Year 5 Place Value to 1,000,000: worked examples and questions with answers

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.

1. Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   6	3	8	2	4	5

2. Find which column the digit is in. The digit is 6 and it sits in the hundred thousands column.
   1 hundred thousand = 100,000
3. Multiply the digit by the value of the column. There are 6 hundred thousands.
   6 × 100,000 = 600,000

Check. Say it in words: 6 hundred thousands is six hundred thousand. ✓

Watch out. The digit is 6 but its value is 600,000. The same digit is worth different amounts in different columns.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.

1. Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.

   Thousands		Ones
   TTh	Th	H	T	O
   9	2	8	1	6

2. Find which column the digit is in. The digit is 9 and it sits in the ten thousands column.
   1 ten thousand = 10,000
3. Multiply the digit by the value of the column. There are 9 ten thousands.
   9 × 10,000 = 90,000

Check. Say it in words: 9 ten thousands is ninety thousand. ✓

Watch out. The digit is 9 but its value is 90,000. The same digit is worth different amounts in different columns.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.

1. Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   4	0	7	1	5	3

2. Find which column the digit is in. The digit is 7 and it sits in the thousands column.
   1 thousand = 1,000
3. Multiply the digit by the value of the column. There are 7 thousands.
   7 × 1,000 = 7,000

Check. Say it in words: 7 thousands is seven thousand. ✓

Watch out. The digit is 7 but its value is 7,000. The same digit is worth different amounts in different columns.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. The value of a digit depends on its column. Find the column, then multiply the digit by the value of the column.

1. Write the number in a place-value table. Each column has a name and a value. The coloured digit is the one we want.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   5	2	0	8	9	4

2. Find which column the digit is in. The digit is 9 and it sits in the tens column.
   1 ten = 10
3. Multiply the digit by the value of the column. There are 9 tens.
   9 × 10 = 90

Check. Say it in words: 9 tens is ninety. ✓

Watch out. The digit is 9 but its value is 90. The same digit is worth different amounts in different columns.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.

1. Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.

   Thousands		Ones
   TTh	Th	H	T	O
   3	8	2	0	5

2. Read each part and say it in words. Say the thousands period as a number and then add the word thousand.
   Thousands period: 38 → thirty-eight thousand
   Hundreds: 2 → two hundred
   Last two digits: 5 → five
3. Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.
   thirty-eight thousand, two hundred and five

Check. Read it out loud. It sounds like 38,205. ✓

Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.

1. Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   2	7	0	0	4	0

2. Read each part and say it in words. Say the thousands period as a number and then add the word thousand.
   Thousands period: 270 → two hundred and seventy thousand
   Last two digits: 40 → forty
3. Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.
   two hundred and seventy thousand and forty

Check. Read it out loud. It sounds like 270,040. ✓

Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.

1. Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   6	0	4	3	0	0

2. Read each part and say it in words. Say the thousands period as a number and then add the word thousand.
   Thousands period: 604 → six hundred and four thousand
   Hundreds: 3 → three hundred
3. Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.
   six hundred and four thousand, three hundred

Check. Read it out loud. It sounds like 604,300. ✓

Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Say the number in parts, from left to right: the thousands period first, then the hundreds, then the last two digits.

1. Write the number in a place-value table. The comma splits the digits into the Thousands period and the Ones period.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   9	0	0	0	0	9

2. Read each part and say it in words. Say the thousands period as a number and then add the word thousand.
   Thousands period: 900 → nine hundred thousand
   Last two digits: 9 → nine
3. Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.
   nine hundred thousand and nine

Check. Read it out loud. It sounds like 900,009. ✓

Watch out. Zeros are never said aloud. 400,060 is “four hundred thousand and sixty”: nothing is said for the empty columns, but they still need a 0 when you write the digits.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.

1. Split the words into parts. Each part belongs to one period or column.
   “fifty-two thousand” → the Thousands period is 52
   “six hundred” → 6 in the hundreds column
   “eight” → 0 in the tens column and 8 in the ones column
2. Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).

   Thousands		Ones
   TTh	Th	H	T	O
   5	2	6	0	8

3. Write the number. Put a comma between the periods.
   52,608

Check. Say 52,608 in words: fifty-two thousand, six hundred and eight. It matches. ✓

Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.

1. Split the words into parts. Each part belongs to one period or column.
   “three hundred and forty thousand” → the Thousands period is 340
   no hundreds are said → 0 in the hundreds column
   “seven” → 0 in the tens column and 7 in the ones column
2. Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   3	4	0	0	0	7

3. Write the number. Put a comma between the periods.
   340,007

Check. Say 340,007 in words: three hundred and forty thousand and seven. It matches. ✓

Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.

1. Split the words into parts. Each part belongs to one period or column.
   “six hundred and six thousand” → the Thousands period is 606
   “six hundred” → 6 in the hundreds column
   “six” → 0 in the tens column and 6 in the ones column
2. Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   6	0	6	6	0	6

3. Write the number. Put a comma between the periods.
   606,606

Check. Say 606,606 in words: six hundred and six thousand, six hundred and six. It matches. ✓

Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.

Key words. A digit is one of 0 to 9. The value of a digit is what it is worth. A period is a group of three columns: Ones, Thousands, Millions.

Method. Listen for the words “thousand” and “hundred”. They tell you which period and column each part goes in.

1. Split the words into parts. Each part belongs to one period or column.
   “nine hundred thousand” → the Thousands period is 900
   no hundreds are said → 0 in the hundreds column
   “ninety” → 9 in the tens column and 0 in the ones column
2. Write the digits in a place-value table. Write a zero in every column that was not mentioned. Each period has three digits (except the first).

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   9	0	0	0	9	0

3. Write the number. Put a comma between the periods.
   900,090

Check. Say 900,090 in words: nine hundred thousand and ninety. It matches. ✓

Watch out. A zero is a place holder. Without it the digits slip into the wrong columns and the number changes.

Key words. To partition a number is to split it into parts, one part for each digit.

Method. Partition means splitting a number into the value of each of its digits.

1. Write the number in a place-value table. This shows how many of each column there are.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   4	8	2	6	1	5

2. Work out the value of each digit. Digit times the value of its column.
   4 hundred thousands = 400,000
   8 ten thousands = 80,000
   2 thousands = 2,000
   6 hundreds = 600
   1 ten = 10
   5 ones = 5
3. Write the values as an addition. Start with the biggest value.
   482,615 = 400,000 + 80,000 + 2,000 + 600 + 10 + 5

Check. Add them up: 400,000 + 80,000 + 2,000 + 600 + 10 + 5 = 482,615. ✓

Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.

Key words. To partition a number is to split it into parts, one part for each digit.

Method. Partition means splitting a number into the value of each of its digits.

