Revision 1: Place value, ordering, multiples and factors
Year 6 Summer 1
Compare whole numbers up to 1 million and use the < and > signs
Previous learning
Core for Year 5
Extension
Understand, read and begin to write these words:
Understand, read and write these words:
Understand, read and write these words:
order, more than, less than, ascending, descending, …
place value, most significant digit, numeral, write in figures, …
order, more than, less than, ascending, descending, …
place value, most significant digit, numeral, write in figures, …
order, more than, less than, ascending, descending, …
place value, most significant digit, numeral, write in figures, …
Compare and order four-digit numbers.
Compare and order numbers to 1 million, e.g.
Compare and order larger numbers, e.g.
Respond to questions like these, including the follow-up
question ‘How do you know?’
• Which is greater: 17 216 or 17 261?
• Which is the smallest planet? And the biggest?
Write a list of planets in order of size.
• Which is longer: 43 157 m or 43 51 m?
• Which number is larger: 7216 or 7261?
• Which is longer: 3157 m or 3517 m?
• Jo has walked 4356 metres. Ny has walked 4365 metres.
Who has walked further? How many metres further?
• Make six different four-digit numbers with these four digits:
2, 0, 5, 3. Use all four digits each time.
Write the six numbers in order, starting with the smallest.
• Write the number half way between 4000 and 4100.
How did you work it out?
• Jo has cycled 14 356 metres.
Ny has cycled 15 365 metres.
Who has cycled further? How many metres further?
Planet
• Write these numbers in ascending/descending order:
Mars
14 521
126 451
25 124
2154
15 214.
• A car costs more than £8600 but less than £9100.
Tick the prices that the car could cost.
£8569 F
£9090 F
£9130 F
£8999 F
Earth
Jupiter
Diameter
(miles)
7 926
Distance to Sun
(miles)
92 957 100
88 846
483 632 000
4 222
141 635 300
Mercury
3 032
35 983 610
Neptune
30 778
2 798 842 000
Saturn
74 898
888 188 000
Uranus
31 763
1 783 950 000
Venus
7 521
67 232 360
• Which planet is closest to the Sun? Furthest away? Write a
list of planets in order of their distance away from the Sun.
Use correctly the symbols for less than (<), greater than (>),
equals (=), e.g.
Use correctly the symbols for less than (<), greater than (>),
equals (=), e.g.
• Use = or < or >. Write the correct sign in each box.
• Write the largest whole number to make this statement true.
F
F
F
F
60 + F < 83
4×4
4×7
5×5
10 × 6
2×8
9×3
5×7
6 × 10
• Here are five digit cards.
• Here is a number sentence.
Use each card once to complete the statements below.
F + 17 > 75
Circle all the numbers below that make the number
sentence correct.
30
40
50
60
70
© 1 | Year 6 | Summer TS1 | Revision 1: Place value, ordering, multiples and factors
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Order numbers with up to two decimal places, including different numbers of places, and place them on a number line
Previous learning
Core for Year 6
Extension
Order numbers with one decimal place and place them on a
number line, e.g.
Order decimals with up to 2 places (including different
numbers of places) and place them on a number line.
Order decimals with up to 3 places (including different
numbers of places) and place them on a number line.
• Write the missing number in the box.
Know that to order decimals, digits in the same position must
be compared, working from the left, beginning with the first
non-zero digit, e.g.
Know that to order decimals, digits in the same position must
be compared, working from the left, beginning with the first
non-zero digit, e.g.
• Which number is larger, 4.15 or 4.7?
• Which number is larger, 4.615 or 4.67?
• Write in the numbers missing from the two empty boxes.
4.15 or 4.7
4.15 or 4.7
the ones digits are the same.
the tenths digit 7 in 4.7 is greater than
than the tenths digit 1 in 4.15,
so 4.7 > 4.15.
4.615 or 4.67
4.615 or 4.67
4.615 or 4.67
the ones digits are the same.
the tenths digits are the same.
the hundredths digit 7 is greater
than the digit 1, so o 4.67 > 4.615.
• Write in the missing number.
• Draw an arrow to show the position of 0.115.
• Write the number that each arrow is pointing to.
