Transcript Buckland Primary School

Buckland Primary School
Welcome to our
KS2 parent
workshop for
maths
Our Aims
*To build your understanding of how to
support your child’s maths at home.
* To understand what being ‘fluent’ in number
means.
*To give you strategies for helping your child
to derive, learn and know number facts .
Putting into context
From September 2014 teachers have been following a new National
Curriculum which has 3 main aims:
The national curriculum for mathematics aims to ensure that all pupils:
become fluent in the fundamentals of mathematics, including through
varied and frequent practice with increasingly complex problems over
time, so that pupils develop conceptual understanding and the ability to
recall and apply knowledge rapidly and accurately.
reason mathematically by following a line of enquiry, conjecturing
relationships and generalisations, and developing an argument,
justification or proof using mathematical language
can solve problems by applying their mathematics to a variety of
routine and non-routine problems with increasing sophistication,
including breaking down problems into a series of simpler steps and
persevering in seeking solutions.
Year group requirements
Reception
Year 1
Year 2
Children count reliably with
numbers from 1 to 20, place
them in order and say
which number is one more
or one less than a given
number.
Represent and use number
bonds and related
subtraction facts within 20
Recall and use addition and
subtraction facts to 20
fluently, and derive and use
related facts up to 100
Add and subtract one-digit
and two-digit numbers to
20
Using quantities and objects,
they add and subtract two
Recognise and represent ½
single-digit numbers and
of object, shape or quantity
count on or back to find
the answer.
Solve problems involving
multiplication and division
They solve problems,
including doubling, halving
and sharing.
Recall and use multiplication
and division facts for the 2,
5 and 10 multiplication
tables, including recognising
odd and even numbers.
Recognise, find, name and
write fractions ⅓, ¼, 2⁄4 and
¾ of a length, shape, set of
objects or quantity
Year 3
Year 4
Year 5
Year 6
count from 0 in
multiples of 4, 8, 50
and 100; find 10 or 100
more or less than a
given number
count in multiples of 6, 7,
9, 25 and 1000
find 1000 more or less
than a given number
count forwards or
backwards in steps of
powers of 10 for any given
number up to 1 000 000
read, write, order and
compare numbers up to
10 000 000
add and subtract
numbers mentally,
including:
a three-digit number
and ones
a three-digit number
and tens
a three-digit number
and hundreds
recall and use
multiplication and
division facts for the
3, 4 and 8
multiplication tables
add and subtract
fractions with the
same denominator
within one whole
recall multiplication and
division facts for
multiplication tables up to
12 × 12
use place value, known and
derived facts to multiply
and divide mentally,
including: multiplying by 0
and 1; dividing by 1;
multiplying together three
numbers
recognise and use factor
pairs and commutativity in
mental calculations
add and subtract fractions
with the same denominator
find the effect of dividing
a one- or two-digit number
by 10 and 100, identifying
the value of the digits in
the answer as ones, tenths
and hundredths
add and subtract numbers
mentally with increasingly large
numbers
identify multiples and
factors, including finding
all factor pairs of a
number, and common
factors of 2 numbers
multiply and divide
numbers mentally, drawing
upon known facts
multiply and divide whole
numbers and those
involving decimals by 10,
100 and 1,000
perform mental
calculations, including with
mixed operations and large
numbers
solve problems involving
addition, subtraction,
multiplication and division
identify common
factors, common
multiples and prime
numbers
24x15
How would you do this mentally?
24 × 10 and then halve this to
get 24 × 5, adding these two
results together.
record method as (24 × 10)
+ (24 × 5).
Alternatively, 24 × 5 = 120
(half of 24 × 10), then multiply
120 by 3 to get 360
4.4 × 18.6
Roughly, what answer do you expect
to get?
The
Connections
Model
Symbols
Numerals
Calculation
signs
Pictures/images
Number lines
Language
Place value cards
Processing
instructions
Hundred squares
Interpreting word
problems
Explaining their
thinking
Using mathematical ,
academic and
everyday language.
Numicon
Concrete
experiences
Drawing their own
representations
Real or physical materials
Small worlds
Money
Cubes
Counters
Fingers
Children need all
4 experiences
in order to build connections
Counting
• Counting is a child’s first experience of number and maths.
• Learning to count can support understanding of the number
system.
• It’s one tool for building up calculation strategies.
• Counting backwards is no more difficult than counting
forwards.
• Our maths lessons all begin with counting.
Help your child to use counting
in steps to solve calculations.
Recognise, Read, Write Numbers
Where can children read big numbers?
Sun’s Distance to Earth:149,600,000 km
Where can children see images of big numbers?
.
Encourage reading and writing
of big numbers. Allow them to try first.
From Counting to Calculation
Noticing numbers
What do you notice about these two numbers ?