1. Write the number in a place-value table. This shows how many of each column there are.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   7	0	3	0	4	0

2. Work out the value of each digit. Digit times the value of its column.
   7 hundred thousands = 700,000
   0 ten thousands = nothing to write
   3 thousands = 3,000
   0 hundreds = nothing to write
   4 tens = 40
   0 ones = nothing to write
3. Leave out the zeros. A zero means the column is empty, so there is nothing to add.
4. Write the values as an addition. Start with the biggest value.
   703,040 = 700,000 + 3,000 + 40

Check. Add them up: 700,000 + 3,000 + 40 = 703,040. ✓

Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.

Key words. To partition a number is to split it into parts, one part for each digit.

Method. Partition means splitting a number into the value of each of its digits.

1. Write the number in a place-value table. This shows how many of each column there are.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   2	5	0	0	0	8

2. Work out the value of each digit. Digit times the value of its column.
   2 hundred thousands = 200,000
   5 ten thousands = 50,000
   0 thousands = nothing to write
   0 hundreds = nothing to write
   0 tens = nothing to write
   8 ones = 8
3. Leave out the zeros. A zero means the column is empty, so there is nothing to add.
4. Write the values as an addition. Start with the biggest value.
   250,008 = 200,000 + 50,000 + 8

Check. Add them up: 200,000 + 50,000 + 8 = 250,008. ✓

Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.

Key words. To partition a number is to split it into parts, one part for each digit.

Method. Partition means splitting a number into the value of each of its digits.

1. Write the number in a place-value table. This shows how many of each column there are.

   Thousands		Ones
   TTh	Th	H	T	O
   9	6	0	7	0

2. Work out the value of each digit. Digit times the value of its column.
   9 ten thousands = 90,000
   6 thousands = 6,000
   0 hundreds = nothing to write
   7 tens = 70
   0 ones = nothing to write
3. Leave out the zeros. A zero means the column is empty, so there is nothing to add.
4. Write the values as an addition. Start with the biggest value.
   96,070 = 90,000 + 6,000 + 70

Check. Add them up: 90,000 + 6,000 + 70 = 96,070. ✓

Watch out. Write 300,000 for 3 hundred thousands, not just 3. Each part keeps its full value.

Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.

Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.

1. Read the parts: 6 hundred thousands, 4 thousands and 9 tens. Each part tells us which column it goes in and how many.
2. Put each digit in its column. Start with the biggest column on the left.
   6 hundred thousands → write 6 in the HTh column
   0 ten thousands → write 0 in the TTh column (nothing here, so write a zero)
   4 thousands → write 4 in the Th column
   0 hundreds → write 0 in the H column (nothing here, so write a zero)
   9 tens → write 9 in the T column
   0 ones → write 0 in the O column (nothing here, so write a zero)
3. Read the digits across the table. Put commas between the periods.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   6	0	4	0	9	0

   
   The number is 604,090.

Check. Say it in words: six hundred and four thousand and ninety. It matches the parts. ✓

Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.

Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.

Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.

1. Read the parts: 3 hundred thousands, 7 ten thousands and 2 hundreds. Each part tells us which column it goes in and how many.
2. Put each digit in its column. Start with the biggest column on the left.
   3 hundred thousands → write 3 in the HTh column
   7 ten thousands → write 7 in the TTh column
   0 thousands → write 0 in the Th column (nothing here, so write a zero)
   2 hundreds → write 2 in the H column
   0 tens → write 0 in the T column (nothing here, so write a zero)
   0 ones → write 0 in the O column (nothing here, so write a zero)
3. Read the digits across the table. Put commas between the periods.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   3	7	0	2	0	0

   
   The number is 370,200.

Check. Say it in words: three hundred and seventy thousand, two hundred. It matches the parts. ✓

Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.

Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.

Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.

1. Read the parts: 800,000 + 5,000 + 40 + 3. Each part tells us which column it goes in and how many.
2. Put each digit in its column. Start with the biggest column on the left.
   8 hundred thousands → write 8 in the HTh column
   0 ten thousands → write 0 in the TTh column (nothing here, so write a zero)
   5 thousands → write 5 in the Th column
   0 hundreds → write 0 in the H column (nothing here, so write a zero)
   4 tens → write 4 in the T column
   3 ones → write 3 in the O column
3. Read the digits across the table. Put commas between the periods.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   8	0	5	0	4	3

   
   The number is 805,043.

Check. Say it in words: eight hundred and five thousand and forty-three. It matches the parts. ✓

Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.

Key words. A place holder is a zero that holds an empty column so the other digits stay in the right place.

Method. Put each part into its own column of a place-value table. Write a zero in any column with nothing in it.

1. Read the parts: 200,000 + 90,000 + 6. Each part tells us which column it goes in and how many.
2. Put each digit in its column. Start with the biggest column on the left.
   2 hundred thousands → write 2 in the HTh column
   9 ten thousands → write 9 in the TTh column
   0 thousands → write 0 in the Th column (nothing here, so write a zero)
   0 hundreds → write 0 in the H column (nothing here, so write a zero)
   0 tens → write 0 in the T column (nothing here, so write a zero)
   6 ones → write 6 in the O column
3. Read the digits across the table. Put commas between the periods.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   2	9	0	0	0	6

   
   The number is 290,006.

Check. Say it in words: two hundred and ninety thousand and six. It matches the parts. ✓

Watch out. A zero is a place holder. 405,060 and 45,060 are very different numbers.

Method. To find how many thousands are in a number, read all the digits from the left up to the thousands column as one number.

1. Write the number in a place-value table. Find the thousands column.

   Thousands		Ones
   TTh	Th	H	T	O
   7	2	0	0	0

2. Read the digits up to the Th column. Every column on the left is a bigger column. They can all be swapped for thousands. 1 ten thousand is 10 thousands, and so on.
   The digits 72, read as one number, are 72.
3. Write the answer.
   72 thousands

Check. 72 × 1,000 = 72,000. ✓

Watch out. Do not just read the digit in that column. There are 72 thousands in 72,000, not 2.

Method. To find how many hundreds are in a number, read all the digits from the left up to the hundreds column as one number.

1. Write the number in a place-value table. Find the hundreds column.

   Thousands		Ones
   TTh	Th	H	T	O
   4	5	3	0	0

2. Read the digits up to the H column. Every column on the left is a bigger column. They can all be swapped for hundreds. 1 thousand is 10 hundreds, and so on.
   The digits 453, read as one number, are 453.
3. Write the answer.
   453 hundreds

Check. 453 × 100 = 45,300. ✓

Watch out. Do not just read the digit in that column. There are 453 hundreds in 45,300, not 3.

Method. To find how many tens are in a number, read all the digits from the left up to the tens column as one number.

1. Write the number in a place-value table. Find the tens column.

   Thousands	Ones
   Th	H	T	O
   8	7	4	0

2. Read the digits up to the T column. Every column on the left is a bigger column. They can all be swapped for tens. 1 hundred is 10 tens, and so on.
   The digits 874, read as one number, are 874.
3. Write the answer.
   874 tens

Check. 874 × 10 = 8,740. ✓

Watch out. Do not just read the digit in that column. There are 874 tens in 8,740, not 4.