• Put a ring around the smallest number.
0.27
0.207
0.027
2.07
2.7
• Write the number that is halfway between 5.61 and 5.62.
• Circle all the numbers that are greater than 0.6.
0.5
0.8
0.23
0.09
0.67
• Write these numbers in order of size. Start with the smallest.
5.01
15.0
0.51
1.50
5.1
• Write a number that is bigger than 0.3 but smaller than 0.4.
• What number is exactly halfway between 3.1 and 3.2?
© 2 | Year 6 | Summer TS1 | Revision 1: Place value, ordering, multiples and factors
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Order a set of positive and negative integers
Previous learning
Core for Year 6
Extension
Use, read and begin to write these words:
Use, read and write these words:
Use, read and write these words:
positive number, negative number, …
plus, minus, above zero, below zero, …
positive number, negative number, integer, …
plus, minus, above zero, below zero, …
positive number, negative number, integer, …
plus, minus, above zero, below zero, …
Read a positive and negative temperature scale, e.g.
Order a set of positive and negative temperatures, e.g.
• What temperature does this thermometer show?
• Which temperature is colder: –4°C or –2°C?
• Write these temperatures in order from hottest to coldest.
92°C
37°C
–12°C
73°C
12°C
–2°C
Order positive and negative integers on a number line, e.g.
Order positive and negative integers on a number line, e.g.
Order a set of positive and negative numbers, e.g.
• Fill in the missing numbers on this part of the number line.
• Draw an arrow to point to –2.
• What number is the arrow pointing to?
Order a set of positive and negative numbers, e.g.
Order a set of positive and negative integers, e.g.
Order a set of positive and negative integers, e.g.
•
• Put these numbers in order, least first:
• Put these numbers in order, least first:
Put these shuffled cards (from –15 to 5) in order.
–2
–8
–1
–6
–37
–4
4
29
–4
–28.
Find the difference between a positive and a negative integer, and between two negative integers, in a context such as temperature or on a number line
Previous learning
Core for Year 6
Extension
Calculate a rise or fall in temperature, e.g.
Find the difference between a positive and a negative
integer, and between two negative integers, e.g.
Find the difference between a positive and a negative
integer, and between two negative integers, e.g.
• The temperature rises by 15 degrees. Mark the new
temperature reading on the thermometer.
• What is the difference between these two temperatures?
• A and B are two numbers on the number line below.
• The temperature in York is 4°C.
Rome is 7 degrees colder than York.
What is the temperature in Rome?
• What temperature is 10 degrees higher than –8°C?
• The temperature is –3°C. How much must it rise to reach 5°C?
inside
outside
–2°C
–7°C
• The temperature is –5 °C. It falls by 6 degrees.
What is the temperature now?
• The temperature is –11 °C. It rises by 2 degrees.
What is the temperature now?
• The temperature at the North Pole is –20 °C.
How much must it rise to reach –5 °C?
© 3 | Year 6 | Summer TS1 | Revision 1: Place value, ordering, multiples and factors
The difference between A and B is 140.
Write the values of A and B.
• Circle two numbers with a difference of 8.
–5
–4
–3
–2
–1
0
1
2
3
4
5
• Write two numbers with a sum of –6.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Compare two fractions such as
1
3
,
3
4
5
6
or
by changing them to fractions with the same denominator
Previous learning
Core for Year 6
Extension
Use, read and begin to write these words:
Use, read and write these words:
Use, read and write these words:
fraction, part, whole, equivalent, cancel, ….
numerator, denominator, recurring…
proper fraction, improper fraction, mixed number,…
fraction, part, whole, equivalent, cancel, ….
numerator, denominator, recurring, …
proper fraction, improper fraction, mixed number,…
fraction, equivalent, numerator, denominator, ….
proper fraction (e.g.
3
4
), improper fraction (e.g.
7
4
),
3
4
mixed number (e.g. 1 ) …
Change two fractions with different denominators to fractions
with the same denominator, e.g.
Use equivalence to order fractions, e.g. change halves,
quarters and tenths to hundredths to compare them.
