Download The children - Fawkham CE Primary School

Explaining how we
teach mathematics,
and what you can do
to help your child
become a confident
mathematician.
Welcome to
session two
Fawkham C.of E. Primary School
What are we going to talk about
this afternoon?
Multiplication and Division
•Strategies
•Calculation methods
•Vocabulary:
vital and constantly referred to through all our teaching.
•Using and applying:
using the calculation methods in situations that
have meaning.
We use a consistent, progressive approach
•KS1 –
•KS2 Produced by Mrs. S. Connor
Fawkham C of E Primary School
Focus on mental calculation strategies
Informal written method leading to 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?
There are 4 cars in the garage 4 more arrive.
How many cars are in the garage now.
The children:
understand and use one-to-one correspondence when counting.
know that the last number name spoken is the answer to questions such as
“How many objects are there?”
hold one number in their heads and count on when adding numbers.
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Understanding multiplication
Know by heart addition doubles of all numbers to at least 5.
Begin to know: addition facts for all pairs of numbers to a
total of up to at least 10
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?
Double and
What is double 10?
halve dart
What is double 4? How could we work out double 14?
board
The children:
understand that double 5 is 5 + 5 and use their knowledge of addition to find
doubles.
use their knowledge of doubles to 10 to find new doubles.
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Understanding multiplication
Understand the operation of multiplication as
repeated addition or as describing an
array.
Activities:
How could you arrange 12 counters in equal rows?
Can you record your arrangement in a number
sentence using addition?
Can you record it using multiplication?
How can you use your knowledge of number facts to find a quicker
way of working out 3 + 3 + 3 + 3 that does not involve addition?
Can you use a picture to confirm that 3 x 2 = 6?
Does 2 x 6 give the same answer as 6 x 2?
Can you draw an array of dots to show why this is true?
Explain your thinking.
The children:
Know that repeated addition such as 2 + 2 + 2 + 2 could be
represented by 2 x 4.
Are able to interpret and use images and models (e.g. sets, arrays,
jumps along a number line) to carry out simple multiplication
calculations.
Produced by Mrs. S. Connor
Can read and record number sentences.
Fawkham C of E Primary School
Arrays are a useful visual tool for
multiplication and division
I have 12 counters.
How could I arrange them into
equal rows?
Produced by Mrs. S. Connor
Fawkham C of E Primary School
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
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Can you think of any other ways
to arrange the 12 counters?
Produced by Mrs. S. Connor
Fawkham C of E Primary School
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
Produced by Mrs. S. Connor
Fawkham C of E Primary School
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
0
+5
5
10
Produced by Mrs. S. Connor
Fawkham C of E Primary School
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=5x4
(5 lots of 4 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
Produced by Mrs. S. Connor
Fawkham C of E Primary School
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.
Produced by Mrs. S. Connor
Fawkham C of E Primary 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.
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Know by heart the 2, 3, 4, 5 and 10
multiplication tables
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 25 + 25 + 25 + 25 as a multiplication calculation?
Using the numbers 2, 4, 15, 30 and 50. Work out six different multiplication
calculations.
How do you work out 4 x 30? 40 x 30?
The children:
can use their knowledge of multiplication to check calculations and solve problems
respond rapidly to oral or written questions and, where appropriate, explain the strategy
used, e.g. 7 times 4 (known off by heart); what is the product of 15 x 4 (they explain strategy)?
are able to work out e.g. the 6 times table by adding the 2 times table facts to the 4 times
table facts or doubling the 3 times table facts.
Tables
wheel
Place value
Darts
Hit the
button
Produced by Mrs. S. Connor
Fawkham C of E Primary School
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
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Know by heart all multiplication facts
up to 10 x 10
Extend written methods
Work out 47 x 5 by partitioning 47,
e.g. (40 x 5) + (7 x 5) = 200 + 35 = 235 and by the grid method.
72 x 38 = ? What is the approximate answer?
Use the grid method to work out the exact answer.
X with
arrow cards
Look at these multiplications.
43
63
64
46
x6
x4
x3
x6
Which gives the biggest answer? Can you explain why?
The children:
use pencil and paper methods to support, record or explain calculations,
achieving consistent accuracy
approximate first and explain orally how their method works
know that when calculations are set out in columns units should line up
under units, tens under tens, etc.