Method. To find how many hundreds are in a number, read all the digits from the left up to the hundreds column as one number.

1. Write the number in a place-value table. Find the hundreds column.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   1	0	0	0	0	0

2. Read the digits up to the H column. Every column on the left is a bigger column. They can all be swapped for hundreds. 1 thousand is 10 hundreds, and so on.
   The digits 1000, read as one number, are 1,000.
3. Write the answer.
   1,000 hundreds

Check. 1,000 × 100 = 100,000. ✓

Watch out. Do not just read the digit in that column. There are 1,000 hundreds in 100,000, not 0.

Method. A six-digit number cannot start with 0. The smallest digit for the hundred thousands column is 1, and every other column is 0.

1. Choose the first digit. It cannot be 0, so the smallest choice is 1.
   HTh = 1
2. Make every other column as small as possible. 0 is the smallest digit.
   TTh = 0, Th = 0, H = 0, T = 0, O = 0
3. Write the number.
   100,000

Check. 99,999 has only five digits, and 100,000 is one more than 99,999. ✓

Method. Use the biggest digit, 9, in every column.

1. Choose the biggest digit for each column. 9 is the biggest digit.
   HTh = 9, TTh = 9, Th = 9, H = 9, T = 9, O = 9
2. Write the number.
   999,999

Check. One more makes a seven-digit number: 1,000,000. ✓

Method. Add 1 to the ones column and carry the 1 all the way along. Then write the answer in digits and words.

1. Write the number in a place-value table. Every column is a 9.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   9	9	9	9	9	9

2. Add 1 to the ones. 9 + 1 = 10, so write 0 and carry 1. The next column is also 9, so the carry keeps going.
   9 ones + 1 = 10 ones → 1 ten
   9 tens + 1 ten = 10 tens → 1 hundred
   … and so on, all the way to the left
3. Write the new number. Every column is now 0 and there is a new column on the left, the Millions column.

   Millions	Thousands			Ones
   M	HTh	TTh	Th	H	T	O
   1	0	0	0	0	0	0

   
   1,000,000
4. Say it in words. 1,000,000 is 1 thousand thousands. We call it one million.
   one million

Check. 10 × 100,000 = 1,000,000, so there are 10 hundred thousands in one million. ✓

Watch out. 999,999 has six digits. One more has seven. A new column appears when every column is full.

Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.

Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.

1. Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   356,742	3	5	6	7	4	2
   356,724	3	5	6	7	2	4

2. Compare the digits from the left. The first column where they are different decides which number is bigger.
   hundred thousands: 3 and 3 are the same, so look at the next column.
   ten thousands: 5 and 5 are the same, so look at the next column.
   thousands: 6 and 6 are the same, so look at the next column.
   hundreds: 7 and 7 are the same, so look at the next column.
   tens: 4 and 2 are different. 4 > 2, so 356,742 is bigger.
3. Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.
   356,742 > 356,724

Check. Picture a number line: 356,724 is to the left of 356,742. ✓

Watch out. Start at the LEFT (the biggest column). Do not start with the ones.

Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.

Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.

1. Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   89,999		8	9	9	9	9
   100,001	1	0	0	0	0	1

2. Count the digits. A number with more digits is bigger (when no number starts with 0).
   100,001 has 6 digits and 89,999 has 5 digits, so 100,001 is bigger.
3. Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.
   89,999 < 100,001

Check. Picture a number line: 89,999 is to the left of 100,001. ✓

Watch out. Start at the LEFT (the biggest column). Do not start with the ones.

Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.

Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.

1. Write each side as one number. We can only compare numbers when they are written the usual way.
   400,000 + 5,000 = 405,000
   450,000 = 450,000
2. Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   405,000	4	0	5	0	0	0
   450,000	4	5	0	0	0	0

3. Compare the digits from the left. The first column where they are different decides which number is bigger.
   hundred thousands: 4 and 4 are the same, so look at the next column.
   ten thousands: 0 and 5 are different. 0 < 5, so 405,000 is smaller.
4. Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.
   405,000 < 450,000

Check. Picture a number line: 405,000 is to the left of 450,000. ✓

Watch out. Start at the LEFT (the biggest column). Do not start with the ones.

Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.

Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.

1. Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   620,300	6	2	0	3	0	0
   62,030		6	2	0	3	0

2. Count the digits. A number with more digits is bigger (when no number starts with 0).
   620,300 has 6 digits and 62,030 has 5 digits, so 620,300 is bigger.
3. Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.
   620,300 > 62,030

Check. Picture a number line: 62,030 is to the left of 620,300. ✓

Watch out. Start at the LEFT (the biggest column). Do not start with the ones.

Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.

Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.

1. Write each side as one number. We can only compare numbers when they are written the usual way.
   seven hundred thousand = 700,000
   700,000 = 700,000
2. Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   700,000	7	0	0	0	0	0
   700,000	7	0	0	0	0	0

3. Compare the digits from the left. The first column where they are different decides which number is bigger.
   Every column is the same.
4. Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.
   700,000 = 700,000

Check. Both are 700,000. ✓

Watch out. Equal numbers can be written in different ways, so write both as digits first.

Key words. < means “less than” and > means “greater than”. The wide end of the sign faces the bigger number.

Method. Compare the digits from the left, one column at a time. The first column that is different tells you which number is bigger.

1. Write both numbers in a place-value table. Lining up the columns lets us compare digit by digit.

   	Millions	Thousands			Ones
   	M	HTh	TTh	Th	H	T	O
   999,999		9	9	9	9	9	9
   1,000,000	1	0	0	0	0	0	0

2. Count the digits. A number with more digits is bigger (when no number starts with 0).
   1,000,000 has 7 digits and 999,999 has 6 digits, so 1,000,000 is bigger.
3. Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.
   999,999 < 1,000,000

Check. Picture a number line: 999,999 is to the left of 1,000,000. ✓

Watch out. Start at the LEFT (the biggest column). Do not start with the ones.

Key words. Ascending order means smallest first. Descending order means biggest first.

Method. Put the numbers in a place-value table, then compare columns from the left. Smallest first.

1. Write all the numbers in a place-value table. This lines up the digits so we can compare them.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   534,210	5	3	4	2	1	0
   534,120	5	3	4	1	2	0
   543,210	5	4	3	2	1	0
   53,421		5	3	4	2	1

2. Compare the numbers in pairs, from the left. Where the digits in a column match, move on to the next column.
   53,421 and 534,120: 534,120 has 6 digits and 53,421 has 5 digits, so 534,120 is bigger.
   534,120 and 534,210: hundreds: 1 and 2 are different. 1 < 2, so 534,120 is smaller.
   534,210 and 543,210: ten thousands: 3 and 4 are different. 3 < 4, so 534,210 is smaller.
3. Write them smallest first. Check you have used every number once.
   53,421, 534,120, 534,210, 543,210

Check. Count the numbers: 4 in the question and 4 in the answer. ✓

Watch out. Tick each number off as you write it, so you do not miss one.

