Transcript Maths Meeting PowerPoint January 2016

Cardinal Road Infant
and Nursery School
Calculation Evening,
January 2016
Objectives for the
evening:
•To share how we teach maths at Cardinal
Road.
•To give an understanding of progression in
maths.
Rapid recall
Models, images &
concrete materials
Understanding
Use of ICT
The Four
Rules
Problem solving
and role play
Mental
calculations
Stories / rhymes
Efficient written
methods
Foundation Stage
• Children need to leave the Foundation Stage (the end of
Reception) with a solid understanding of numbers and their
value.
• This is the first stage in being able to calculate – if you cannot
count you cannot progress.
Foundation Stage
22-36 months (pre Nursery)
• Children begin to be aware of numbers in the environment.
• They can say a few numbers in order and experiment using
them in their everyday play.
• They are able to ‘give me one’ ‘give me two’
• Children begin to be aware that if you add another object to
a group it will become more and if you take away from a
group it will become less.
Foundation Stage
30-50 months (Nursery)
•
•
•
•
•
Children will learn number names through songs and rhymes.
They will learn to recite numbers to 10 and beyond in order.
They will recognise numbers of personal significance.
They will begin to link the abstract numeral to the quantity.
Children will have a short carpet time focusing on Maths and will be
provided with plenty of opportunity to experiment with number and
counting throughout the nursery environment during play.
Foundation Stage
40-60 months (Reception)
• Children now explicitly make the link that numbers identify how many
objects are in a set and match numeral to quantity .
• Children use their fingers, marks on paper or pictures to show
numbers.
• Children compare two groups of objects, saying when they have
more and less and the same number.
• They separate groups of three or four objects in different ways,
beginning to recognise that the total is still the same.
• Shows an interest in representing numbers.
• Realise that not only objects, but anything can be counted,
including steps, claps or jumps.
Foundation Stage
Early Learning Goal (ELG) End of Reception
Expectation
• Children count reliably with numbers from 1 to 20.
• They can count backwards and forwards from any given number
from 1-20.
• They can place them in order and say which number is one more
or one less than a given number.
• Children understand that as you move forwards the number
value increases and decreases when I move backwards
• Using quantities and objects, they add and subtract two singledigit numbers by counting on or back to find the answer.
• They solve problems, including doubling, halving and sharing.
ADDITION AND
SUBTRACTION
PROGRESSION FOR ADDITION AND
SUBTRACTION
• Counting
• One more / less
• Addition as combining two groups, then counting on
• Subtraction as take away or difference (eg how many
more is … than …?)
• Ten more/less
• Recall of addition/subtraction facts to 10, 20 and
beyond
• Understand that subtraction and addition are inverses
ADDITION
Year 1
Addition
A 2 digit and a 1 digit number
10 + 3 =
I buy 10 cakes and my friend buys 3 cakes.
How many cakes did we buy altogether?
An understanding of place Value
25
47
So that in Year 2……
8
Year 2
Addition by partitioning
74 + 48
70 + 40 = 110
4 + 8 = 12
122
Addition by partitioning
374 + 248
300 + 200 = 500
70 + 40 = 110
4 + 8 = 12
622
300 + 70 + 4
200 + 40 + 8
500 + 110 + 12
COLUMN ADDITION
374
+ 248
622
1 1
Extended to:
1247 + 367
£2.36 + £6.48
3.5 + 4.8
7.48 + 2.6
12.5 km + 6.08 km
MORE
TRADITIONAL
METHODS
ARE STILL
USED!
SUBTRACTION
Earlier work involves taking away objects
from groups, counting back on a number
line or using number beads.
Counting on fingers etc
Year 1 (2 digit and 1 digit number)
Taking away – jumps of 1
(modelled using bead strings)
13 – 5 = 8
-1
8
-1
9
-1
10
-1
11
-1
12
13
Year 2
Number lines - taking away
74 – 26 = 48
− 20
−4
−2
48
50
54
74
MULTIPLICATION
AND DIVISION
Progression for multiplication and division
• Counting
• Doubling and halving
context
• Multiplication as repeated addition and describing an
array
• Division as grouping and sharing
• Understand that multiplication and division are
inverses (Year 2)
• Recall of multiplication and division facts
• Multiply two / three-digit numbers by 10 / 100
COUNTING IN CONTEXT
How many 10p coins are here?
How much money is that?
How many toes are there on 2 feet?
How many gloves in 3 pairs?
If Sarah counts in 2s and Nigel counts in 5s, when
will they reach the same number?
How many lengths of 10m can you cut from 80m of
rope?
DOUBLING AND HALVING IN CONTEXT
There are 8 raisins. Take half of them.
How many have you taken?
One snake is 20cm long.
Another snake is double that length.
How long is the longer snake?
I double a number and then double the
answer.
I now have the number 32.
What number did I start with?
2 x 3 or 3 x 2
Multiplication
3 plates, 2 cakes on each plate
pictures
(Children could draw a picture to help them work out the answer)
2 x 3 or 3 x 2
3 plates, 2 cakes on each plate
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Number tracks and number lines
(modelled using bead strings)
2 x 3 or 3 x 2
[two, three times] or [three groups of two]
Arrays
5 x 3 or 3 x 5
14 x 2 = 28
x
2
10
20
4
8
Array creator
Arrays then can lead into what we
call grid multiplication- partitioning
numbers for multiplication
43 x 6
X
6
40
240
3
18
40 x 6 = 240
3 x 6 = 18
43
x 6
258
1
DIVISION
6÷2
Division
6 cakes shared between 2
pictures
6 cakes put into groups of 2
(Children could draw a picture to help them work out the answer)
6÷2
6 cakes shared between 2
6 cakes put into groups of 2
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Number tracks and number lines - grouping
(modelled using bead strings)
8÷2=4
6÷2=3
0
2
4
6
Number lines / Arrays
15 ÷ 5 = 3
0
5
10
15
Sharing equally
8 sweets are shared between 2 people.
How many do they each receive?
GROUPING OR REPEATED
SUBTRACTIONASKING IN A DIFFERENT WAY!
There are 8 sweets. How many
people can have two sweets each?
As children progress in division, they will
continue to use:
repeated subtraction using a number line. They
may use an empty number line or a hand drawn
jumping line.
e.g. 24 ÷ 4 = 6 - children will start at 0 and
jump forwards in 4’s to find how many 4’s go
into 24 or they may do a multiplication
(repeated addition from earlier)
Children will also move onto remainders
e.g. 13 ÷ 4 = 3 r 1
24 ÷ 4 = 6
0
4
8
12
16
20
24
Useful websites
and resources
• Transum http://www.transum.org/Software/ - provides a
mathematics challenge for every day of the year!
• Nrich http://nrich.maths.org/public/ - thousands of FREE
mathematics enrichment materials for ages 5 to 19 years. The resources
are designed to develop problem-solving and mathematical thinking
skills.
• Woodlands http://resources.woodlands-junior.kent.sch.uk/maths/
- interactive maths games and activities for both KS1 and 2
• I Love Maths Games – games, puzzles and investigations
http://www.ilovemathsgames.com/
• Professor Kageyama’s maths training for DS consoles
Maths for mums and dads – Rob Eastaway
Rob Eastaway has been Director of Maths Inspiration since it began in 2004.
He is an author whose books on everyday maths include the bestselling Why Do
Buses Come In Threes? and The Hidden Maths of Sport. He appears regularly
on BBC Radio 4 and 5 Live to talk about the maths of everyday life and has
given maths talks across the world to audiences of all ages
http://www.bbc.co.uk/news/11260872