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Using and applying
This is when the problem appears in a story that is, or could be real.
How can we use multiplication to help us solve this word problem?
Sam had 6 packets of balloons for his party.
Each packet contained 38 balloons.
How many balloons would Sam blow up
altogether?
The first problem is to identify the sum needed.
Produced by Mrs. S. Connor
Fawkham C of E Primary School
What would the calculation look like?
6 x 38 =
What would the
approximate answer be?
We know that 38 rounds to 40
6 x 4 = 24 so……
6 x 40 = 240
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Grid
method
TU x U
6
38 x 6 = 228
30
8
180 48
180
48+
8
120
100
228
(0+ 8)
(80 + 40)
(100 + 0)
Grid
multiplication
Having worked out an approximate answer
does this answer look likely to be correct?
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Use written methods of multiplication of numbers
including decimals
What two numbers multiplied together result in the answer 370?
Give the children some worked examples that are incorrect.
Are they correct? How do you know? How could we put them right?
If we know 357 x 27 = 9639, what other multiplication and division facts
can we derive? e.g. 357 x 2.7 = 963.9
What is the approximate answer to 4.96 x 3? What is the exact answer?
Which of these calculations do you think will give the larger answer: 13.7
x 8 or 13.8 x 7? Carry out the calculation to confirm your answer.
The children:
are aware that approximating first enables checking whether the answer is
realistic.
understand that an appropriate written method should be chosen according to
the numbers involved.
are secure in using mental jottings, informal methods or standard written
methods appropriate to the problem.
Increasingly complex contexts should be used including multiplication and
division by TU and U.t
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Pupils learn to multiplyTU by TU; for example;
23 x 14 = (20 x 10) + (20 x 4) + (3 x 10) + (3 x 4)
This is set out in the grid method.
23 x 14 =
x
10
4
Produced by Mrs. S. Connor
Fawkham C of E Primary School
20
200
80
3
30
12
= 230
=
92
322
1
Then pupils will then be taught a more traditional
method.
For example:
23
x 14
12
80
30
200
322
(4 x 3)
(4 x 20)
(10 x 3)
(10 x 20)
Produced by Mrs. S. Connor
Fawkham C of E Primary School
leading to:
23
x 14
92 (4 x 23)
230 (10 x 23)
322
They will progress to
using bigger numbers
and decimals.
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
The family of sums
4 x 5 = 20
Using arrays
5 x 4 = 20
20 ÷ 4 = 5
20 ÷ 5 = 4
Produced by Mrs. S. Connor
Fawkham C of E Primary School
20 spots in groups of 5 (columns).
20 spots in groups of 4 (rows).
Learn to divide a two digit number by a
single digit, including with remainders.
We do this by ‘chunking’ Taking away chunks of the number.
78 ÷ 6
78 take away 60 (10 lots of 6)
Leaving 18 (3 lots of 6)
So we can see that
78 ÷ 6 is 13
52 ÷ 3
Take away 30
(10 lots of 3)
Leaving 22
Take away 21
(7 lots of 3)
Leaving 1 remainder
So we can see that
52 ÷ 3 is 17 r 1
Produced by Mrs. S. Connor
Fawkham C of E Primary School
12 remainder 3 or
7 86
-70
(10 x 7)
16
-14
( 2 x 7)
2
Produced by Mrs. S. Connor
Fawkham C of E Primary School
2
7
chunking
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).
6 times table is the 4 times table plus the 2 times table, or 5 times table + 6.
Multiples of the 5 times table always end in 0 or 5.
Little rhymes that help with some of the trickiest multiplication facts:
I ate and I ate till I was sick on the floor 8 times 8 is 64.
Produced by Mrs. S. Connor
Fawkham C of E Primary School
5, 6, 7, 8 56 is 7 x 8
These are some of the activities that
we carry out, trying to make learning
tables fun and keep the children
motivated.
Number
grids
Produced by Mrs. S. Connor
Fawkham C of E Primary School
Function
machines
Matching
pairs
Thank you for attending
Questions?
Please look at some of the resources
we use.
Don’t forget the next sessions
Tuesday 2:30-3:00
24th November
1st December
Produced by Mrs. S. Connor
Fawkham C of E Primary School