Key words. Ascending order means smallest first. Descending order means biggest first.

Method. Put the numbers in a place-value table, then compare columns from the left. Smallest first.

1. Write all the numbers in a place-value table. This lines up the digits so we can compare them.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   706,040	7	0	6	0	4	0
   760,040	7	6	0	0	4	0
   706,400	7	0	6	4	0	0
   76,040		7	6	0	4	0

2. Compare the numbers in pairs, from the left. Where the digits in a column match, move on to the next column.
   76,040 and 706,040: 706,040 has 6 digits and 76,040 has 5 digits, so 706,040 is bigger.
   706,040 and 706,400: hundreds: 0 and 4 are different. 0 < 4, so 706,040 is smaller.
   706,400 and 760,040: ten thousands: 0 and 6 are different. 0 < 6, so 706,400 is smaller.
3. Write them smallest first. Check you have used every number once.
   76,040, 706,040, 706,400, 760,040

Check. Count the numbers: 4 in the question and 4 in the answer. ✓

Watch out. Tick each number off as you write it, so you do not miss one.

Key words. Ascending order means smallest first. Descending order means biggest first.

Method. Put the numbers in a place-value table, then compare columns from the left. Smallest first.

1. Write all the numbers in a place-value table. This lines up the digits so we can compare them.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   999,001	9	9	9	0	0	1
   990,901	9	9	0	9	0	1
   909,901	9	0	9	9	0	1
   999,010	9	9	9	0	1	0

2. Compare the numbers in pairs, from the left. Where the digits in a column match, move on to the next column.
   909,901 and 990,901: ten thousands: 0 and 9 are different. 0 < 9, so 909,901 is smaller.
   990,901 and 999,001: thousands: 0 and 9 are different. 0 < 9, so 990,901 is smaller.
   999,001 and 999,010: tens: 0 and 1 are different. 0 < 1, so 999,001 is smaller.
3. Write them smallest first. Check you have used every number once.
   909,901, 990,901, 999,001, 999,010

Check. Count the numbers: 4 in the question and 4 in the answer. ✓

Watch out. Tick each number off as you write it, so you do not miss one.

Key words. Ascending order means smallest first. Descending order means biggest first.

Method. Put the numbers in a place-value table, then compare columns from the left. Biggest first.

1. Write all the numbers in a place-value table. This lines up the digits so we can compare them.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   250,639	2	5	0	6	3	9
   205,639	2	0	5	6	3	9
   250,369	2	5	0	3	6	9
   25,639		2	5	6	3	9
   205,936	2	0	5	9	3	6

2. Compare the numbers in pairs, from the left. Where the digits in a column match, move on to the next column.
   25,639 and 205,639: 205,639 has 6 digits and 25,639 has 5 digits, so 205,639 is bigger.
   205,639 and 205,936: hundreds: 6 and 9 are different. 6 < 9, so 205,639 is smaller.
   205,936 and 250,369: ten thousands: 0 and 5 are different. 0 < 5, so 205,936 is smaller.
   250,369 and 250,639: hundreds: 3 and 6 are different. 3 < 6, so 250,369 is smaller.
3. Write them biggest first. Check you have used every number once.
   250,639, 250,369, 205,936, 205,639, 25,639

Check. Count the numbers: 5 in the question and 5 in the answer. ✓

Watch out. Tick each number off as you write it, so you do not miss one.

Key words. Ascending order means smallest first. Descending order means biggest first.

Method. Put the numbers in a place-value table, then compare columns from the left. Biggest first.

1. Write all the numbers in a place-value table. This lines up the digits so we can compare them.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   418,000	4	1	8	0	0	0
   481,000	4	8	1	0	0	0
   4,180			4	1	8	0
   408,100	4	0	8	1	0	0

2. Compare the numbers in pairs, from the left. Where the digits in a column match, move on to the next column.
   4,180 and 408,100: 408,100 has 6 digits and 4,180 has 4 digits, so 408,100 is bigger.
   408,100 and 418,000: ten thousands: 0 and 1 are different. 0 < 1, so 408,100 is smaller.
   418,000 and 481,000: ten thousands: 1 and 8 are different. 1 < 8, so 418,000 is smaller.
3. Write them biggest first. Check you have used every number once.
   481,000, 418,000, 408,100, 4,180

Check. Count the numbers: 4 in the question and 4 in the answer. ✓

Watch out. Tick each number off as you write it, so you do not miss one.

Method. The number halfway between two numbers is the same distance from both. Find the gap between them, halve it, then add that to the smaller number.

1. Find the gap between the two numbers. Subtract the smaller from the bigger.
   350,000 − 250,000 = 100,000
2. Halve the gap. Halfway is half of the gap away from each number.
   100,000 ÷ 2 = 50,000
3. Add half the gap to the smaller number. This moves us to the middle.
   250,000 + 50,000 = 300,000

Check. Another way: add the numbers and halve. 250,000 + 350,000 = 600,000 and 600,000 ÷ 2 = 300,000. ✓

Watch out. Halfway is not the average of the digits. Use the whole numbers.

Method. The number halfway between two numbers is the same distance from both. Find the gap between them, halve it, then add that to the smaller number.

1. Find the gap between the two numbers. Subtract the smaller from the bigger.
   175,000 − 125,000 = 50,000
2. Halve the gap. Halfway is half of the gap away from each number.
   50,000 ÷ 2 = 25,000
3. Add half the gap to the smaller number. This moves us to the middle.
   125,000 + 25,000 = 150,000

Check. Another way: add the numbers and halve. 125,000 + 175,000 = 300,000 and 300,000 ÷ 2 = 150,000. ✓

Watch out. Halfway is not the average of the digits. Use the whole numbers.

Method. The number halfway between two numbers is the same distance from both. Find the gap between them, halve it, then add that to the smaller number.

1. Find the gap between the two numbers. Subtract the smaller from the bigger.
   720,000 − 680,000 = 40,000
2. Halve the gap. Halfway is half of the gap away from each number.
   40,000 ÷ 2 = 20,000
3. Add half the gap to the smaller number. This moves us to the middle.
   680,000 + 20,000 = 700,000

Check. Another way: add the numbers and halve. 680,000 + 720,000 = 1,400,000 and 1,400,000 ÷ 2 = 700,000. ✓

Watch out. Halfway is not the average of the digits. Use the whole numbers.

Method. The number halfway between two numbers is the same distance from both. Find the gap between them, halve it, then add that to the smaller number.

1. Find the gap between the two numbers. Subtract the smaller from the bigger.
   99,000 − 1,000 = 98,000
2. Halve the gap. Halfway is half of the gap away from each number.
   98,000 ÷ 2 = 49,000
3. Add half the gap to the smaller number. This moves us to the middle.
   1,000 + 49,000 = 50,000

Check. Another way: add the numbers and halve. 1,000 + 99,000 = 100,000 and 100,000 ÷ 2 = 50,000. ✓

Watch out. Halfway is not the average of the digits. Use the whole numbers.

