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Transcript
Multiplication and division facts: tables for 2, 3, 5 and 10
Year 3 Autumn 10
Count on in 2s, 3s, 5s, and 10s, look at patterns and investigate general statements
Previous learning
Core for Year 3
Extension
Understand and begin to read these words:
Understand and read these words:
Understand, read and begin to write these words:
odd, even, pattern, continue, next, every other, rule, …
odd, even, sequence, pattern, predict, continue, next, rule, …
property, …
odd, even, sequence, pattern, predict, continue, next, rule,
relationship, … sort, classify, property, …
Count in 2s and identify odd and even numbers
Count in 2s and identify odd and even numbers
• Count from 0 in steps of two to 30 or more. Count back
again. Recognise that the numbers are even numbers.
• Count from 0 in steps of two to 100. Count back again.
Recognise that the numbers are even numbers.
Identify properties of odd and even numbers and make
general statements, e.g.
• Count from 1 in steps of two to 30 or more. Count back
again. Recognise that the numbers are odd numbers.
• Count from 1 in steps of two to 99. Count back again.
Recognise that the numbers are odd numbers.
Respond to questions such as:
Respond to questions such as:
• Is 18 odd or even? How do you know?
• Is 74 odd or even? How do you know? What about 83?
• Ring the even numbers in this list:
• Ring the odd numbers in this list:
5
8
18
21
29
70
77
88
26, 24, 22, 20...
• What odd number comes after 13? After 7?
• What even number comes after 18? Before 30?
35, 37, 39, 41...
• The rule for the sequence of odd numbers is:
‘Start at 1, and keep adding 2.’
• The last digit of an even number is 0, 2, 4, 6 or 8.
• The last digit of an odd number is 1, 3, 5, 7 or 9.
91
94
• The numbers on both sides of an odd number are even.
• If you add two odd numbers, the answer is even.
• Continue these sequences:
• Continue these sequences:
13, 15, 17, 19...
65
34
• The rule for the sequence of even numbers is:
‘Start at 0, and keep adding 2.’
68, 66, 64...
Describe the rule for each sequence.
• If you add two even numbers, the answer is even.
• If you add one odd and one even number, the answer is
odd.
• What is the next odd number after 89? Before 61?
• What is the next even numbers after 48? Before 80?
Count on and back in steps of 5 or 10.
Count on and back in steps of 5 or 10.
Count on and back, including in 9s, e.g.
Using a number line, bead bar or 100-square as support:
Using a number line or 100-square as support:
• Count from 0 in steps of 5 and 10 to 100.
Count back again.
• Count from 0 in steps of 5 and 10 to 100.
Count back again.
• Count on from 0 in steps of 9 to 90. Count back again to 0.
What is the pattern in the digits?
• Describe the pattern in the digits of each sequence.
• Count on from any single-digit number in steps of 5 and 10
to beyond 100. Discuss the patterns in the digits.
• What is the multiple of 9 before 27? After 54?
How can you work it out?
• Describe the pattern in the digits of each sequence.
• Look at these numbers. Count along the line.
Which numbers are missing?
0, 5, 10, 15, 20, ...
90, 80, 70,60, …
What are the next three numbers in each sequence?
2, 7, 12, 17, ...
78, 76, 74, 72, …
What is the rule for each sequence?
What are the next three numbers in each sequence?
© 1 | Year 3 | Autumn TS10 | Multiplication and division facts: tables for 2, 3, 5 and 10
• What is an easy way to add 9? (e.g. add 10, subtract 1)
9
18
…
36
…
54
…
72
…
90
• What are the next three numbers: 38, 47, 56, 65…
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 3
Extension
Count on and back in steps of 2.
Count on and back in steps of 3.
Count on and back in steps of 4.
• Count on from 0 in steps of 2 to 30.
Count back again to 0.
• Count on from 0 in steps of 3 to 30.
Count back again to 0.
• Count on from 0 in steps of 4 to 40.
Count back again to 0.
• Look at these numbers. Count along the line.
Which numbers are missing?
• Look at these numbers. Count along the line.
Which numbers are missing?
• Look at these numbers. Count along the line.
Which numbers are missing?
2
4
…
…
10
…
14
…
…
20
3
6
…
…
15
…
21
…
…
30
4
8
…
16
…
24
…
32
…
40
3
5
…
…
11
…
15
…
…
21
4
7
…
…
16
…
22
…
…
31
5
9
…
17
…
25
…
33
…
41
5
8
…
…
17
…
23
…
…
32
6
10
…
18
…
26
…
34
…
42
7
11
…
19
…
27
…
35
…
43
• What is the even number before 18? After 12?
