Year 5 Place Value to 1,000,000: check-up and SATs-style questions

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
   2	4	5	3	1	0

2. Find which column the digit is in. The digit is 4 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 4 ten thousands.
   4 × 10,000 = 40,000

Check. Say it in words: 4 ten thousands is forty thousand. ✓

Watch out. The digit is 4 but its value is 40,000. 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. 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
   3	0	5	0	8	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: 305 → three hundred and five thousand
   Last two digits: 80 → eighty
3. Join the parts together. Put “and” before the last two digits (the tens and ones) when there are hundreds or thousands before them.
   three hundred and five thousand and eighty

Check. Read it out loud. It sounds like 305,080. ✓

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.

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	1	5	0	0	0

2. Take 1 from the ten thousands digit. 10,000 less means 1 less ten thousand.
   1 − 1 = 0 ten thousands
3. Write the new number. The digits that did not change stay the same.
   215,000 − 10,000 = 205,000

Check. Do the opposite: 205,000 + 10,000 = 215,000. ✓

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

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
   472,510	4	7	2	5	1	0
   427,510	4	2	7	5	1	0
   472,150	4	7	2	1	5	0
   47,251		4	7	2	5	1

2. Compare the numbers in pairs, from the left. Where the digits in a column match, move on to the next column.
   47,251 and 427,510: 427,510 has 6 digits and 47,251 has 5 digits, so 427,510 is bigger.
   427,510 and 472,150: ten thousands: 2 and 7 are different. 2 < 7, so 427,510 is smaller.
   472,150 and 472,510: hundreds: 1 and 5 are different. 1 < 5, so 472,150 is smaller.
3. Write them smallest first. Check you have used every number once.
   47,251, 427,510, 472,150, 472,510

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

Method. Counting back in 10,000s means taking away 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 back 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.
   305,000 − 10,000 = 295,000  (0 ten thousands: swap 1 from the next column for 10 ten thousands, then take 1 ten thousand away)
   295,000 − 10,000 = 285,000  (the ten thousands digit goes 9 → 8)
   285,000 − 10,000 = 275,000  (the ten thousands digit goes 8 → 7)
3. Write the numbers in order.
   295,000, 285,000, 275,000

Check. Go the other way from the last number: 275,000 + 10,000 = 285,000. ✓

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. To round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 10,000 that 683,472 is between. Rounding to the nearest 10,000 means choosing the closest multiple of 10,000.
   680,000  <  683,472  <  690,000
2. Look at the thousands digit (the digit just to the right of the ten thousands digit). This digit tells us if we are past halfway.
   The thousands digit is 3.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   3 is 4 or less, so round down.
4. Write the rounded number. All the digits to the right of the ten thousands column become zeros.
   683,472 ≈ 680,000 (to the nearest 10,000)

Check. Distances: 683,472 − 680,000 = 3,472 and 690,000 − 683,472 = 6,528. 680,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further along.

Method. Draw a number line, start at 3 and jump down 8. When you pass 0 the numbers change between positive and negative.

1. Show the start on a number line. This lets us see where zero is.
2. Go down 8. Split the jump into two parts if it crosses zero: the part that reaches 0, then the part that goes past it.
   3 down 8: go down 3 to reach 0, then 5 more below zero → −5
3. Write the answer. This is the new temperature.
   −5°C

Check. Do the opposite: −5 + 8 = 3. ✓

Watch out. Going down past zero gives a negative number. Going up from a negative number gets closer to zero.

Method. On a number line, numbers further to the left are smaller. Mark each number, then read them off from left to right.

1. Put the numbers on a number line. The line shows which are below zero.
2. Read from left to right. Left is smallest, right is biggest.
   −10, −6, −1, 2
3. Write them smallest first. Check you have used every number once.
   −10, −6, −1, 2

Check. The numbers below zero are the smallest. Of those, the one with the biggest digit (like −9) is furthest from zero, so it is the smallest. ✓

Watch out. −9 is smaller than −2. The further below zero, the smaller the number.

Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.

Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).

1. Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.
   474 = 400 + 70 + 4
2. Write 400 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).
   400 = CD
3. Write 70 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).
   70 = LXX
4. Write 4 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).
   4 = IV
5. Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.
   CD + LXX + IV = CDLXXIV

Check. Read it back: 400 + 50 + 10 + 10 + 4 = 474. ✓

Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.

Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.

Method. Split the Roman numeral into groups, write the value of each group, then add them up.

1. Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.
   M = 1,000
   CM = 1000 − 100 = 900  (small symbol in front, so take it away)
   L = 50
   X = 10
   X = 10
   X = 10
   V = 5
   I = 1
   I = 1
   I = 1
2. Add the values. Add the biggest groups first.
   1,000 + 900 + 50 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 1,988
3. Write the answer.
   1988

Check. Write 1,988 in Roman numerals: M + CM + LXXX + VIII = MCMLXXXVIII. ✓

Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.

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	6	5	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
   396,500	3	9	6	5	0	0
   406,500	4	0	6	5	0	0

   
   396,500 + 10,000 = 406,500

Check. Do the opposite: 406,500 − 10,000 = 396,500. ✓

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. The thousands column is the fourth from the right. Look at each number.