Method. Think about which digit goes in the hundred thousands column, then the ten thousands, and so on. The biggest columns matter most.

1. Put the digits in order, biggest first. The biggest digit in the biggest column makes the biggest number.
   9, 7, 5, 3, 2, 0
2. Write them in that order. Biggest digit in the hundred thousands column, the next in the ten thousands, and so on.
   975,320

Check. Try swapping two digits. The new number is not bigger than 975,320. ✓

Watch out. A six-digit number cannot start with a zero.

Method. Think about which digit goes in the hundred thousands column, then the ten thousands, and so on. The biggest columns matter most.

1. Put the digits in order, smallest first. The smallest digit in the biggest column makes the smallest number.
   0, 2, 3, 5, 7, 9
2. Check the first digit. A six-digit number cannot start with 0, because then it would only have five digits. Use the smallest digit that is not 0 first, then put the 0 straight after it.
   First digit 2
3. Write the number.
   203,579

Check. Try swapping two digits. The new number is not smaller than 203,579. ✓

Watch out. A six-digit number cannot start with a zero.

Method. Think about which digit goes in the hundred thousands column, then the ten thousands, and so on. The biggest columns matter most.

1. A number is even if its last digit (the ones digit) is even. Even digits are 0, 2, 4, 6, 8.
   Even digits here: 0, 2
2. Try each possible ones digit. Make the rest of the number as small as possible each time. The other five digits go smallest first (but not starting with 0).
   Ones digit 0: smallest number is 235,790
   Ones digit 2: smallest number is 305,792
3. Choose the smallest of these numbers. Compare from the left.
   The smallest even number is 235,790.

Check. Try swapping two digits. The new number is not smaller than 235,790. ✓

Watch out. A six-digit number cannot start with a zero.

Method. Think about which digit goes in the hundred thousands column, then the ten thousands, and so on. The biggest columns matter most.

1. Which digits can go first? The number must be less than 500,000, so the first digit must be smaller than 5 (and not 0).
   Possible first digits: 1, 2, 4
2. Choose the biggest first digit. The first digit matters most.
   First digit = 4
3. Put the other digits in order, biggest first. This makes the number as close to the limit as possible.
   4 then 8, 6, 2, 1, 0
4. Write the number.
   486,210

Check. Try swapping two digits. The new number is not bigger than 486,210. ✓

Watch out. A six-digit number cannot start with a zero.

Method. Think about which digit goes in the hundred thousands column, then the ten thousands, and so on. The biggest columns matter most.

1. Which digits can go first? The number must be more than 500,000, so the first digit must be bigger than 5 (and not 0).
   Possible first digits: 6, 8
2. Choose the smallest first digit. The first digit matters most.
   First digit = 6
3. Put the other digits in order, smallest first. This makes the number as close to the limit as possible.
   6 then 0, 1, 2, 4, 8
4. Write the number.
   601,248

Check. Try swapping two digits. The new number is not smaller than 601,248. ✓

Watch out. A six-digit number cannot start with a zero.

Method. Put the numbers in order and pick the one you need. Compare the numbers from the left.

1. Write all the numbers in a place-value table. This lines them up.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   185,420	1	8	5	4	2	0
   158,240	1	5	8	2	4	0
   185,240	1	8	5	2	4	0
   98,765		9	8	7	6	5
   205,010	2	0	5	0	1	0

2. Put them in order, biggest first. Compare column by column from the left.
   1. Elford: 205,010
   2. Ashby: 185,420
   3. Corton: 185,240
   4. Bexley: 158,240
   5. Dunmore: 98,765
3. Pick the one with the most people. It is number 1 in the list.
   Elford (205,010)

Check. All the other numbers are smaller than 205,010 in the way we need. ✓

Watch out. Read the question again: is it the biggest, the smallest or the second biggest?

Method. Put the numbers in order and pick the one you need. Compare the numbers from the left.

1. Write all the numbers in a place-value table. This lines them up.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   185,420	1	8	5	4	2	0
   158,240	1	5	8	2	4	0
   185,240	1	8	5	2	4	0
   98,765		9	8	7	6	5
   205,010	2	0	5	0	1	0

2. Put them in order, smallest first. Compare column by column from the left.
   1. Dunmore: 98,765
   2. Bexley: 158,240
   3. Corton: 185,240
   4. Ashby: 185,420
   5. Elford: 205,010
3. Pick the one with the fewest people. It is number 1 in the list.
   Dunmore (98,765)

Check. All the other numbers are different than 98,765 in the way we need. ✓

Watch out. Read the question again: is it the biggest, the smallest or the second biggest?

Method. Put the populations in descending order, then write the town names in that order.

1. Put the populations in a place-value table. This lines up the digits.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   185,420	1	8	5	4	2	0
   158,240	1	5	8	2	4	0
   185,240	1	8	5	2	4	0
   98,765		9	8	7	6	5
   205,010	2	0	5	0	1	0

2. Put them in order, biggest first. Compare from the left. 185,420 and 185,240 are the same until the hundreds column: 4 is more than 2.
   205,010 → Elford
   185,420 → Ashby
   185,240 → Corton
   158,240 → Bexley
   98,765 → Dunmore
3. Write the town names in that order.
   Elford, Ashby, Corton, Bexley, Dunmore

Check. There are 5 towns in the table and 5 in the answer. ✓

Watch out. Be careful with 185,420 and 185,240: they use the same digits but in different columns.

Key words. Counting in steps of 10 means adding 10 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting on in 10s means adding 10 each time. Only the tens digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting on in steps of 10, which is 1 ten.
   Each jump is +10.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   4,570 + 10 = 4,580  (the tens digit goes 7 → 8)
   4,580 + 10 = 4,590  (the tens digit goes 8 → 9)
   4,590 + 10 = 4,600  (9 tens + 1 ten = 10 tens: write 0 and carry 1 to the next column)
3. Write the numbers in order.
   4,580, 4,590, 4,600

Check. Go the other way from the last number: 4,600 − 10 = 4,590. ✓

Watch out. Only the tens digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Key words. Counting in steps of 100 means adding 100 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting on in 100s means adding 100 each time. Only the hundreds digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting on in steps of 100, which is 1 hundred.
   Each jump is +100.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   28,300 + 100 = 28,400  (the hundreds digit goes 3 → 4)
   28,400 + 100 = 28,500  (the hundreds digit goes 4 → 5)
   28,500 + 100 = 28,600  (the hundreds digit goes 5 → 6)
3. Write the numbers in order.
   28,400, 28,500, 28,600

