For each 7-digit or 6-digit number, write the value of the underlined digit.
(a)In 5,3<u>8</u>4,271 what is the value of the digit 8?(1)
(b)In <u>5</u>,384,271 what is the value of the digit 5?(1)
(c)In 6<u>9</u>2,015 what is the value of the digit 9?(1)
(d)In 69<u>2</u>,015 what is the value of the digit 2?(1)
2
Convert each number between words and figures.
(a)Write 2,065,340 in words.(1)
(b)Write "four million, seven hundred and two thousand and eighteen" in figures.(1)
(c)Write 30,509,001 in words.(1)
(d)Write "six million and forty" in figures.(1)
3
Convert between Roman numerals and Arabic (standard) numbers.
(a)Write 14 as a Roman numeral.(1)
(b)Write 29 as a Roman numeral.(1)
(c)What number does XLII represent?(1)
(d)What number does XIX represent?(1)
4
Here are six numbers: -8, 3, -1, 6, -5, 0. Order them from smallest to largest.
(2)
5
Round each number as instructed.
(a)Round 4,382 to the nearest 100.(1)
(b)Round 67,451 to the nearest 1,000.(1)
(c)Round 8,073 to the nearest 10.(1)
6
3,482,650 sensors are counted at a factory. Round this number as instructed.
(a)Round 3,482,650 to the nearest 100,000.(1)
(b)Round 3,482,650 to the nearest 10,000.(1)
7
Answer these questions about temperature.
(a)At 6am the temperature was -7 degrees C. By noon it had risen by 12 degrees C. What was the temperature at noon?(2)
(b)At midnight the temperature was -3 degrees C. It then fell by 6 degrees C. What was the new temperature?(2)
(c)The temperature in Leeds was -4 degrees C and in Truro was 9 degrees C. What is the difference between the two temperatures?(2)
8
Convert between Roman numerals and Arabic (standard) numbers.
(a)Write 87 as a Roman numeral.(1)
(b)Write 149 as a Roman numeral.(1)
(c)What number does CDXL represent?(1)
(d)What number does DCCXCIV represent?(1)
9
The Great Fire of London happened in the year written as MDCLXVI in Roman numerals. Write this year using standard (Arabic) numerals.
(2)
10
Write <, > or = between each pair of numbers.
(a)3,482,910 ___ 3,428,910(1)
(b)5,096,214 ___ 5,096,241(1)
(c)900,000 ___ 89,999(1)
(d)4,000,001 ___ 4,000,010(1)
11
Calculate XVI + XIV, giving your answer as a Roman numeral.
(2)
12
Here is a number sequence that decreases by the same amount each time: 17, 11, 5, ___, ___, ___. Find the next three terms.
(3)
13
A newspaper and a football club round attendance figures before publishing them.
(a)A stadium had 58,742 people at a match. The newspaper reports this rounded to the nearest thousand. What figure did the newspaper report?(2)
(b)The away end had 7,368 fans. The club rounds this to the nearest hundred for its report. What figure did the club report?(2)
14
Write 4,509,632 as the sum of its place value parts (expanded form).
(3)
15
A lift starts at floor -3 (the second basement level). It travels up 8 floors to make its first stop, then travels down 5 floors to make its second stop.
(a)What floor is the lift at after the first stop?(2)
(b)What floor is the lift at after the second stop?(2)
16
Priya writes the Roman numeral for 99 as IC. Explain why this is incorrect, and write the correct Roman numeral for 99.
(3)
17
A 6-digit number has: a 7 in the hundred thousands place; a 0 in the thousands place; it rounds to 730,000 when rounded to the nearest ten thousand; the sum of all six digits is 21. Find a number that fits all these clues. (There may be more than one correct answer; give one.)
(4)
18
The height above sea level (positive) or below sea level (negative) of four locations is given: Point A: -35m, Point B: 120m, Point C: -8m, Point D: 0m.
(a)Order the four locations from lowest to highest.(2)
(b)What is the difference in height between Point A and Point B?(2)
19
A weather station records temperatures and sensor readings over one week.
(a)The lowest temperature recorded that week was -6 degrees C and the highest was 9 degrees C. Work out the difference between the highest and lowest temperatures.(2)
(b)The station's sensors took 428,750 individual readings that week. Round this number to the nearest ten thousand.(2)
(c)A scientist says: "430,000 rounded to the nearest hundred thousand is 500,000." Is the scientist correct? Explain your answer.(2)
20
The Battle of Hastings took place in the year MLXVI. The Battle of Bosworth took place in the year MCDLXXXV.
(a)Write each year using standard (Arabic) numerals.(2)
(b)Calculate how many years passed between the two battles.(2)
21
Amir is thinking of a whole number. It is negative. Ignoring the sign, the tens digit is 4. The number is between -50 and -30. Ignoring the sign, the units digit is an odd number greater than 5. The sum of its digits (ignoring the sign) is 11. What is Amir's number?
(4)
22
A museum's annual visitor total, written in Roman numerals, was MMMCDLII.
