Transcript Calculation - Marlow Church of England Infant School

Maths Information Evening
4th February 2015
What is Maths?
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At all levels learning maths is about solving problems
using key processes such as:
Looking for patterns and relationships between
numbers.
Making sense of and checking information.
Communicating and presenting maths using words and
diagrams (symbols and graphs).
Reasoning and developing mathematical arguments.
Calculating
Comparing
Manipulating, organising and interpreting information.
Developing a child’s mathematical
understanding
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Playing and talking about games together
encourages their mathematical thinking and
supports their learning at school.
Activities that are seen as a ‘puzzle’ or
‘finding out’ about something, enhance
children’s confidence and develop their
problem solving skills.
Encourage them to play with numbers
practically and in their heads to develop
mental calculation strategies.
Developing a child’s mathematical
understanding
Practise and consolidate skills such as: mental
arithmetic, solving number sums or working out
angles. (use objects to make a physical
representation of the calculation whenever
possible… this deepens children’s understanding
making a stronger foundation for future abstract
thinking)
 Many parents will find that the way maths is
taught is different from their own experience. If
there are aspects of maths you would like to
know more about, talk to your child’s teacher.
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Maths in the Foundation Stage
Split into 2 areas of focus: ‘Number’ and ‘Shape,
Space and Measure’.
 Both are integrated into our provision on a daily
basis and taught with a themed approach
throughout the year.
 For example: shape pictures, shape hunts in our
environment, ordering numbers on a washing line,
forming numbers with chalk. There are endless
opportunities for maths to be integrated in
Foundation Stage!
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Maths in Key Stage 1
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In Year 1 Autumn term
◦ taught twice a week with provision activities
available
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Year 1 Spring and Summer term
◦ taught 5 times a week
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Year 2
◦ taught 5 times a week
Weekly problem solving session
 Taught across the curriculum where
possible
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General Number Skills
1:1 Correspondence
 Number formation
 Maths vocabulary
 Place value
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These skills are ‘the cement’ that hold the building
blocks of maths learning together and they run
through every area and level of maths learning
Place value
Have a look at the place value equipment
on the table. Can you find different ways of
representing the number 67?
Calculation
Addition - Stage 1
Counting songs/rhymes and experiencing
maths through play.
 Pictorial addition
 Using number lines.
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0
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1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Bead bars.
Can you use the bead bars to make these
numbers? 17, 14, 19, 12
Can you use pictures to show one of these
addition number sentences?
7 + 3 = 10
4 + 9 = 11
8 + 7 = 15
4+1=5
9 + 3 = 12
Swap it with a partner and work out which
number sentence they’ve drawn.
Stage 2
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Children will begin to use empty number lines.
They will use their knowledge of tens and units
to add two-digit numbers e.g. 34 + 23
+10
+10
+1 +1 +1
34
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44
54 55 56 57
Units can then be done in one jump or by
bridging the ten.
Blank Number Lines
Draw yourself a blank number line.
Can you find the answer to this number
sentence by adding the tens and units?
48 + 36 = ?
Can you add the tens and units in one
jump?
Bridging the Ten
Use a blank number line and bridge to the
nearest ten to find the answer to this
number sentence.
38 + 57 = ?
Stage 3
Children will continue to use empty number
lines with increasingly large numbers
 Count on from the largest number, irrespective
of the order of the calculation.
 Using compensation:
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+50
-1
73
49 + 73 = 122
122 123
which becomes 73+
50-1= 122
Using Compensation
Use compensation to find the answer to
this number sentence on a blank number
line.
54 + 39 = ?
Is there another way you could write the
number sentence?
Stage 3
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Children will begin to use informal pencil and paper
methods (jottings) to support, record and explain
partial mental methods building on existing mental
strategies.
Partitioning – tens and units
67 + 52
60 + 50 =
7+2=
Partitioning
Add these numbers together using
partitioning and an informal jotting method.
61 + 35 = ?
Calculation
Subtraction – Stage 1
Counting songs/rhymes and experiencing maths
through play.
 Pictorial subtraction
9–5=4
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Using a number line to ‘count back’ or ‘find the
difference’ e.g. 6-3=
-1
0
1
2
3
-1 -1
4
5
6
7
8
9
10
Pictorial Subtraction
Can you use pictures to show one of these
subtraction number sentences?
7–5=2
9–1=8
10 – 6 = 4
14 – 7 = 7
5–3=2
Stage 1
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0
Children then use number lines and
number tracks to support their own
calculations:
-1 -1 -1 -1 -1
13 – 5 = 8
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Stage 2
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Counting back in tens and ones: 47 – 23 =
-1
24
-1
25
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-1
26
-10
27
-10
37
47
Subtracting the units in one jump:
-3
24
-10
27
-10
37
47
Subtracting on a Number Line
Find the answer to this on a blank number
line.