• Which is larger: 0.76 or
• Which is smaller: 0.5 or
3
4
3
5
4
5
=
4×3
5×3
= 12
2
3
=
2×5
3×5
= 10
1
3
2
5
? Explain how you know.
• Which is larger,
? Explain how you know.
• Mark each of the fractions
or
? Explain how you know.
1
3
1
3
3
5
and
5
6
Use understanding of equivalence to compare and order
fractions, e.g.
• Which of these fractions is largest?
4
5
on the number line.
3
4
7
10
5
8
• Write these fractions in order of size starting with the
smallest.
• Here are four fractions.
1
8
15
Compare simple fractions by converting them to fractions with
the same denominator, e.g.
Order fractions by comparing them with one half, e.g.
3
4
15
• Write a fraction less than
Write each fraction in the correct box on the number line.
4
9
3
4
.
9
10
17
20
• Which of the fractions below are smaller than
1
10
© 4 | Year 6 | Summer TS1 | Revision 1: Place value, ordering, multiples and factors
3
5
4
9
1
2
1
100
1
?
9
1
8
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Recognise multiples of 2 to 10 up to the 10th multiple
Previous learning
Core for Year 5
Extension
Use, and read these words:
Use, read and begin to write these words:
Use, read and write these words:
times, multiply, multiplied by, product, multiple, …
divide, divided by, group, share, divides exactly by, factor,
divisor, divisible by, test of divisibility, …
double, halve, …
times, multiply, multiplied by, product, multiple, prime, …
divide, divided by, group, share, quotient, divides exactly by,
factor, divisor, divisible by, test of divisibility, …
double, halve, …
times, multiply, multiplied by, product, multiple, prime, …
divide, divided by, group, share, quotient, divides exactly by,
factor, divisor, divisible by, test of divisibility, …
double, halve, …
Recognise multiples of 2 to 10 up to the tenth multiple, e.g.
Recognise multiples of 2 to 10 up to the tenth multiple, e.g.
Recognise multiples of 2 to 10 beyond the 10th multiple, e.g.
• Chant and recognise sequences of multiples to the tenth
multiple, e.g. multiples of 6:
• Chant and recognise sequences of multiples to the tenth
multiple, e.g. multiples of 6:
• Chant and recognise sequences of multiples to at least the
tenth multiple, e.g.
6, 12, 18, 24, 30, … 60.
• Recognise that all multiples:
of 10 end in 0 and of 5 end in 0 or 5
of 2 end in 0, 2, 4, 6, 8
of 9 have a digit sum of 9
of 3 have a digit sum of 3, 6 or 9.
7, 14, 21, 28, 35, … 70, 77, 84, …
6, 12, 18, 24, 30, … 60.
• Recognise that the units digit in the sequence of multiples:
• Investigate patterns in the sums of multiples, e.g.
multiples of 5 and 6
of 10, is always 0;
of 5, alternates between 0 and 5
of 2, cycles through 2, 4, 6, 8, 0
of 4, cycles through 4, 8, 2, 6, 0
of 9, decreases by 1 each time
of 8, decreases by 2 each time
of 7, decreases by 3 each time
of 6, decreases by 4 each time.
Patterns of the
units digits
in multiples of 4
• Recognise patterns of multiples of 2 to 10 on a 100-square,
e.g.
• Investigate patterns of multiples on a multiplication square,
e.g. multiples of 4.
Multiples of 3 („)
Multiples of 4 („)
© 5 | Year 6 | Summer TS1 | Revision 1: Place value, ordering, multiples and factors
5
10
15
20
25
30
35
40
45
50
6
12
18
24
30
36
42
48
54
60
11
22 33 44
multiples of 3 and 7
55
66
77
88
99
110
30
3
6
9
12
15
18
21
24
27
7
14
21
28
35
42
49
56
63
70
10
20
30
40
50
60
70
80
90
100
Predict the sequence of the sum of multiples of 7 and 8.
• Recognise patterns in the last two digits of multiples of
100, 50 or 25.
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Find common multiples
Previous learning
Core for Year 6
Extension
Recognise multiples of 2 to 10 up to the tenth multiple, e.g.
Find common multiples, e.g.
Identify common multiples, e.g.
