Download Double, twice, multiply, lots of, count on, repeated addition, pattern

MULTIPLICATION – STAGE 1
Solve problems
including doubling
Counting – Children should be able to count on in 1’s, 2’s, 5’s and 10’s. They should be familiar with rhymes,
songs and stories – for example 'One Two buckle my shoe' and 'The animals went in 2 by 2'
Count repeated groups
of the same size by
counting on and back in
1s, 2s, 5s and 10s
Lit t le Red Riding Hood had 5 st rawbe rrie s in he r b ask e t , how many would she have in 2 b ask e t s? Mr T ick le
t ick le s 3 pe ople e ach d ay, how many will he t ick le in 2/ 3/ 5 days?
Begin to use vocabulary
associated with
multiplication
Record using marks
which they can
interpret and explain
Can you make a Lego tower of 10 bricks? How many bricks will
you use if you make 3/6/10 towers?
Can you give each of your toys 2 cakes for their picnic, how many cakes are there altogether?
Counting how many hands or feet
are in a group of children.
Counting the legs or spots on a
group of mini beasts
Pair socks and count in twos.
Children will be encouraged to use real life examples of doubling eg: counting butterfly spots on wings etc.
Double, twice, multiply, lots of, count on, repeated addition,
pattern, twos, fives, tens, hundred square,
MULTIPLICATION – STAGE 2
Solve practical problems
that involve combining
groups of 2, 5 or 10.
These will include using
measures, objects and
quantities.
Counting – Children should be able to count on from zero in ones, twos, fives or tens and recognise odd and
even numbers
2’s – 2,4,6,8,10
5’s – 5,10,15,20,25,30,etc…
10’s – 10,20,30,40, etc…
Children should recognise and use the patterns of last digits, e.g. 0 and 5 when counting in fives.
Double numbers and
quantities to 20 and
recall doubles of
numbers up to 10.
How many toes altogether on four feet?
Use coins to count in 1s, 2s, 5s and 10s. Children could listen as they dropped into tin and count in 2s, 5s or
10s to total
What is double 12?
Children can use practical resources to solve initially but will then be expected to know
their doubling facts.
Double, twice, multiply, lots of, count on, repeated addition, pattern, twos, fives, tens, hundred square, lots of, groups
of, X, times, multiply, multiplied by, once, twice, three times… ten times… times as (big, long, wide… and so on), odd,
even, pattern,
MULTIPLICATION – STAGE 3
Represent repeated
addition and arrays as
multiplication; use
practical and informal
written methods and
related vocabulary to
support multiplication.
Counting – Children should be able to count in 2s, 3s, 5s and 10s (linking also to counting in 5s to telling the time to 5
minutes)
Known Facts – Children should know multiplication facts for 2, 5 and 10 times tables. Children should link the 10 times
tables to place value.
Children solve multiplication problems using the following strategies:
1. Counting aloud - Using fingers to keep track
Use symbols x and = to
record and interpret
number sentences.
2. Repeated addition
Understand that
4X 5 = can be read as 4 groups of 5 or 5+5+5+5 =
multiplication can be done
in any order.
3. Known Facts – Know multiplication facts for 2, 5 and 10 times tables.
Solve a number sentence
with a missing number
Recognise and use the
inverse (opposite)
relationship between x
and ÷
Solve problems in a
variety of problems
including using £ OR p
4.
Drawing pictures
5. Drawing arrays
4 groups of 5 or 5 groups of 4
Solving Problems
Children should be able to use the strategies above to solve:
§ Word problems eg: Timmy had four packs of sweets. Each pack has five sweets in. How many sweets does
Timmy have altogether? Sally, Tommy and Tina each have £5. How much do they have in total?
§ Missing number problems Eg: __ x 5 = 15
Double, twice, multiply, lots of, count on, repeated addition, pattern, twos, fives, tens, hundred square, lots of, groups
of, X, times, multiply, multiplied by, once, twice, three times… ten times… times as (big, long, wide… and so on), odd,
even, pattern, array, row, column, inverse, multiples
MULTIPLICATION – STAGE 4
Use known tables and
practical and informal
written methods to
multiply 2-digit numbers
Use known multiplication
facts to derive other
facts
Understand that division is
the inverse of
multiplication and vice
versa; use this to derive
and record related
multiplication number
sentences.
Counting – Children will be expected to count in 2s, 3s, 5s and 10s (linking to counting in 5s to telling the time to 5 minutes) 50s
and 100s
Known Facts Children should recall and use x facts for the 2, 3, 4, 5, 8, 10 times table
Drawing
3 x 13
3 lots of 13
Use knowledge of doubling
to connect 2, 4 and 8
tables
Partitioning (As a written method or
mentally)
Consolidating understanding of the above methods will then lead to the grid method.
x
4
Use multiplication
knowledge to solve
problems
Arrays
3 x 14
10
40
3
12
40
+12
52
Solving Problems
Children should be able to use the strategies above to solve:
§ Word problems eg: Star stickers come in packs of 12, how many stickers are in 4 packs?
§ Missing number problems Eg: 8 x __ = 32
Double, twice, multiply, lots of, repeated addition, X, times, multiply, multiplied by, groups of, multiplication, product, once, twice, three
times… ten times… odd, even, pattern, array, row, column, times as (big, long, wide… and so on),
MULTIPLICATION – STAGE 5
Multiply numbers to 1000 by
10 and then 100 (whole
number answers)
understanding the effect;
relate this to scaling up or
down.
Understand the impact of
multiplying by 0 and 1.