Can you add the tens and units in one
jump?
74 – 53 = ?
Stage 2
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Subtracting the tens in one jump and the
units in one jump:
-3
24
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-20
27
47
Bridging through the ten: 42 – 25 = 17
-3
17
-2
20
-20
22
42
Bridging the Ten
Find the answer to this subtraction by
bridging to the nearest ten.
73 – 59 = ?
Stage 3
Partitioning:
This is trickier to show children when subtracting as
there will be some situations where the children need
to take away too many units.
89
–
80 – 50
57 =
9–7
30 + 2 = 32
Calculation
Multiplication – Stage 1
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Experience through play:
Can you draw a picture to show:
4 lots of 5
4x5
4 groups of 5
Stage 2
Repeated addition:
3 times 5 is 5 + 5 + 5 = 15
3 lots of 5 or 5 x 3 = 15
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+5
0
1
+5
2
+5
3
4
5
+5
6
7
or
+5
8
9 10 11
+5
12 13 14 15
Repeated Addition
Write 5 x 4 as a repeated addition number
sentence.
Can you show this on a blank number line?
Stage 2 - Commutativity
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Children should know that 3 x 5 has the
same answer as 5 x 3. This can also be
shown on the number line.
+5
0
1
+3
2
+5
3
4
+3
5
6
7
+3
+5
8
9
10
+3
11 12 13 14 15
+3
Commutativity
On a number line can you show:
2x5
And
5x2
Don’t forget to add the repeated additions
above or below your jumps!
Stage 2 - Arrays
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Children should be able to model a multiplication
calculation using an array. This knowledge will support
with the development of the grid method.
5 x 3 = 15
3 x 5 = 15
Which multiplication sums does this array
show in the columns?
In the rows?
Calculation
Division – Stage 1
Introducing division should be practical,
using equipment to demonstrate and letting
children experience sharing through play.
6 sweets shared between 2 people, how
many do they each get?
Stage 2
Grouping or repeated subtraction:
There are 6 sweets. How many people can
get 2 sweets each?
Repeated subtraction on a number line: 12 ÷ 3 = 4
-3
0
1
-3
2
3
4
-3
5
6
7
-3
8
9
10
11
12
Grouping to Divide
Use the objects in your pots.
Can you share them equally between you
and your partner?
Can you find a quarter by sharing them
between 4 people?
Stage 2
Repeated subtraction to divide using an empty number
line:
24 ÷ 4 = 6
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-4
0
-4
4
-4
8
-4
12
-4
16
-4
20
24
Can you use a blank number line to find the
answer to this?
30 ÷ 5 = ?
Calculations involving remainders:
13 ÷ 4 = 3 r 1
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-4
0
1
-4
5
-4
9
13
Find the answer to this division and show
how many remainders there are:
27 + 5 =
Problem Solving
Key skill
 Teaches children to think, reason and
communicate
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There is a problem on each table to be
solved. Work as a team and talk to each
other about how you’re going to solve the
problem.
Can you find a way of recording it?
Helping Your Child At Home
Do!
• ‘Little and often’! Counting sultanas as you eat them or stairs when
going up to a first floor flat is a much better way of rehearsing counting
than sitting over a workbook.
• Give LOTS of praise. Resist the temptation to say, ‘but’ or to point
out mistakes every time. Children need encouragement and positive
reinforcement to be confident, and a confident child makes a better
learner.
• Play games! Dice, dominoes, track games and cards all make
excellent
excuses for using and applying our number skills. And at the same time
your child is learning the important skills of losing with grace and
winning
with style!
• Remember that your focussed attention is a far more
important and pleasurable commodity for any child than
any amount of TV or video game activity. Every child
wants to be doing things one-on-one with someone they
love and trust.
Helping Your Child At Home
Don’t!
• Push a skill, especially if a child is becoming confused or is feeling
pressured. It always pays to talk to the teacher if you feel your child is not
understanding something, rather than confuse them further by teaching
them in a different way.
• Force workbooks on your child. They will do plenty of writing in
their maths books at school. At home, you have the opportunity to help
them memorise their number facts and perform mathematical calculations
in their heads.
• Stress written sums laid out as you used to do them! Nowadays
it is the development of what we call ‘numerical fluency’ that counts.
Children need to be comfortable with numbers, to understand how they
work and to be confident in doing mental calculations.
• Tell your child that you were no good at maths
at school.