8
Fill in the gap: 2000 + 300 + 40 + ___ = 2341
9
Count on in thousands from 5054. What number do you reach after 4 counts?
10
Count on in hundreds from 5549. What number do you reach after 5 counts?

Total 19 marks. Allow about 19 minutes.

Exercise 1X  Practice test questions

Non-calculator
1
FWhat is 1000 less than 6518?[1 mark]
2
FWhat digit is in the hundreds place of 6891?[1 mark]
ThousandsHundredsTensOnes
3
FCount back in fifties from 8350. What number do you reach after 2 counts?[1 mark]
4
FCount on in fifties from 6900. What number do you reach after 3 counts?[1 mark]
5
FCount back in fifties from 7000. What number do you reach after 4 counts?[2 marks]
6
FCount back in hundreds from 2214. What number do you reach after 3 counts?[2 marks]
7
FFill in the gap: 6000 + ___ = 6060[2 marks]
8
FWrite "nine thousand three hundred and thirty-nine" in figures.[3 marks]
9
FCount back in hundreds from 4836. What number do you reach after 2 counts?[3 marks]
10
FWrite "six thousand two hundred and fifty-five" in figures.[3 marks]

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