Multiply 3 1 digit numbers
and understand this can be
done in any order
Multiply TU by TU and TU by
HTU using a formal written
layout
Recognise and use factor
pairs (in relationship to
multiplying by multiples of 10)
and commutativity in mental
calculations
Counting – Children will be expected to count in 2s, 3s, 5s, 10s (linking to counting in 5s to telling the time to 5 minutes)
25s, 50s and 100s
Known Facts Children should know and use multiplication facts from 0x0 to 10 x 10 and derive 11 and 12
times tables from this. They should know the impact of multiplying by 0 and 1.
Solve 2 x 5 x 4 = Children to understand that this can be solved in any order.
Grid method (linking with a Grid method for TU x TU
Grid method for TU x HTU
clear visual image):
18x 47
234 x 42
400
8000
13 x 6 =
+
+ 1200
x
10
8
320
x
200
30
4
160
70
40 400 320
400
40 8000 1200 160
56
7
70
60
846
2
400
60
8
8
56
9828
1
Use factor pairs to solve
50 x 8 = (5 x 10 x 8)
Solving Problems
Solve 2 step problems
Children should be able to use the strategies above to solve:
including using the distributing
§ Word problems eg: Materials is sold in 100cm pieces. I need 50cm of material to make a curtain. I
law to multiply TU by U
need to make 4 curtains. How many pieces of material do I need to buy?
§ Missing number problems Eg: 8 x__ = 560 OR ___ x ___ = 24 What could the missing numbers
be?
Double, twice, multiply, lots of, repeated addition, X, times, multiply, multiplied by, groups of, multiplication, product,
once, twice, three times… ten times… odd, even, pattern, array, row, column, times as (big, long, wide… and so on),
MULTIPLICATION – STAGE 6
Refine and use efficient
formal written methods
to multiply numbers up to
4 digits by a 1 or 2 digit
number
Use understanding of
place value to multiply
whole numbers and
decimals by 10, 100 and
1000
Multiply and divide
numbers mentally drawing
on known facts
Multiply proper fractions
and mixed numbers by
whole numbers
Counting Children will be expected to count on from any number to 1 million in Ts, Hs, Ths, TThs, HThs
Known Facts – Children should know and use multiplication facts from 0x0 to 10 x 10 and derive 11 and 12 times tables
from this.
Grid Method for ThHTU by U
1869 X 6 =
X
1000
800
60
6
6000 4800 360 54
Grid Method for ThHTU by TU
2718 x 47
9
X
2000
700
10
8
40 80000 28000 400 320
7 14000 4900
70
56
6000
4800
360
54
11214
Mental Methods
7.7 x 100 = Mental
80000 strategy to be used
28000 drawing on known facts and
400 place value.
320
14000
4900
70
56
127746
Understand notation of square and cube numbers
5³
Solve as 5x5x 5
Understand that
Multiply proper fractions and mixed numbers by whole numbers
multiplication can be done
2x4=8
in any order
2 x 1/3 = 2/3
Recognise and understand
the notation of square
and cube numbers
Apply knowledge to
multi-step problems in a
variety of contexts
8 + 2/3 = 8 2/3
Solving Problems
Children should be able to use the strategies above to solve:
§ Word problems eg A pack of plums costs 68p. Mark bought thirteen packs of plums. How much change did he get from a
£10 note? Each panda in the zoo needs 3/5 of a bamboo plant every day. If there are 14 pandas in the zoo altogether how
many bamboo plants does the zoo need every day? How many would they need for a week?
§ Missing number problems Eg: 90 x __ = 27000
Double, twice, multiply, lots of, repeated addition, X, times, multiply, multiplied by, groups of, multiplication, product, once,
twice, three times… ten times… odd, even, pattern, array, row, column, times as (big, long, wide… and so on),
MULTIPLICATION – STAGE 7
Multiply multi digit
numbers (up to 4
digits) by a 2 digit
number using a
formal written
method
Use efficient
written methods to
multiply integers
and decimals by a
one-digit (and then
two digit) integer.
Counting Children will be expected to count on from any number to 1 million in Ts, Hs, Ths, TThs, HThs
Known Facts – Children should know and use multiplication facts from 0x0 to 10 x 10 and derive 11 and 12 times tables from
this.
Grid Method
2718 x 47
X
40
7
2000
700
10
80000
14000
28000
4900
400
70
Multiply 1 digit
numbers with 2dp
with whole numbers
Relate fractions to
multiplication
Multiply simple
pairs of proper
fractions and give
answer in the
simplest form
8
320
56
80000
28000
400
320
14000
4900
70
56
127746
Long multiplication
54
32
8 (2 x 4)
100 (2 x 50)
120 (30 x 4)
1500 (30 x 50)
1728
Leading to short multiplication
54
x 32
108
1620
1728
Relate fractions to multiplication
e.g. 6 x ½ = ½ of 6 = 6 ÷ 2
Multiplying fractions
Multiply decimals eg:4.9 x 32
using an appropriate method.
Multiply the numerators and then multiply the denominators.
Solving Problems
Children should be able to use the strategies above to solve:
§ Word Problems Eg: A box contains 36 tins of sweetcorn. Each tin weighs 475 grams. What is the total weight of the tins in the box?
Missing number problems Eg: __ x 8 = 4.8
Double, twice, multiply, lots of, repeated addition, X, times, multiply, multiplied by, groups of, multiplication, product, once, twice, three
times… ten times… odd, even, pattern, array, row, column, times as (big, long, wide… and so on),