How can you work it out?
• What is the multiple of 3 before 30? After 21?
How can you work it out?
• What is the multiple of 4 before 40? After 24?
How can you work it out?
• Ring the numbers which are multiples of 3:
• Ring the numbers which are multiples of 4:
14
24
12
20
14
27
• What do you notice when you count from zero in:
tens
10
20
30
40
fives
5
10
15
20
• What do you notice when you count from zero in:
twos
2
4
6
8
threes
3
6
9
12
(2s are double 1s; 3s are 1s plus 2s)
© 2 | Year 3 | Autumn TS10 | Multiplication and division facts: tables for 2, 3, 5 and 10
32
12
26
18
28
• What do you notice when you count from zero in:
twos
2
4
6
8
(10s are double 5s)
ones
1
2
3
4
14
fours
4
8
12
16
eights
8
16
24
32
(4s are double 2s; 8s are double 4s)
• What do you notice when you count from zero in:
threes
3
6
9
12
sixes
6
12
18
24
nines
9
18
27
36
(6s are double 3s; 9s are 3s plus 6s)
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Recognise multiples of 2, 5 and 10
Previous learning
Core for Year 3
Extension
Understand and use these words
Understand and read these words:
Use, read and write these words:
multiple, property, …
multiple, divides by, property, …
multiple, divides exactly by, divisible by, property, …
Recognise multiples of 5 and 10, e.g.
Recognise multiples of 2, 5 and 10, e.g.
Recognise multiples of 2, 3, 4, 5 and 10 to at least the tenth
multiple.
• Count on in steps of 5 and 10 highlighting numbers on a
number line or square. Describe the patterns in the digits.
• Use ICT to highlight multiples of 2, 5 and 10 on a 100square. Describe the patterns made.
• Use ICT to highlight multiples on a number grid.
• Recognise that all multiples of:
• Recognise that all multiples:
– 10 end in 0;
– of 10 end in 0;
– 5 end in 0 or 5.
– of 5 end in 0 or 5;
Begin to recognise that multiples of:
– of 2 end in 0, 2, 4, 6, 8;
– of 2 end in 0, 2, 4, 6, 8.
– of 100 end in 00.
– Use different sizes of grid to explore multiples of 3.
– Describe and explain which grids produce ‘diagonal’
patterns, and which produce ‘vertical’ patterns.
– Try multiples of 4.
• Count in 50s to 1000 and in 25s to 500, then back.
Write three different multiples of 50. Of 25.
How can you recognise multiples of 50? Of 25?
• Begin to identify two-digit multiples of 10, 5 or 2, e.g.
that 65 is a multiple of 5, or that 32 is a multiple of 2.
• Recognise that all multiples:
– of 1000 end in 000;
– of 50 end in 00 or 50;
– of 6 include the multiples of 2 and the multiples of 3.
Respond to questions such as:
Respond to questions such as:
Respond to questions such as:
• Ring the numbers which are multiples of 10:
• What is the multiple of 5 before 45? After 65?
How can you work it out?
• What is the multiple of 4 before 36? After 28?
How can you work it out?
• Ring the numbers which are multiples of 5:
• Ring the numbers that are multiples of 4.
70
45
12
80
10
27
15
35
52
55
• What is the:
multiple of 10 before 140?
multiple of 100 after 500?
the next multiple of 5 after 195?
© 3 | Year 3 | Autumn TS10 | Multiplication and division facts: tables for 2, 3, 5 and 10
59
95
3
8
20
27
34
36
48
50
• Which of the numbers above are multiples of both 5 and 2?
• Sean counts his books in fours. He has 1 left over.
He counts his books in fives. He has 3 left over.
How many books has Sean?
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Understand the relationship between multiplication and division and write the division fact to go with a multiplication fact
Previous learning
Core for Year 3
Extension
Understand and use these words
Understand and read these words:
Use, read and write these words:
lots of, groups of, times, multiply, … share equally, divide,
divided by, equal groups of, left over, remainder, …
groups of, times, multiply, multiplied by, product, … share
equally, divide, divided by, equal groups of, remainder, …
groups of, times, multiply, multiplied by, product, … share
equally, divide, divided by, equal groups of, remainder, …
and understand and use the × and ÷ signs.
and read and write the × and ÷ signs.
and read and write the × and ÷ signs.
Understand multiplication as repeated addition, e.g.