(a)Convert MMMCDLII to standard (Arabic) numerals.(2)
(b)The museum wants to display this figure rounded to the nearest hundred on a sign. What number should the sign show?(2)
(c)The following year, visitor numbers fell by 168 compared to the figure in part (a). Calculate the new number of visitors, then write it as a Roman numeral.(4)
Mark scheme · KS2.M-PV Place Value, Negative Numbers and Roman Numerals
Question 1
(a) B1 80,000 cao
(a) Answer: 80,000
(b) B1 5,000,000 cao
(b) Answer: 5,000,000
(c) B1 90,000 cao
(c) Answer: 90,000
(d) B1 2,000 cao
(d) Answer: 2,000
Question 2
(a) B1 two million, sixty-five thousand, three hundred and forty oe
(a) Answer: two million, sixty-five thousand, three hundred and forty
(b) B1 4,702,018 cao
(b) Answer: 4,702,018
(c) B1 thirty million, five hundred and nine thousand and one oe
(c) Answer: thirty million, five hundred and nine thousand and one
(d) B1 6,000,040 cao
(d) Answer: 6,000,040
Question 3
(a) B1 XIV cao
(a) Answer: XIV
(b) B1 XXIX cao
(b) Answer: XXIX
(c) B1 42 cao
(c) Answer: 42
(d) B1 19 cao
(d) Answer: 19
Question 4
M1 at least 4 of the 6 numbers placed in the correct relative order oe
A1 -8, -5, -1, 0, 3, 6 fully correct cao
Answer: -8, -5, -1, 0, 3, 6
Question 5
(a) B1 4,400 cao
(a) Answer: 4,400
(b) B1 67,000 cao
(b) Answer: 67,000
(c) B1 8,070 cao
(c) Answer: 8,070
Question 6
(a) B1 3,500,000 cao
(a) Answer: 3,500,000
(b) B1 3,480,000 cao
(b) Answer: 3,480,000
Question 7
(a) M1 counts on from -7 through 0, e.g. on a number line, or -7 + 12 oe
(a) A1 5 degrees C cao
(a) Answer: 5 degrees C
(b) M1 counts back from -3 by 6, or -3 - 6 oe
(b) A1 -9 degrees C cao
(b) Answer: -9 degrees C
(c) M1 9 - (-4) oe, or counts the gap across zero on a number line
(c) A1 13 degrees C cao
(c) Answer: 13 degrees C
Question 8
(a) B1 LXXXVII cao
(a) Answer: LXXXVII
(b) B1 CXLIX cao
(b) Answer: CXLIX
(c) B1 440 cao
(c) Answer: 440
(d) B1 794 cao
(d) Answer: 794
Question 9
M1 breaks the numeral into M(1000) + D(500) + C(100) + L(50) + X(10) + VI(6) oe
A1 1666 cao
Answer: 1666
Question 10
(a) B1 > cao
(a) Answer: >
(b) B1 < cao
(b) Answer: <
(c) B1 > cao
(c) Answer: >
(d) B1 < cao
(d) Answer: <
Question 11
M1 converts both to Arabic numbers and adds, 16 + 14 = 30 oe
A1 XXX cao
Answer: XXX
Question 12
B1 identifies the term-to-term rule as subtract 6 oe
B1 -1 and -7 correct
B1 -13 correct
Answer: -1, -7, -13
Question 13
(a) M1 identifies the hundreds digit (7) as the rounding digit
(a) A1 59,000 cao
(a) Answer: 59,000
(b) M1 identifies the tens digit (6) as the rounding digit
B1 valid explanation, e.g. a smaller numeral can only be subtracted from the numeral immediately above it in the standard sequence, so I can only come before V or X, not C oe
B1 correct method, e.g. 99 = 90 + 9 = XC + IX oe
B1 XCIX cao
Answer: XCIX
Question 17
M1 sets up the number in the form 7_0___ using the hundred-thousands and thousands clues
M1 uses the rounding clue correctly, e.g. recognises the thousands digit must be less than 5 for the number to round down to 730,000, so the ten-thousands digit is 3
A1 uses the digit sum (21) to find valid hundreds/tens/units digits, e.g. working shown
A1 any number consistent with all four clues cao, e.g. 730,353 (ft any number that satisfies every clue)
Answer: 730,353 (accept any number of the form 730,abc where a + b + c = 11 and a is 0-4)
Question 18
(a) M1 correctly places at least 3 of the 4 locations
(a) A1 A (-35m), C (-8m), D (0m), B (120m) fully correct cao
(a) Answer: A (-35m), C (-8m), D (0m), B (120m)
(b) M1 120 - (-35) oe, or counts the gap across zero
(b) A1 155m cao
(b) Answer: 155m
Question 19
(a) M1 9 - (-6) oe
(a) A1 15 degrees C cao
(a) Answer: 15 degrees C
(b) M1 identifies the thousands digit (8) as the rounding digit
(b) A1 430,000 cao
(b) Answer: 430,000
(c) B1 no, with valid reason, e.g. the ten-thousands digit is 3, which is less than 5, so it rounds down oe
(c) B1 400,000 stated as the correct value cao
(c) Answer: No; 430,000 rounds to 400,000, not 500,000.
Question 20
(a) B1 1066 cao (MLXVI)
(a) B1 1485 cao (MCDLXXXV)
(a) Answer: 1066 and 1485
(b) M1 ft 1485 - 1066 oe using their answers to part (a)
(b) A1 419 years cao
(b) Answer: 419 years
Question 21
M1 recognises the number lies in the 40s (ignoring sign), from the tens digit and the range clue
M1 narrows the units digit to 7 or 9 from the odd-and-greater-than-5 clue, giving 47 or 49
A1 uses the digit sum clue (4 + 7 = 11, not 4 + 9 = 13) to select 47
A1 -47 cao
Answer: -47
Question 22
(a) M1 MMM(3000) + CD(400) + L(50) + II(2) oe
(a) A1 3,452 cao
(a) Answer: 3,452
(b) M1 ft rounds their part (a) answer using the tens digit (5)
(b) A1 3,500 cao
(b) Answer: 3,500
(c) M1 ft their part (a) answer - 168
(c) A1 3,284 cao
(c) M1 converts 3,284 into MMM + CC + LXXX + IV oe