Transcript Document

Explaining how we
teach mathematics,
and what you can do
to help your child
become a confident
mathematician.
Welcome to multiplication
and division
Fawkham C.of E. Primary School
Multiplication and Division
•Calculation methods
•Using and applying:
using the calculation methods in situations that have meaning.
•Vocabulary:
vital and constantly referred to through all our teaching.
We use a consistent, progressive approach
•KS1 –
•KS2 -
Focus on mental calculation strategies
Mental calculation strategies and a
standard written method
Starting to understand multiplication:
Begin to relate addition to combining 2 groups of objects,
counting all the objects.
Activities:
Count out 3 cakes. Now count out 3 more cakes.
How many cakes are there altogether?
Know how to use the
relevant vocabulary:
There are 4 cars in the garage 4 more arrive.
How many cars are in the garage now.
Understanding multiplication
Double and
halve dart
board
Know by heart addition doubles of all numbers
to at least 10 then to 20.
Activities:
There are 6 counters in the red cup and 6 counters in the
blue cup.
How many counters are there altogether?
Can you record this to show me what you did?
What is double 4?
Which two numbers would make a total of 8, 12, 14?
What is double 10?
What is double 4? How could we work out double 14?
Understanding multiplication
Understand the operation of multiplication as
repeated addition or as describing an
array.
Arrays are a useful visual tool for
multiplication and division
I have 12 counters.
How could I arrange them into
equal rows?
What number
sentences
could you write
to go with this
array?
6 + 6 = 12
2 + 2 + 2 + 2 + 2 + 2 = 12
2 x 6 = 12
6 x 2 = 12
We can also say that
12 ÷ 6 = 2 and 12 ÷ 2 = 6
Can you think of any other ways
to arrange the 12 counters?
What number
sentences could
you write to go with
this array?
4 + 4 + 4 = 12
3 + 3 + 3 + 3 = 12
3 x 4 = 12
4 x 3 = 12
We can also say that
12 ÷ 4 = 3 and 12 ÷ 3 = 4
Multiplication using jumps along a number line
(repeated addition).
2x5
means jumps of 2 made 5 times
+2
0
+2
2
+2
4
+2
6
+2
8
10
or 2 jumps of 5 (5 x 2)
+5
0
+5
5
10
Multiplication facts are absolutely vital for
progress with maths.
The children need to know them thoroughly, so that
they can use the knowledge not just in multiplication
problems, but also in division, fractions,
percentages, ratio etc.
It is important that they learn
division alongside multiplication.
Multiplication can be seen as repeated addition
4+4+4+4+4=4x5
(make 20)
Division can be seen as repeated subtraction.
20 – 4 – 4 – 4 – 4 – 4 = 0
(How many 4s have we taken away?) so 20 ÷ 4 = 5
Times table awards
By the time the children come into year 3 they should already be
confident with the 2, 5 and 10 times tables.
To help motivate the children to learn their times tables
in class 2 we have times table awards.
For being able to recite the times table they earn a bronze
sticker.
For being able to answer random questions from the times table
they earn a silver sticker.
For being able to answer division questions, word problems,
fraction questions using that times table they earn a certificate
with a gold sticker that is presented in front of the school.
Speed races
By the time the children leave year 2 they should know their number bonds
(as listed last week), doubles etc.
In Class 2 we revise these, then move onto ensuring that they can recall
mixed up times tables with the added pressure of time.
They answer 50 questions in 3 minutes, if they get them all right they
move onto the next list next time. If they get less than 48 correct they
get the same list again next time.
They are rewarded with merit marks when they improve their best score.
Know by heart the multiplication tables
then use these facts to derive new facts
Two numbers multiplied together make 20. What
could the two numbers be?
A baker puts 5 buns in each of 10 rows. How many
buns are there?
How would you write 5 + 5 + 5 + 5
as a multiplication calculation?
Using the numbers 2, 4, 15, 30 and 60. Work out six
different multiplication calculations.
Do you know 4 x 3?
Can you work out 4 x 30? 40 x 30?
Tables
wheel
Hit the
button
10
Multiplying and dividing by
10 and 100
We learn how to move the digits.
The bully 10 or 100 pushes the digits over.
Multiply by 10 move the digits one place to the left
Multiply by 100 move the digits two places to the
left
Divide by 10 move the digits one place to the right
Divide by 100 move the digits two places to the
right.
Moving the digits
over demonstration
Written multiplication method
Division goes alongside multiplication
Division as sharing
To start with the children learn to share objects into equal groups
Then write the number sentence; 6 shared between 2 is 3 each, 6 ÷ 2 = 3
We use visual images, record jottings and use number sentences for division.
Division as grouping or chunking (repeated subtraction)
Using a number line
20 ÷ 5 = 4
0
5
10
15
20 divided into groups
of 5 equals 4
20
Division on a
number line
Or this one
The family of sums
4 x 5 = 20
Using arrays
5 x 4 = 20
20 ÷ 4 = 5
20 ÷ 5 = 4
20 spots in groups of 5 (columns).
20 spots in groups of 4 (rows).
Division methods with remainders.
The children need to know
when to round the remainder
up or down,
e.g.
How many boxes do we need?
How many boxes will we fill?
Useful tricks:
Knowing that the two times table is also the doubles number bonds that they
should already know (all answers are even numbers).
4 times table is double the two times table (all answers are even numbers).
8 times table is double the four times table (if they can double two digit
numbers quickly in their head this is a useful skill) (all answers are even
numbers).
6 times table is double the 3 times table (all answers are even numbers).
2 x 6 = 12, 4 x 6 = 24, 6 x 6 = 36, 8 x 6 = 48 (this only works for the even multiples)
Multiples of the 5 times table always end in 0 or 5.
Little rhymes that help with some of the trickiest multiplication facts:
5, 6, 7, 8
56 is 7 x 8
I ate and I ate till I was sick on the floor 8 times 8 is 64.
These are some of the activities that
we carry out, trying to make learning
tables fun and keep the children
motivated.
Number
grids
Function
machines
Matching
pairs
8 x table
+10
-2
+8
When the children can add 10 quite quickly in their
head and can take away 2 they can work out their 8
times table.
Add 10 and take away 2 to work out the answers to the
8 times tables.
9 x table
Digit sums
0
9 0+9=9
18 1 + 8 = 9
27 2 + 7 = 9
36 3 + 6 = 9
45 4 + 5 = 9
54 5 + 4 = 9
63 6 + 3 = 9
72 7 + 2 = 9
81 8 + 1 = 9
90 9 + 0 = 9
0x9= 0
1x9= 9
2 x 9 = 18
3 x 9 = 27
4 x 9 = 36
5 x 9 = 45
6 x 9 = 54
7 x 9 = 64
8 x 9 = 72
9 x 9 = 81
10 x 9 = 90
Finger trick
Thank you for reading this.
We hope you find it useful.
Wizard
number
What is the
Number?