Understand multiplication as repeated addition or as
describing an array, and that:
Understand multiplication as repeated addition, describing an
array or as scaling (e.g. finding a number 5 times as big).
3 + 3 + 3 + 3 + 3 = 5 lots of 3
5 × 3 means 5 multiplied by 3 (3 lots of 5)
5×3=5+5+5
+3
0
+3
3
+3
6
+3
9
3 × 5 means 3 multiplied by 5 (5 lots of 3)
3×5=3+3+3+3+3
+3
12
15
3 units
scaled by a factor of 5
15 units
and similarly
3×5
5 + 5 + 5 = 3 lots of 5
Know from arrays and hops along a number line that:
5 lots of 3 = 3 lots of 5
or
5 times 3 = 3 times 5
zzzzz
zzzzz
zzzzz
5×3
Know that multiplication is commutative so:
5 multiplied by 3 = 3 multiplied by 5
zzzzz
zzzzz
zzzzz
or
5×3=3×5
Interpret 5 × 3 or 3 × 5 as 3 fives or 5 threes.
Understand division as:
Understand division as:
• grouping, or repeated subtraction: e.g. Tom has 6 apples.
How many packs of 2 apples can he make?
• grouping, or repeated subtraction, interpreting, for
example, 35 ÷ 5 as ‘How many 5s make 35?’
• A box holds 4 cakes.
How many boxes do I need to hold 23 cakes?
• sharing equally.
sharing equally: e.g. 6 sweets are shared equally between
2 people. How many sweets does each person get?
Understand that division can leave a remainder, and that the
answer to a division may be rounded up or down, depending
on the context, e.g.
Know that division cannot be done in any order so 35 ÷ 5
does not equal 5 ÷ 35.
• 5 kg of potatoes fill a bag.
How many bags can I fill with 17 kg of potatoes?
Understand the relationship between multiplication and
division, e.g.
Understand the inverse relationship between multiplication
and division.
Know that if 5 threes or 3 fives are 15, then the answer to the
question ‘How many 3s make 15?’, or 15 ÷ 3, is 5.
Say or write a division statement corresponding to a given
multiplication statement and vice versa, e.g.
Interpret 6 ÷ 2 as ‘How many 2s make 6?’
© 4 | Year 3 | Autumn TS10 | Multiplication and division facts: tables for 2, 3, 5 and 10
5 × 3 = 15 means that 15 ÷ 3 = 5
• If 3 × 10 = 30, what is 10 × 3, or 30 ÷ 3, or 30 ÷ 10?
3 × 5 = 15 means that 15 ÷ 5 = 3
• If 20 ÷ 5 = 4, what is 20 ÷ 4, or 5 × 4, or 4 × 5?
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Know by heart multiplication facts for the 2, 3, 5 and 10 times tables and begin to learn corresponding division facts
Previous learning
Core for Year 3
Extension
Build up and begin to learn facts for 2 times table.
Know by heart multiplication facts for 2, 5 and 10 times
tables.
Revise multiplication facts for 2, 3, 4, 5 and 10 times tables.
Recite tables for 2, 5 and 10 and use strategies to remember
them, e.g.
Recite tables for 2, 3, 4, 5 and 10 and use strategies to
remember tables facts learned in previous years (see Core
for Year 3), and:
• Recognise that 5s are half 10s, so if 7 tens are 70, then 7
fives are half of 70, or 35.
• Recognise that 4s are double 2s, so as 7 twos are 14,
7 fours are double 14 or 28.
• Recognise that multiples of 5 alternate between ending in 5
and ending in 0.
• Recognise that 3s are 2s plus 1s, so 6 threes are 6 twos
plus 6 ones, or 12 + 6 = 18.
• Recognise that multiples of 10 end in 0.
• Recognise that the digit sum of multiples of 3 is 3, 6 or 9.
Build up and begin to learn facts for 10 times table.
Learn facts for 3 times table
Learn facts for 9 times table
• Count on from 0 in steps of 10 to 100. Count back to 0.
• Build up and recite the table of 3s, e.g.
• Build up and recite the table of 9s, e.g.
• Count on from 0 in steps of 2 to 20. Count back again to 0.
• What is the multiple of 2 before 18? After 12?
How can you work it out?
• Look at these numbers. Count along the line.
Which numbers are missing?
2
4
…
8
…
…
12
16
…
20
• Build up and recite the table of 2s, e.g.
zz
zz
zz
1 two is 2
2 twos are 4
3 twos are 6, etc
NOT
1 times 2 is 2
2 times 2 is 4
3 times 2 is 6, etc
• Recognise the relationship between counting in 2s,
doubles of numbers 1 to 10, and even numbers to 20.
