Year 4 Place Value: check-up and SATs-style questions

Key words. Counting in steps of 7 means adding 7 again and again. The numbers you say are multiples of 7 if you start from 0.

Method. Counting on in 7s means adding 7 each time. Use each new number to start the next jump.

1. Find the size of each jump. We are counting on in steps of 7.
   Each jump is +7.
2. Work out the numbers one jump at a time. Always start from the number you have just found.
   28 + 2 = 30 (a tens number), then + 5 more = 35
   35 + 5 = 40 (a tens number), then + 2 more = 42
   42 + 7 = 49
3. Write the numbers in order.
   35, 42, 49

Check. Go the other way from the last number: 49 − 7 = 42. ✓

Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.

Key words. The value of a digit is how much it is worth. A place-value table has columns: ones (O), tens (T), hundreds (H), thousands (Th).

Method. The value of a digit depends on its column. Find the column, then work out the digit times the column value.

1. Write the number in a place-value table. Each column has its own name and value.

   Th	H	T	O
   3	8	4	7

2. Find which column the digit is in. The coloured digit is 4, in the tens column.
   1 ten = 10
3. Multiply the digit by the value of the column. There are 4 tens.
   4 × 10 = 40

Check. Say it in words: 4 tens is forty. ✓

Watch out. The digit is 4, but its value is 40. The value depends on where the digit sits.

Method. Say the number in parts, from the biggest column to the smallest: thousands, then hundreds, then the last two digits.

1. Write the number in a place-value table. This helps us see each part.

   Th	H	T	O
   6	0	5	0

2. Say each part in words. Put "thousand" after the thousands and "hundred" after the hundreds.
   6 thousands → six thousand
   50 (the last two digits) → fifty
3. Join the parts together. Put "and" before the last part, just before the tens and ones.
   six thousand and fifty

Check. Read it out loud. It sounds like 6,050. ✓

Watch out. The words for 4,065 are four thousand and sixty-five. There are no hundreds, so you do not say "hundred".

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

1. Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.

   Th	H	T	O
   5	2	0	6

2. Take 1 from the thousands digit. 1,000 less means 1 less thousand.
   5 − 1 = 4 thousands
3. Write the new number. Digits in the other columns stay the same unless we carried or exchanged.
   5,206 − 1,000 = 4,206

Check. Do the opposite: 4,206 + 1,000 = 5,206. ✓

Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).

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.

   	Th	H	T	O
   6,089	6	0	8	9
   6,098	6	0	9	8

2. Compare the digits from the left. The first column where they are different decides which number is bigger.
   thousands: 6 and 6 are the same, so look at the next column.
   hundreds: 0 and 0 are the same, so look at the next column.
   tens: 8 and 9 are different. 8 < 9, so 6,089 is smaller.
3. Write the correct symbol. < means “is less than”, > means “is greater than”, = means “is equal to”.
   6,089 < 6,098

Check. Picture a number line: 6,089 is to the left of 6,098. ✓

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

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 3,578 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   3,500  <  3,578  <  3,600
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 7.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   7 is 5 or more, so round up.
4. Write the rounded number. Digits to the right of the hundreds column become zeros.
   3,578 ≈ 3,600 (to the nearest 100)

Check. Distances: 3,578 − 3,500 = 78 and 3,600 − 3,578 = 22. 3,600 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 2 and jump down 6. 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 6. Split the jump into two parts: the part that reaches 0, then the part that goes past it.
   2 − 6: go down 2 to reach 0, then 4 more below zero → −4
3. Write the answer.
   −4°C

Check. Do the opposite: −4 + 6 = 2. ✓

Watch out. Going down past zero gives a negative number. Going up from a negative number makes it 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.
   −10, −6, −1, 2

Check. The numbers below zero are the smallest. Of those, the one with the biggest digit (like −9) is the 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 the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.

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

1. Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.
   64 = 60 + 4
2. Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).
   60 = LX
3. Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).
   4 = IV
4. Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.
   LX + IV = LXIV

Check. Read it back: L (50) + X (10) + IV (5 − 1) = 64. ✓

Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.

Method. Count on in 25s, one jump at a time. Each jump is one number.

1. Decide what each jump means. Every number adds 25, so we count on in 25s. We start at 350.
   Jump = +25
2. Count on 4 times. Use the new number as the start of the next jump.
   350 + 20 = 370, then + 5 = 375
   375 + 20 = 395, then + 5 = 400
   400 + 20 = 420, then + 5 = 425
   425 + 20 = 445, then + 5 = 450
3. Write the answer. Tom says four numbers. The last one is the answer.
   450

Check. Check with a times fact: 25 × 4 = 100, and 350 + 100 = 450. ✓

Watch out. Count the jumps carefully. Using your fingers or tally marks helps you keep track of how many you have made.

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

1. Find the thousands digit. 1,000 is one thousand, so only the thousands digit (and maybe the next one) should change.

   Th	H	T	O
   6	7	4	5

2. Add 1 to the thousands digit. 1,000 more means 1 more thousand.
   6 + 1 = 7 thousands
3. Write the new number. Digits in the other columns stay the same unless we carried or exchanged.
   6,745 + 1,000 = 7,745

Check. Do the opposite: 7,745 − 1,000 = 6,745. ✓

Watch out. Do not change every digit! Only the digit in the column you are working on changes (unless you carry or exchange).

Method. The tens digit is the second digit from the right. Look at each number.

