Transcript Maths workshop for parentsx

September 2016
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Deep and sustainable
Conceptual and procedural fluency
Ability to build on knowledge
Ability to reason and make connections
Be flexible thinkers – think about things in
different ways
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Teachers reinforce an expectation that all
pupils are capable of achieving high standards
in mathematics
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Teaching is supported by carefully planned
lessons and resources to develop deep
conceptual and procedural knowledge
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The large majority of pupils progress through
the curriculum content at the same pace.
Differentiation is achieved by emphasising
deep knowledge and through individual
support and intervention
Sally
knows all her tables up to 12 x 12
When asked what is 13 x 4, she looks blank Does she have fluency and conceptual
understanding?
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The 2014 National Curriculum for maths has
been designed to raise standards in maths, with
the aim that the large majority of the pupils
will achieve mastery.
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To master mathematics children need lots of
practice of different concepts, through
relatively small, sequenced steps, which must
each be mastered before they move on to the
next stage.
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Concrete and pictorial representations of
mathematics are chosen carefully, along with
written work , to help build children’s
procedural and conceptual knowledge and
fluency.
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The focus is on the development of deep
structural knowledge and the ability to make
connections.
Making connections deepens knowledge of
concepts and procedures so that it is sustained
and helps to cut down the time needed to
master later concepts and techniques.
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High quality materials to support classroom
teaching include the use of textbooks.
Maths No Problem textbooks have been trialled
by Maths Hubs around the country with very
positive results over the last two years.
We have invested in Maths No Problem
textbooks and work books, initially in years 1,2
and 3.
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Children in years 4, 5 and 6 will also be taught
within the principles of a mastery curriculum,
although without textbooks initially. Teachers
use their subject knowledge and experience,
alongside guidance from e.g. NCETM to plan
and teach lessons precisely
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Pupils work on the same tasks and engage in
common discussions.
Precise questioning enables children to develop
fluency and think about underlying
mathematical concepts.
Differentiation occurs in the support and
intervention provided – not in the topics
taught.
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Although there is no ‘traditional’
differentiation in content taught, the
questioning and scaffolding individual pupils
receive in class as they work through problems
will differ
Higher-attainers are challenged through more
demanding problems which deepen their
knowledge of the same content
Core essentials of a lesson
1
Metacognition
2
Visualisation
3
Generalisation
4
5
Number Sense
Communication
https://www.youtube.com/watch?v=PfPc
n3SohrI
Singapore maths Dr Ban HarYeap
http://teacher.mathsnoproblem.co.uk/academy/
video-library/how-to-guides/extend-foradvanced-learners/
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Pupils’ difficulties and misconceptions are
identified through immediate assessment and
intervention – usually through individual or
small group support later the same day or
within the lesson or before the next lesson.
There are meant to be fewer ‘closing the gap’
group interventions because there should be
fewer gaps to close..
Fewer Things
 Greater Depth
 Class working together
 Longer time on topics
 Together these reflect the features of
a Mastery Curriculum for Mathematics
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Use of number bonds
and the number bond
diagram
5
3
2
Making number bonds
Lesson
1
In focus
How many cupcakes are there on each plate?
Is there another way to put the cupcakes on the two plates?
Making number bonds
Let’s Learn
1
2
5
3
This is a number bond
2 and 3 make 5
Making number bonds
Making number bonds
Making number bonds
Making number bonds
Guided Practice
5+2=7
2+5=7
7-5=2
7-2=5
7
5
2
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Try playing number games with playing cards,
dominoes and board games such as snakes and
ladders or Lotto.
Useful materials would include dice, counters e.g.
pennies or buttons, uncooked pasta or building
bricks.
When playing cards you can vary the games e.g.
taking cards from the centre – first to 20, finding
pairs, adding pairs.
Dominoes – play traditionally or try spreading them
face down - each player chooses a domino at the
same time. Add the two numbers on the domino
together. Whoever has the largest number gets to
keep both dominoes. The person with most
dominoes wins
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in 1s, 2s, 10s, 100s forwards and backwards and
starting from a different number e.g. 3,5,7,9…
11,9,7,5,3…
Counting activities are very important and
feature as part of our maths work throughout
school. T
Try looking at house numbers when you are out
walking – what do they notice about the
numbers? Can they guess which number might
come next?
Count how many steps there are between your
house and school. Count on car journeys – start
at different numbers, count forwards and
backwards. Can you start at 50 and count
on/back in 5s?
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Talking and sharing our thinking and
reasoning is very important support that we
can all give to children in their maths work, e.g.
“That’s a triangle because it’s got three sides.”
“ I know that... Because...”
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Children needs lots and lots of experience
looking at clocks and telling the time – far more
than we can devote to it at school
O’clock, then half past, then quarter past and
quarter to
How much time has gone by/ how long is it
to...
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Lots of experience in handling money is
needed:
Value of different coins
Which has the most/least value
How many pennies = 2p, 5p,10p, 20p? Etc
How much change will they get?
Use real money – play shops
Talk about the cost of items when shopping
Let children hand over money and receive
change when shopping
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Reception
Children are encouraged
to:
Find one more than a
given number
Relate addition to
combining two groups
Start to put ‘largest
number in head’ and
count on
All exploration is
encouraged through play.
Lots of counting in
different contexts takes
place
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Drop counters into a
container. Add on or take
away counters.