• What is the multiple of 10 before 70? After 40?
How can you work it out?
• Look at these numbers. Count along the line.
Which numbers are missing?
10
20
…
40
…
60
…
80
…
100
• Build up and recite the table of 10s, e.g.
zzzzzzzzzz
zzzzzzzzzz
zzzzzzzzzz
1 ten is 10
2 tens are 20
3 tens are 30, etc.
zzz
zzz
zzz
1 three is 3
2 threes are 6
3 threes are 9, etc
NOT
1 times 3 is 3
2 times 3 is 6
3 times 3 is 9, etc
• Recognise that 3s are 2s plus 1s, so 6 threes are 6 twos
plus 6 ones, or 12 + 6 = 18.
• Recognise that the digit sum of multiples of 3 is 3, 6 or 9.
• What is the multiple of 3 before 18? After 24?
How can you work it out?
• Recognise the relationship between the 10 times table and
counting in 10s.
• Recognise that numbers in the 10 times table end in 0.
zzzzzzzzz
zzzzzzzzz
zzzzzzzzz
1 nine is 9
2 nines are 18
3 nines are 27, etc.
• What is an easy way to add 9? (e.g. add 10, subtract 1)
• What do you notice when you count from zero in:
tens
10
20
30
40
ones
1
2
3
4
nines
9
18
27
36
(9s are 10s minus 1s)
• What are 5 nines? (5 tens minus 5 ones or 50 – 5 = 45)
• What do you notice about the pattern of the digits when
you count in 9s? What about the sum of the digits?
• Use the commutative law, e.g. if 9 twos are 18 then
2 nines are 18.
© 5 | Year 3 | Autumn TS10 | Multiplication and division facts: tables for 2, 3, 5 and 10
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999
Previous learning
Core for Year 3
Extension
Build up division facts for the 2 and 10 times tables,
interpreting 12 ÷ 2 and 70 ÷ 10 as
Build up division facts for the 3 times table, interpreting
15 ÷ 3 as
Learn division facts for the 9 times table, interpreting
72 ÷ 9 as
‘How many twos make 12?’, ‘How many tens make 70?’
‘How many nines make 72?’,
‘How many threes make 15?’,
which corresponds to the table statement 5 threes are 15,
so 15 ÷ 3 = 5.
which corresponds to the table statement 8 nines are 72,
so 72 ÷ 9 = 8.
Know that multiplying or dividing any number by 1 leaves the
number unchanged, e.g. 12 × 1 = 12, 12 ÷ 1 = 12.
Know that multiplying any number by 0 gives 0, and that
dividing by 0 is impossible.
Respond quickly to varied questions, such as:
Respond quickly to varied questions, such as:
Respond quickly to varied questions, such as:
• 8 lots of 2… 2 lots of 10…
8 twos… 2 tens… 8 times 2… 2 times 10…
How many twos make 16? How many tens make 90?
16 divided by 2. 8 multiplied by 2.
50 divided by 5. 5 multiplied by 10.
• 3 fives… 5 threes… 3 times 5… 5 times 3…
Multiply 3 by 5… Multiply 5 by 3…
5 multiplied by 3… 3 multiplied by 5…
How many threes make 15?
15 divided by 3… Divide 15 by 3.
• 3 nines… 9 threes… 3 times 9… 9 times 3…
Multiply 3 by 9… Multiply 9 by 3…
9 multiplied by 3… 3 multiplied by 9…
How many nines make 54?…
63 divided by 9… Divide 63 by 9.
• What is the total cost of 8 comics at £2 each?
• 3 friends share £15 equally. How much does each get?
• 9 friends share £81 equally. How much does each get?
• 10 friends share 60p equally. How much does each get?
• Is 15 a multiple of 3? How do you know?
• Is 36 a multiple of 9? How do you know?
• How many lengths of 2 cm can you cut from 16 cm of tape?
• How many 3 litre jugs can you fill with 15 litres of milk?
• How sets of 9 counters can you make from 45 counters?
which correspond to the table statements 6 twos are 12,
so 12 ÷ 2 = 6, and 7 tens are 70, so 70 ÷ 10 = 7.
© 6 | Year 3 | Autumn TS10 | Multiplication and division facts: tables for 2, 3, 5 and 10
Examples adapted from the Framework for teaching mathematics from Reception to Year 6, 1999