Check. Go the other way from the last number: 28,600 − 100 = 28,500. ✓

Watch out. Only the hundreds digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Key words. Counting in steps of 1,000 means adding 1,000 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting on in 1,000s means adding 1,000 each time. Only the thousands digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting on in steps of 1,000, which is 1 thousand.
   Each jump is +1,000.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   351,200 + 1,000 = 352,200  (the thousands digit goes 1 → 2)
   352,200 + 1,000 = 353,200  (the thousands digit goes 2 → 3)
   353,200 + 1,000 = 354,200  (the thousands digit goes 3 → 4)
3. Write the numbers in order.
   352,200, 353,200, 354,200

Check. Go the other way from the last number: 354,200 − 1,000 = 353,200. ✓

Watch out. Only the thousands digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Key words. Counting in steps of 10,000 means adding 10,000 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting on in 10,000s means adding 10,000 each time. Only the ten thousands digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting on in steps of 10,000, which is 1 ten thousand.
   Each jump is +10,000.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   420,000 + 10,000 = 430,000  (the ten thousands digit goes 2 → 3)
   430,000 + 10,000 = 440,000  (the ten thousands digit goes 3 → 4)
   440,000 + 10,000 = 450,000  (the ten thousands digit goes 4 → 5)
3. Write the numbers in order.
   430,000, 440,000, 450,000

Check. Go the other way from the last number: 450,000 − 10,000 = 440,000. ✓

Watch out. Only the ten thousands digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Key words. Counting in steps of 10 means taking away 10 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting back in 10s means taking away 10 each time. Only the tens digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting back in steps of 10, which is 1 ten.
   Each jump is −10.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   6,080 − 10 = 6,070  (the tens digit goes 8 → 7)
   6,070 − 10 = 6,060  (the tens digit goes 7 → 6)
   6,060 − 10 = 6,050  (the tens digit goes 6 → 5)
3. Write the numbers in order.
   6,070, 6,060, 6,050

Check. Go the other way from the last number: 6,050 + 10 = 6,060. ✓

Watch out. Only the tens digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Key words. Counting in steps of 100 means taking away 100 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting back in 100s means taking away 100 each time. Only the hundreds digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting back in steps of 100, which is 1 hundred.
   Each jump is −100.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   71,450 − 100 = 71,350  (the hundreds digit goes 4 → 3)
   71,350 − 100 = 71,250  (the hundreds digit goes 3 → 2)
   71,250 − 100 = 71,150  (the hundreds digit goes 2 → 1)
3. Write the numbers in order.
   71,350, 71,250, 71,150

Check. Go the other way from the last number: 71,150 + 100 = 71,250. ✓

Watch out. Only the hundreds digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Key words. Counting in steps of 1,000 means taking away 1,000 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting back in 1,000s means taking away 1,000 each time. Only the thousands digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting back in steps of 1,000, which is 1 thousand.
   Each jump is −1,000.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   530,000 − 1,000 = 529,000  (0 thousands: swap 1 from the next column for 10 thousands, then take 1 thousand away)
   529,000 − 1,000 = 528,000  (the thousands digit goes 9 → 8)
   528,000 − 1,000 = 527,000  (the thousands digit goes 8 → 7)
3. Write the numbers in order.
   529,000, 528,000, 527,000

Check. Go the other way from the last number: 527,000 + 1,000 = 528,000. ✓

Watch out. Only the thousands digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Key words. Counting in steps of 100,000 means taking away 100,000 again and again. 10, 100, 1,000, 10,000 and 100,000 are powers of 10.

Method. Counting back in 100,000s means taking away 100,000 each time. Only the hundred thousands digit changes (unless we carry or swap).

1. Find the size of each jump. We are counting back in steps of 100,000, which is 1 hundred thousand.
   Each jump is −100,000.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   900,000 − 100,000 = 800,000  (the hundred thousands digit goes 9 → 8)
   800,000 − 100,000 = 700,000  (the hundred thousands digit goes 8 → 7)
   700,000 − 100,000 = 600,000  (the hundred thousands digit goes 7 → 6)
3. Write the numbers in order.
   800,000, 700,000, 600,000

Check. Go the other way from the last number: 600,000 + 100,000 = 700,000. ✓

Watch out. Only the hundred thousands digit changes, unless it is a 9 going up (carry) or a 0 going down (swap). Check the digit before every jump.

Method. To find 10 more, change the tens digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the tens digit. 10 is one ten, so we change the tens digit.

   Thousands	Ones
   Th	H	T	O
   7	9	9	5

2. Add 1 to the tens digit. There are 9 tens. 1 more ten makes 10 tens, which is 1 of the next column and 0 tens. We carry (and the carry carries on if the next digit is also 9).
   9 + 1 = 10 → write 0 in the T column and carry 1
3. Write the new number. The digits that did not change stay the same.

   	Thousands	Ones
   	Th	H	T	O
   7,995	7	9	9	5
   8,005	8	0	0	5

   
   7,995 + 10 = 8,005

Check. Do the opposite: 8,005 − 10 = 7,995. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 100 more, change the hundreds digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the hundreds digit. 100 is one hundred, so we change the hundreds digit.

   Thousands		Ones
   TTh	Th	H	T	O
   5	4	9	5	0

2. Add 1 to the hundreds digit. There are 9 hundreds. 1 more hundred makes 10 hundreds, which is 1 of the next column and 0 hundreds. We carry (and the carry carries on if the next digit is also 9).
   9 + 1 = 10 → write 0 in the H column and carry 1
3. Write the new number. The digits that did not change stay the same.

   	Thousands		Ones
   	TTh	Th	H	T	O
   54,950	5	4	9	5	0
   55,050	5	5	0	5	0

   
   54,950 + 100 = 55,050

Check. Do the opposite: 55,050 − 100 = 54,950. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 1,000 more, change the thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the thousands digit. 1,000 is one thousand, so we change the thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   2	4	9	5	0	0

2. Add 1 to the thousands digit. There are 9 thousands. 1 more thousand makes 10 thousands, which is 1 of the next column and 0 thousands. We carry (and the carry carries on if the next digit is also 9).
   9 + 1 = 10 → write 0 in the Th column and carry 1
3. Write the new number. The digits that did not change stay the same.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   249,500	2	4	9	5	0	0
   250,500	2	5	0	5	0	0

   
   249,500 + 1,000 = 250,500

Check. Do the opposite: 250,500 − 1,000 = 249,500. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 10,000 more, change the ten thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the ten thousands digit. 10,000 is one ten thousand, so we change the ten thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   3	9	5	0	0	0

2. Add 1 to the ten thousands digit. There are 9 ten thousands. 1 more ten thousand makes 10 ten thousands, which is 1 of the next column and 0 ten thousands. We carry (and the carry carries on if the next digit is also 9).
   9 + 1 = 10 → write 0 in the TTh column and carry 1
3. Write the new number. The digits that did not change stay the same.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   395,000	3	9	5	0	0	0
   405,000	4	0	5	0	0	0

   
   395,000 + 10,000 = 405,000

Check. Do the opposite: 405,000 − 10,000 = 395,000. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 100,000 more, change the hundred thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the hundred thousands digit. 100,000 is one hundred thousand, so we change the hundred thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   2	9	9	9	9	9