1. Find the thousands digit in each number. The thousands column is the fourth digit from the right.
   24,600: thousands digit is 4
   60,450: thousands digit is 0
   604,500: thousands digit is 4
   546,000: thousands digit is 6
2. Choose the number with 6 thousands.
   546,000

Check. 546,000 = 500,000 + 40,000 + 6,000. The 6 is worth 6,000. ✓

Watch out. 604,500 has a 6 in the hundred thousands column, not the thousands column.

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.
   “two hundred and six thousand” → the Thousands period is 206
   no hundreds are said → 0 in the hundreds column
   “forty” → 4 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
   2	0	6	0	4	0

3. Write the number. Put a comma between the periods.
   206,040

Check. Say 206,040 in words: two hundred and six thousand and forty. 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 round a number is to change it to a nearby number that is easier to use. ≈ means “is about equal to”.

Method. Look at the digit to the right of the one you are rounding to. If it is 5 or more, round up. If it is 4 or less, round down.

1. Find the two multiples of 100 that 74,950 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   74,900  <  74,950  <  75,000
2. Look at the tens digit (the digit just to the right of the hundreds digit). This digit tells us if we are past halfway.
   The tens digit is 5.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   5 is 5 or more, so round up.
4. Write the rounded number. All the digits to the right of the hundreds column become zeros.
   74,950 ≈ 75,000 (to the nearest 100)

Check. Distances: 74,950 − 74,900 = 50 and 75,000 − 74,950 = 50. 75,000 is the one we choose when exactly halfway (halfway rounds up). ✓

Watch out. Only look at the digit just to the right. Do not round twice. Halfway always rounds up.

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 346,200 to 347,200 is 1 jump.
   The difference is 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 3: 347,200 + 1,000 = 348,200
   Number 4: 348,200 + 1,000 = 349,200
4. Write the missing numbers. Put them in the order they appear.
   348,200, 349,200

Check. Read the whole sequence again and check every jump is +1,000: 346,200, 347,200, 348,200, 349,200, 350,200. ✓

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

Method. Draw a number line, start at −7 and jump up 12. When you pass 0 the numbers change between positive and negative.

1. Show the start on a number line. This lets us see where zero is.
2. Go up 12. Split the jump into two parts if it crosses zero: the part that reaches 0, then the part that goes past it.
   −7 up 12: go up 7 to reach 0, then 5 more → 5
3. Write the answer. This is the new temperature.
   5°C

Check. Do the opposite: 5 − 12 = −7. ✓

Watch out. Going down past zero gives a negative number. Going up from a negative number gets closer to zero.

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
   530,800	5	3	0	8	0	0
   508,300	5	0	8	3	0	0
   538,000	5	3	8	0	0	0
   503,800	5	0	3	8	0	0

2. Compare the numbers in pairs, from the left. Where the digits in a column match, move on to the next column.
   503,800 and 508,300: thousands: 3 and 8 are different. 3 < 8, so 503,800 is smaller.
   508,300 and 530,800: ten thousands: 0 and 3 are different. 0 < 3, so 508,300 is smaller.
   530,800 and 538,000: thousands: 0 and 8 are different. 0 < 8, so 530,800 is smaller.
3. Write them smallest first. Check you have used every number once.
   503,800, 508,300, 530,800, 538,000

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. Change both Roman numerals into years. Then take the earlier year away from the later year.

1. Change MCMXCVIII to a year. M = 1,000, CM = 900, XC = 90, VIII = 8.
   1,000 + 900 + 90 + 8 = 1998
2. Change MMXXV to a year. MM = 2,000, XX = 20, V = 5.
   2,000 + 20 + 5 = 2025
3. Find the difference. Take the earlier year from the later year.
   2025 − 1998 = 27

Check. 1998 + 27 = 2025. ✓

Watch out. 2 marks: 1 for changing both numerals correctly and 1 for the right difference.

Method. Round 98,000 to the nearest 100,000 and compare it with Amira’s answer.

1. Find the two hundred thousands either side. The multiples of 100,000 either side of 98,000 are 0 and 100,000.
   0 < 98,000 < 100,000
2. Look at the ten thousands digit. It is 9, which is 5 or more, so round up.
   98,000 ≈ 100,000
3. Answer Amira. Amira’s answer, 90,000, is not a multiple of 100,000, so it cannot be the answer to this question.
   No. 98,000 rounds to 100,000.

Check. 98,000 is only 2,000 from 100,000. It is 98,000 from 0. ✓

Watch out. 2 marks: 1 for rounding correctly and 1 for explaining that the ten thousands digit is 9.

Method. Use each clue to find a range of numbers. Then see where the two ranges overlap.

1. Use the nearest 100,000 clue. To round to 500,000 the number is from 450,000 to 549,999.
   450,000 to 549,999
2. Use the nearest 10,000 clue. To round to 450,000 the number is from 445,000 to 454,999.
   445,000 to 454,999
3. Find where the ranges overlap. The number must fit both clues.
   The overlap is 450,000 to 454,999
4. Write the smallest and largest.
   Smallest 450,000, largest 454,999

Check. 449,999 rounds to 400,000 (nearest 100,000) and 455,000 rounds to 460,000 (nearest 10,000), so neither works. ✓

Watch out. 3 marks: 1 for each range, 1 for both answers.