1. Find the tens digit in each number. The tens column is the second from the right.
   3,502: tens digit is 0
   5,032: tens digit is 3
   3,052: tens digit is 5
   3,520: tens digit is 2
2. Choose the number with 5 tens.
   3,052

Check. 3,052 = 3,000 + 50 + 2. The 5 is worth 50, which is 5 tens. ✓

Watch out. 5,032 has 5 thousands, not 5 tens.

Method. Listen for the words "thousand" and "hundred". They tell you which column each digit goes in.

1. Split the words into parts. Each part belongs to one or two columns.
   seven thousand → 7 in the thousands column
   no hundreds are said → 0 in the hundreds column
   forty → 4 tens and 0 ones
2. Write the digits in the place-value table. Write 0 in any column that was not mentioned.

   Th	H	T	O
   7	0	4	0

3. Write the number.
   7,040

Check. Say 7,040 in words: seven thousand and forty. ✓

Watch out. If no tens or ones are said, those columns are zeros: “six thousand” is 6,000.

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 5,962 is between. Rounding to the nearest 100 means choosing the closest multiple of 100.
   5,900  <  5,962  <  6,000
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 6.
3. Decide: round up or round down? 5 or more: round up. 4 or less: round down.
   6 is 5 or more, so round up.
4. Write the rounded number. Digits to the right of the hundreds column become zeros.
   5,962 ≈ 6,000 (to the nearest 100)

Check. Distances: 5,962 − 5,900 = 62 and 6,000 − 5,962 = 38. 6,000 is the nearer one. ✓

Watch out. Only the digit just to the right decides. Do not look at digits further 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 4,350 to 5,350 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.
   Number 3: 5,350 + 1,000 = 6,350
   Number 4: 8,350 − 1,000 = 7,350
4. Write the missing numbers.
   6,350, 7,350

Check. Read the whole sequence again and check every jump is +1,000: 4,350, 5,350, 6,350, 7,350, 8,350. ✓

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

Method. Round 4,450 to the nearest 1000 and compare it with Aisha’s answer.

1. Find the two thousands either side. 4,450 is between 4,000 and 5,000.
   4,000 < 4,450 < 5,000
2. Look at the hundreds digit. The digit just to the right of the thousands is 4. That is 4 or less, so round down.
   4,450 ≈ 4,000
3. Answer Aisha. Halfway is 4,500 and 4,450 is before halfway.
   No. 4,450 rounds to 4,000, not 5,000.

Check. 4,450 is 450 from 4,000 and 550 from 5,000. 4,000 is nearer. ✓

Watch out. 2 marks: 1 for showing the correct rounding and 1 for explaining that the hundreds digit is 4.

Method. Draw a number line, start at −5 and jump up 9. 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 9. Split the jump into two parts: the part that reaches 0, then the part that goes past it.
   −5 + 9: go up 5 to reach 0, then 4 more above zero → 4
3. Write the answer.
   4°C

Check. Do the opposite: 4 − 9 = −5. ✓

Watch out. Going down past zero gives a negative number. Going up from a negative number makes it 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.

   	Th	H	T	O
   4,096	4	0	9	6
   4,960	4	9	6	0
   4,069	4	0	6	9
   4,906	4	9	0	6

2. Compare the thousands, then the hundreds, then the tens, then the ones. Where the digits in a column match, move on to the next column.
   4,069 and 4,096: tens: 6 and 9 are different. 6 < 9, so 4,069 is smaller.
   4,096 and 4,906: hundreds: 0 and 9 are different. 0 < 9, so 4,096 is smaller.
   4,906 and 4,960: tens: 0 and 6 are different. 0 < 6, so 4,906 is smaller.
3. Write them smallest first. Check you have used every number once.
   4,069, 4,096, 4,906, 4,960

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

Watch out. Do not forget a number. Tick each one off as you write it.

Method. Change both Roman numerals into numbers. Then take away to find the difference.

1. Change LXXIV to a number. L = 50, XX = 20, IV = 4.
   LXXIV = 50 + 20 + 4 = 74
2. Change XCI to a number. XC = 90 and I = 1.
   XCI = 90 + 1 = 91
3. Find the difference. Ruby scored more, so take Layla’s score from Ruby’s.
   91 − 74 = 17

Check. 74 + 17 = 91. ✓

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

Method. Use each clue to cut down the possible numbers. Start with the clue about 100.

1. Use the clue about the nearest 100. The number rounds to 5,300, so it is between halfway to 5,200 and halfway to 5,400.
   Between 5,250 and 5,349
2. Use the clue about the nearest 1000. 5,300 is between 5,000 and 6,000 and is below 5,500, so it rounds to 5,000 automatically.
   This clue fits every number from 5,250 to 5,349.
3. Use the digits clue. The tens digit is 3 and the ones digit is 9, so the number looks like 5,_39. Which hundreds digit puts it in the range 5,250 to 5,349?
   Hundreds 2: 5,239 → too small (below 5,250)
   Hundreds 3: 5,339 → fits (between 5,250 and 5,349)
4. Write the number.
   5,339

Check. 5,339: nearest 100 is 5,300 (tens digit 3, round down) ✓. Nearest 1000 is 5,000 (hundreds digit 3, round down) ✓. Tens 3 ✓, ones 9 ✓.

Watch out. 3 marks: 1 for the range 5,250 to 5,349, 1 for using the digits clue, 1 for the answer 5,339.