2. Add 1 to the hundred thousands digit. 100,000 more means 1 more hundred thousand.
   2 + 1 = 3 hundred thousands
3. Write the new number. The digits that did not change stay the same.
   299,999 + 100,000 = 399,999

Check. Do the opposite: 399,999 − 100,000 = 299,999. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 10,000 more, change the ten thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the ten thousands digit. 10,000 is one ten thousand, so we change the ten thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   8	9	9	0	0	0

2. Add 1 to the ten thousands digit. There are 9 ten thousands. 1 more ten thousand makes 10 ten thousands, which is 1 of the next column and 0 ten thousands. We carry (and the carry carries on if the next digit is also 9).
   9 + 1 = 10 → write 0 in the TTh column and carry 1
3. Write the new number. The digits that did not change stay the same.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   899,000	8	9	9	0	0	0
   909,000	9	0	9	0	0	0

   
   899,000 + 10,000 = 909,000

Check. Do the opposite: 909,000 − 10,000 = 899,000. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 10 less, change the tens digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the tens digit. 10 is one ten, so we change the tens digit.

   Thousands	Ones
   Th	H	T	O
   5	0	0	0

2. Take 1 from the tens digit. There are 0 tens, so we swap 1 from the next column for 10 tens. If that next digit is also 0 we swap again. Then take 1 away.
   0 tens → swap, then 10 − 1 = 9 tens
3. Write the new number. The digits that did not change stay the same.

   	Thousands	Ones
   	Th	H	T	O
   5,000	5	0	0	0
   4,990	4	9	9	0

   
   5,000 − 10 = 4,990

Check. Do the opposite: 4,990 + 10 = 5,000. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 100 less, change the hundreds digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the hundreds digit. 100 is one hundred, so we change the hundreds digit.

   Thousands		Ones
   TTh	Th	H	T	O
   3	0	0	5	0

2. Take 1 from the hundreds digit. There are 0 hundreds, so we swap 1 from the next column for 10 hundreds. If that next digit is also 0 we swap again. Then take 1 away.
   0 hundreds → swap, then 10 − 1 = 9 hundreds
3. Write the new number. The digits that did not change stay the same.

   	Thousands		Ones
   	TTh	Th	H	T	O
   30,050	3	0	0	5	0
   29,950	2	9	9	5	0

   
   30,050 − 100 = 29,950

Check. Do the opposite: 29,950 + 100 = 30,050. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 1,000 less, change the thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the thousands digit. 1,000 is one thousand, so we change the thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   1	0	0	0	0	0

2. Take 1 from the thousands digit. There are 0 thousands, so we swap 1 from the next column for 10 thousands. If that next digit is also 0 we swap again. Then take 1 away.
   0 thousands → swap, then 10 − 1 = 9 thousands
3. Write the new number. The digits that did not change stay the same.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   100,000	1	0	0	0	0	0
   99,000		9	9	0	0	0

   
   100,000 − 1,000 = 99,000

Check. Do the opposite: 99,000 + 1,000 = 100,000. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 10,000 less, change the ten thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the ten thousands digit. 10,000 is one ten thousand, so we change the ten thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   2	0	5	0	0	0

2. Take 1 from the ten thousands digit. There are 0 ten thousands, so we swap 1 from the next column for 10 ten thousands. If that next digit is also 0 we swap again. Then take 1 away.
   0 ten thousands → swap, then 10 − 1 = 9 ten thousands
3. Write the new number. The digits that did not change stay the same.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   205,000	2	0	5	0	0	0
   195,000	1	9	5	0	0	0

   
   205,000 − 10,000 = 195,000

Check. Do the opposite: 195,000 + 10,000 = 205,000. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 100,000 less, change the hundred thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the hundred thousands digit. 100,000 is one hundred thousand, so we change the hundred thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   6	4	0	0	0	0

2. Take 1 from the hundred thousands digit. 100,000 less means 1 less hundred thousand.
   6 − 1 = 5 hundred thousands
3. Write the new number. The digits that did not change stay the same.
   640,000 − 100,000 = 540,000

Check. Do the opposite: 540,000 + 100,000 = 640,000. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. To find 1,000 less, change the thousands digit by 1. Look out for 9s going up (carrying) and 0s going down (swapping).

1. Find the thousands digit. 1,000 is one thousand, so we change the thousands digit.

   Thousands			Ones
   HTh	TTh	Th	H	T	O
   7	0	0	5	0	0

2. Take 1 from the thousands digit. There are 0 thousands, so we swap 1 from the next column for 10 thousands. If that next digit is also 0 we swap again. Then take 1 away.
   0 thousands → swap, then 10 − 1 = 9 thousands
3. Write the new number. The digits that did not change stay the same.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   700,500	7	0	0	5	0	0
   699,500	6	9	9	5	0	0

   
   700,500 − 1,000 = 699,500

Check. Do the opposite: 699,500 + 1,000 = 700,500. ✓

Watch out. Only the digit in the column you are working on changes, unless you carry or swap. Do not change all the digits.

Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.

1. Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.
   From 7,260 to 7,270 is 1 jump.
   The difference is 10.
2. Say which way and how big each jump is. The numbers are getting bigger, so we count on.
   Each jump is +10.
3. Fill in the missing numbers. Add (or take away) one jump from a number you know. Where two gaps are side by side, fill one first and use it for the next.
   Number 1: 7,260 − 10 = 7,250
   Number 4: 7,270 + 10 = 7,280
4. Write the missing numbers. Put them in the order they appear.
   7,250, 7,280

Check. Read the whole sequence again and check every jump is +10: 7,250, 7,260, 7,270, 7,280, 7,290. ✓

Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.

Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.

1. Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.
   From 850,000 to 550,000 is 3 jumps.
   The difference is 300,000.
   300,000 ÷ 3 = 100,000
2. Say which way and how big each jump is. The numbers are getting smaller, so we count back.
   Each jump is −100,000.
3. Fill in the missing numbers. Add (or take away) one jump from a number you know. Where two gaps are side by side, fill one first and use it for the next.
   Number 2: 850,000 − 100,000 = 750,000
   Number 3: 750,000 − 100,000 = 650,000
4. Write the missing numbers. Put them in the order they appear.
   750,000, 650,000

Check. Read the whole sequence again and check every jump is −100,000: 850,000, 750,000, 650,000, 550,000, 450,000. ✓

Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.

Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.

1. Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.
   From 395,000 to 397,000 is 2 jumps.
   The difference is 2,000.
   2,000 ÷ 2 = 1,000
2. Say which way and how big each jump is. The numbers are getting bigger, so we count on.
   Each jump is +1,000.
3. Fill in the missing numbers. Add (or take away) one jump from a number you know. Where two gaps are side by side, fill one first and use it for the next.
   Number 2: 395,000 + 1,000 = 396,000
   Number 5: 398,000 + 1,000 = 399,000
   Number 6: 399,000 + 1,000 = 400,000
4. Write the missing numbers. Put them in the order they appear.
   396,000, 399,000, 400,000

Check. Read the whole sequence again and check every jump is +1,000: 395,000, 396,000, 397,000, 398,000, 399,000, 400,000. ✓

Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.

Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.

1. Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.
   From 600,000 to 800,000 is 2 jumps.
   The difference is 200,000.
   200,000 ÷ 2 = 100,000
2. Say which way and how big each jump is. The numbers are getting bigger, so we count on.
   Each jump is +100,000.
3. Fill in the missing numbers. Add (or take away) one jump from a number you know. Where two gaps are side by side, fill one first and use it for the next.
   Number 2: 600,000 + 100,000 = 700,000
   Number 4: 800,000 + 100,000 = 900,000
4. Write the missing numbers. Put them in the order they appear.
   700,000, 900,000

Check. Read the whole sequence again and check every jump is +100,000: 600,000, 700,000, 800,000, 900,000, 1,000,000. ✓

Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.

Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.

1. Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.
   From 4,000 to 3,700 is 3 jumps.
   The difference is 300.
   300 ÷ 3 = 100
2. Say which way and how big each jump is. The numbers are getting smaller, so we count back.
   Each jump is −100.
3. Fill in the missing numbers. Add (or take away) one jump from a number you know. Where two gaps are side by side, fill one first and use it for the next.
   Number 2: 4,000 − 100 = 3,900
   Number 3: 3,900 − 100 = 3,800
4. Write the missing numbers. Put them in the order they appear.
   3,900, 3,800

Check. Read the whole sequence again and check every jump is −100: 4,000, 3,900, 3,800, 3,700. ✓

Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.

Method. Work out how much each term changes by. If the jump is always the same, that is the rule.

1. Write the first terms in a place-value table. Look for the one column that changes.

   	Thousands	Ones
   	Th	H	T	O
   5,320	5	3	2	0
   5,420	5	4	2	0
   5,520	5	5	2	0

2. Find the jump between two terms next to each other. The column that changes tells us the size of the jump.
   5,420 − 5,320 = 100 (it goes up)
3. Check the jump is the same all the way along. A rule has to work for every pair of terms.
   5,420 − 5,320 = 100
   5,520 − 5,420 = 100
   5,620 − 5,520 = 100
4. Write the rule and the next two terms. Add 100 each time.
   Rule: add 100.
   Next two terms: 5,720, 5,820

Check. 5,620 + 100 = 5,720 and 5,720 + 100 = 5,820. ✓

Watch out. Check more than one pair of terms. One pair is not enough to be sure of the rule.

Method. Work out how much each term changes by. If the jump is always the same, that is the rule.

1. Write the first terms in a place-value table. Look for the one column that changes.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   800,000	8	0	0	0	0	0
   700,000	7	0	0	0	0	0
   600,000	6	0	0	0	0	0

2. Find the jump between two terms next to each other. The column that changes tells us the size of the jump.
   800,000 − 700,000 = 100,000 (it goes down)
3. Check the jump is the same all the way along. A rule has to work for every pair of terms.
   800,000 − 700,000 = 100,000
   700,000 − 600,000 = 100,000
   600,000 − 500,000 = 100,000
4. Write the rule and the next two terms. Subtract 100,000 each time.
   Rule: subtract 100,000.
   Next two terms: 400,000, 300,000

Check. 500,000 − 100,000 = 400,000 and 400,000 − 100,000 = 300,000. ✓

Watch out. Check more than one pair of terms. One pair is not enough to be sure of the rule.

Method. Work out how much each term changes by. If the jump is always the same, that is the rule.

1. Write the first terms in a place-value table. Look for the one column that changes.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   204,000	2	0	4	0	0	0
   214,000	2	1	4	0	0	0
   224,000	2	2	4	0	0	0

2. Find the jump between two terms next to each other. The column that changes tells us the size of the jump.
   214,000 − 204,000 = 10,000 (it goes up)
3. Check the jump is the same all the way along. A rule has to work for every pair of terms.
   214,000 − 204,000 = 10,000
   224,000 − 214,000 = 10,000
   234,000 − 224,000 = 10,000
4. Write the rule and the next two terms. Add 10,000 each time.
   Rule: add 10,000.
   Next two terms: 244,000, 254,000

Check. 234,000 + 10,000 = 244,000 and 244,000 + 10,000 = 254,000. ✓

Watch out. Check more than one pair of terms. One pair is not enough to be sure of the rule.

Method. Work out how much each term changes by. If the jump is always the same, that is the rule.

1. Write the first terms in a place-value table. Look for the one column that changes.

   	Thousands	Ones
   	Th	H	T	O
   8,090	8	0	9	0
   8,080	8	0	8	0
   8,070	8	0	7	0

2. Find the jump between two terms next to each other. The column that changes tells us the size of the jump.
   8,090 − 8,080 = 10 (it goes down)
3. Check the jump is the same all the way along. A rule has to work for every pair of terms.
   8,090 − 8,080 = 10
   8,080 − 8,070 = 10
   8,070 − 8,060 = 10
4. Write the rule and the next two terms. Subtract 10 each time.
   Rule: subtract 10.
   Next two terms: 8,050, 8,040

Check. 8,060 − 10 = 8,050 and 8,050 − 10 = 8,040. ✓

Watch out. Check more than one pair of terms. One pair is not enough to be sure of the rule.

Method. Look at the two numbers in the number sentence. Find which column changes, or use the opposite (inverse) operation, to find the missing number.

1. Look at the number sentence. The box stands for the number we want.
   245,600 + ? = 345,600
2. Put the two known numbers in a place-value table. Only one column changes, and it shows the size of the jump.

   	Thousands			Ones
   	HTh	TTh	Th	H	T	O
   245,600	2	4	5	6	0	0
   345,600	3	4	5	6	0	0

3. Work out the missing number. Use the opposite operation to check the size of the change.
   345,600 − 245,600 = 100,000
4. Check it in the number sentence. Put the answer back in the box.
   245,600 + 100,000 = 345,600 ✓

Check. The change is 100,000, a power of 10 (or a number made from powers of 10). ✓

Watch out. The box is not always at the start. Think about what the sentence is saying before you choose + or −.

Method. Look at the two numbers in the number sentence. Find which column changes, or use the opposite (inverse) operation, to find the missing number.

1. Look at the number sentence. The box stands for the number we want.
   ? − 1,000 = 87,500
2. Put the two known numbers in a place-value table. Only one column changes, and it shows the size of the jump.

   	Thousands		Ones
   	TTh	Th	H	T	O
   87,500	8	7	5	0	0
   88,500	8	8	5	0	0

3. Work out the missing number. Use the opposite operation to check the size of the change.
   87,500 + 1,000 = 88,500
4. Check it in the number sentence. Put the answer back in the box.
   88,500 − 1,000 = 87,500 ✓