Use coat hangers and pegs
to model addition and
subtraction to 10
Children are encouraged to ‘decompose’ and recombine
numbers to find the answer
As children’s experience
grows of using numbers to
20 and beyond, they begin
to understand place value
in two-digit numbers. For
example, they count 17
straws, use an elastic band
to group together a bundle
of ten and identify that they
have one bundle of ten and
seven single straws.
children’s experience grows
Children learn number bonds – the numbers that
add together to make 10, 20 etc. 10 + 0 = 10, 9 +
1 =10, 8 + 2 = 10
Lesson Objective:
To be able to add a single-digit
number to a 2-digit number
without regrouping the ones.
Lesson Approach:
Use baskets or ten frames to
replicate the problem found in the
anchor task. Ask pupils to add 3
more into one of the baskets. In
which basket should we put the 3
extra apples? Discuss why it is
more useful to add the 3 apples
into the basket that has 3 apples
rather than the baskets that have
10. Show how we add 3 more by
using a number line with 25.
Explain that in this question the
only part of the number 25 that
changes is the units and not the
tens. Show how we can add 3 to 25
by using ten blocks and unit cubes
and the standard column method.
Make sure the concrete element is
simultaneously modelled with the
column method.
National Curriculum:
Add numbers using concrete
objects, pictorial representations,
and mentally, including: a twodigit number and ones.
52 +23
50 2 20
3
50 + 20 + 3 + 2 = 75
Children explore subtraction as ‘take away’,
keeping all items visible e.g. 5 ladybirds on a leaf
and two fly away.
So 7 – 3 would be ‘What is the difference between 7 and 3?’
Children begin to relate
addition to subtraction
through lots of practical
activities and visual
resources.
Multiplication
Children count in repeated groups of the same size -making use of
repeated addition in real life examples, e.g. there are four teddies in
a row; pick out the pattern in eyes 2 + 2 + 2 + 2
Use of counting games in 2s
Leading to bigger numbers in Year 1
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Lots of the ‘same thing’
Bead Bar
Number Line
3
0
Fingers
6
9
“3”
12
“6”
“9”
“12”
Children have lots of
practice doubling and
halving numbers and
relate this to the 2x table
Children use arrays (a
picture representing a
number) and repeated
addition
2x4=2+2+2+2
They then extend to different numbers and show
examples of division facts
5 x 4 = 20, 4 x 5 = 20, 20 ÷ 5 = 4, 20 ÷ 4 = 5
54
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As a staging post, an expanded method which uses a grid is used.
This links directly to the mental method. It is an alternative way of
recording the same steps.
It is better to place the number with the most digits in the lefthand column of the grid so that it is easier to add the partial
products.
38 × 7 = (30 × 7) + (8 × 7) = 210 + 56 = 266
The next step is to move the number being multiplied (38 in the example
shown) to an extra row at the top. Presenting the grid this way helps
children to set out the addition of the partial products 210 and 56.
The next step represents the method of recording in a column format, but
showing the working. We draw attention to the links with the grid method.
Children describe what they do by referring to the actual values of the digits in
the columns. For example, the first step in 38 × 7 is ‘thirty multiplied by seven’,
not ‘three times seven’.
30  8
 7
210
56
266
30  7  210
8  7  56
38
 7
210
56
266
Division
Children use real life examples of division as
sharing – sharing objects into equal groups
Children begin to use examples of division
as grouping
e.g. putting wellies into pairs, pairing socks,
putting two smarties on a cake etc.
Children begin with halving and relate this to dividing by 2.
They may also use number lines and count the number of
hops that make a number, making the links clear between
multiplication and division
Children understand division as grouping. They use
practical examples e.g. putting items into a bowl. How
many groups of 2, 3, 4 etc can I make from 12?
Count back into the bowl – one group of 3, two groups
of 3 etc.
There are 6 sweets. How many people can have 2
each?
How many groups of 2 make 6?
Mental methods for dividing TU ÷ U can be based on partitioning. This allows a
multiple of the divisor and the remaining number to be divided separately. The
results are then added to find the total quotient.
Children should also be able to find a remainder mentally, for example the
remainder when 34 is divided by 6.
One way to work out TU ÷ U mentally is to partition TU into a multiple of
the divisor plus the remaining ones, then divide each part separately.
Informal recording in Year 4 for 84 ÷ 7 might be:
In this example, using knowledge of multiples,
the 84 is partitioned into 70 plus 14 and then
each part is divided separately.
The array is an image for division too
8
7
56
Another way to record is in a grid, with links to the grid method of
multiplication.
As the mental method is recorded, ask: ‘How many sevens in seventy?’
and: ‘How many sevens in fourteen?’
Also record mental division using partitioning:
64 ÷ 4 = (40+24) ÷ 4
96 ÷ 7 = (70 + 26) ÷ 7
= (40 ÷ 4) + (24 ÷ 4)
= (70 ÷ 7) + (26 ÷ 7)
+ 10 + 6 = 16
= 10 + 3 R 5 = 13 R 5
87 ÷ 3 = (60 + 27) ÷ 3
= (60 ÷ 3) + (27 ÷ 3)
+ 20 + 9 = 29
Remainders after division can be recorded
similarly.
‘Short’ division of TU ÷ U is introduced as a more compact recording of the
mental method of partitioning.
Short division of a two-digit number is introduced to children who are confident
with multiplication and division facts and with subtracting multiples of 10
mentally, and whose understanding of partitioning and place value is sound.
For 81 ÷ 3, the dividend of 81 is split into 60, the highest multiple of 3 that is
also a multiple 10 and less than 81, to give 60 + 21. Each number is then
divided by 3.
81 ÷ 3 = (60 + 21) ÷ 3
= (60 ÷ 3) + (21 ÷ 3)
= 20 + 7
= 27
This is then shortened to:
The short division method is
recorded like this:
20  7
3 60  21
27
3 8 21