• Chant and recognise sequences of multiples to the tenth
multiple, e.g. multiples of 6:
• Generate the sequences of multiples of 2 (top row) and
multiples of 3 (bottom row). Scan the sequences to identify
the numbers in common (i.e. the common multiples).
• Sort the multiples of two different number on a Venn
diagram to identify their common multiples, e.g.
6, 12, 18, 24, 30, … 60.
• Recognise patterns in the digits of sequences of multiples.
2
4
6
8
10
12
14
16
18
20
3
6
9
12
15
18
21
24
27
30
This diagram shows the set of numbers from 1 to 25.
6, 12 and 18 are common multiples of 2 and 3.
• Recognise patterns of multiples on a 100-square, and that:
multiples of 4 are also multiples of 2
multiples of 6 are also multiples of 3 and of 2
multiples of 8 are also multiples of 4 and of 2
multiples of 9 are also multiples of 3
multiples of 10 are also multiples of 5 and of 2
• Find the smallest number that is a common multiple of two
numbers such as:
8 and 12
12 and 16
6 and 15
Multiples of 4 („)and multiples of 8 („)
Revise finding factors of two-digit numbers and use factors to multiply when appropriate
Previous learning
Core for Year 6
Extension
Know that factors occur in pairs, e.g.
Know that factors occur in pairs, e.g.
Find the prime factors of any two-digit number, e.g.
Know that:
Know that:
Know that, for example:
• A factor is a number that divides exactly into a bigger
number, e.g.
• Factors occur in pairs, e.g. since 12 = 3 × 4, both 3 and 4
are factors of 12. The simplest factor pair of any number is
the number itself and 1.
15 is not prime, but can be written as the product 3 × 5.
3 and 5 are prime numbers which are factors of 15.
They are called the prime factors of 15.
• If a is a factor of b, then b ÷ a is also a factor of b, e.g.
as 6 is a factor of 48, then 48 ÷ 6 = 8 is also a factor of 48.
12 is not prime, but can be written as the product of its
prime factors:
• If a number n is a multiple of, say, 2, then 2 is a factor of
the number n.
12 = 2 × 2 × 3
5 is a factor of 15
because 5 divides exactly 3 times into 15.
6 is not a factor of 15
because 6 does not divide exactly into 15.
© 6 | Year 6 | Summer TS1 | Revision 1: Place value, ordering, multiples and factors
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 6
Extension
Find factors of two-digit numbers, e.g.
Revise finding factors of two-digit numbers, e.g.
Write a number as the product of its prime factors, e.g.
• Find the factor pairs of, say, 20 by arranging 20 counters in
the shape of different rectangles:
• Find the factor pairs of 36 by arranging 36 counters in the
shape of different rectangles.
• To write 72 as the product of its prime factors, look for the
smallest prime factor of 72, which is 2.
20 × 1, 10 × 2, 5 × 4
There are no other pairs of numbers which have a product
of 20.
So the six factors of 20 are 1, 2, 4, 5, 10 and 20.
The factor pairs of 36 are:
1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6
The nine factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Divide 72 by 2
Repeat with the new number (36).
Look for the smallest prime factor of 36, which is 2.
Divide 36 by 2
• Make a ‘factor finder’.
72 ÷ 2 = 36
36 ÷ 2 = 18
Repeat. Look for the smallest prime factor of 18, which is 2.
Divide 18 by 2
18 ÷ 2 = 9
2 is not a factor of 9, so pick the next smallest prime
number (3) to see if it is a factor of 9.
Divide 9 by 3
9÷3=3
Repeat with the new number (3).
By colouring factors on a grid, show for example that
factors of 6 are also factors of 12.
Use factors to multiply when appropriate, e.g.
15 × 6 = 15 × 2 × 3
= 30 × 3
= 90
© 7 | Year 6 | Summer TS1 | Revision 1: Place value, ordering, multiples and factors
Divide 3 by 3
3÷3=1
So 72 = 2 × 2 × 2 × 3 × 3
Use factors to multiply when appropriate, e.g.
35 × 12 = 35 × 2 × 6
= 70 × 6
= 420
A few examples are adapted from the Framework for teaching mathematics from Reception to Year 6, 1999