26
65
2 tens and 3 units
16 and 10
Double 13
4 less than 30
Close to one quarter of 100
It is divisible by 2
Is 2/5 of 65
6 tens and 5 units
5 more than 60 and 5 less than 70
odd number
5 lots of 13
it is halfway between 60 and 70
it is 35 less than 100
Encourage your child to notice things about numbers.
e.g. Which number is before it /after it?
How many more would you need to have 10?
Is it greater than your age or less?
Activities that encourage children
to notice numbers
Odd One 0ut
Which number is
the odd one out ?
½ 2/4 ¾ 0.5
Why?
Same / Different
What’s the same about these numbers?
£13.1
£13.01
How are these numbers different?
Calculation Strategies
•
•
•
•
25+27=
30-16 =
120-111=
56+99=
How can what you notice about
these numbers help
you calculate the answers?
Number Fact Strategies
* Quick mental recall of key number facts are important for
helping children make connections with all 4 operations
(add/subtract, multiply/divide).
* 1:1 correspondence
* Doubles and near doubles
* Number facts to 5/10/20 and beyond
* Adjusting (+/- 9 or 11)
* Partitioning (tens and units) – using a 100 square efficiently to
jump in tens and units
* Bridging up or down to 10
* Know the inverse fact
Doubles
Connect add the same again and x2 with double
When play games suggest doubling points.
Check your child can double numbers to 20.
Halves
If I know double 4 equals 8 I also know half of 8 equals 4
Use the words: half, quarters, thirds, equal, fair
when sharing food, toys, lengths, or time.
Near Doubles
25 + 26 =
How could this
help with
5.1kg-2.6kg=
Partitioning
48+36=
Bridging up or down to 10 or 100
37+8=
37
+3
40
+5
45
320-70=
-50
250
300
-20
320
Make any number to 100
or beyond
Race to 100 game
Race to zero
Dice games
Inverse Operations
If I know 7 +3 makes 10, what is 10-7=
If you know 1 fact, there are usually 3 facts you can have for free.
Robber maths or mind the gap?
* 43 – 13 =
The number you need to
subtract is small enough to
‘pick up and take away’
74 – 69 =
The gap between the 2
numbers is smaller so it is
more efficient to find the
difference (probably by
counting on)
Multiplication
Models for multiplication
Lots of the ‘same thing’
Bead Bar
Number Line
0
6
3
9
12
Fingers
“3
”
“6
”
“9
”
“12
”
25
Represent the fact
with objects or pictures
Recognise multiplication is commutative
5 x 4 is the same as 4 x 5
Scaling Model for
multiplication
3 times
as tall
Division
Grouping and Sharing
12 divided by 3 = 4
Grouping – we know how many are in each group but not how many groups
there will be. The answer is the number of groups.
Sharing – we know how many groups there are but not how many are in
each group. The answer is the number in each group.
Use the language of division in every day life. E.g.10 cakes divided by 5 equals 2 each
10 socks sorted in pairs makes 5 pairs.
Repeated Subtraction
24 divided by 4 =
24 – 4 – 4 – 4 – 4 – 4 - 4
Bingo
Choose 5 numbers and write them down.
7
14 21 28 35
42 49 56 63 70
What helps children to
memorise facts?
• Written
• Visual
• Kinaesthetic
• Pattern
• Aural
Patterns
7+8=
Multiples of 8: what pattern is repeated?
8
16 24 32 40
48 56 64 72 80
Facts for
free
8x3=24
24÷3=8
24÷8=3
Nearby facts
3x7=21
3x9=27
4x8=32
2x8=16
Equivalent facts
12x2=24
2x12=24
4x6=24
6x4=24
1x24=24
24x1=24
Place value
30x8=240
3x80=240
30x80=2400
300x8=2400
3x800=2400
300x80=24000
30x800=24000
300x800=240000
3x8=24
Visual Learners
6 x 4 = 24
6+6+6+6=24
24 ÷ 4 =6
Visual Learners
56
7
8
Use pictures relevant to your child
to trigger memory
Make a set of triangle cards
for tricky times table facts.
Auditory Learners
https://www.youtube.com/watch?v=uvqTizEfrhU
Chant, rhyme, sing, whisper or
shout and record .
Kinaesthetic Learners
The Macarena
1. Right hand straight out in front, palm down.
2. Left hand out, palm down.
3. Turn right palm up.
4. Turn left palm up.
5. Right hand to left shoulder.
6. Left hand to right shoulder (both arms crossed over the
chest).
7. Right hand to back of your head.
8. Left hand to left of head (you should now look like you’re
doing sit-ups).
9. Right hand touches left hip.
10. Left hand crosses to the right hip.
11. Right hand to right hip.
12).Left hand to left hip.
Q &A
Thank you for coming.
Did I meet the aims?
To build your understanding of how to support your child’s
maths at home.
To understand what being ‘fluent’ in number means.
To give you strategies for helping your child to derive,
learn and know number facts .
Please take a moment to
complete our workshop
feedback form.
This will help us to improve our
provision for you in the future.
Sharon Genovesi