Transcript Calculation in Key Stage 1 - Marlow C of E Infant School

Maths Information Evening
14th May 2014
What is progress in 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.
How do I know my child is
progressing?
Remember that all children progress at
different rates.
 Age-related bands in Foundation Stage –
children to come out as ‘Expected’ ELG in all
areas. (Number & Shape, Space and Measure)
 We then expect children to make 2 full levels
of progress across KS1 – children to come out
as Level 2.
 Each level is split into 3 sub-levels – a, b and c.
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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 the Foundation Stage
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Number - By the end of the year children are
expected to be able to:
- Count reliably from 1 – 20
- Order numbers to 20 and say what is one
more and one less.
- Using objects, add/subtract 2 single digit
numbers.
- Count on and back to find the answer.
- Solve problems, including doubling, halving and
sharing.
Maths in the Foundation Stage
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Shape, Space and Measure - By the end of the
year, children are expected to be able to:
Use everyday language to talk about size,
weight, capacity, position, distance, time and
money.
Compare quantities and objects to solve
problems.
Recognise, create and describe patterns.
Explore shapes and use mathematical language
to describe them.
General Number Skills
1:1 Correspondence
 Number formation
 Place value
 Maths vocabulary
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Calculation in Key Stage 1
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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Bead bars.
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
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.
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
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.
67
+ 24
80 (60 + 20)
11 (7 + 4)
91
267
+ 85
200
140 (60 + 80)
12 (7 + 5)
352
67 + 52
60 + 50 =
7+2=
Your Turn!
Have a look at this sum:
8 + 4 = 12
Find the picture representation of this on your table.
It should look like this:
+
= 12
Use the number line to work out this sum.
Count on in ones from the biggest number.
13 + 5 = ?
Can you use the beads to show the same
sum?
Now draw yourself a blank number line to add
two 2 digit numbers together:
38 + 45 = ?
Can you make it quicker by bridging the ten?
Calculation in Key Stage 1
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
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
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
Stage 2
If the numbers involved in the calculation are close
together or near to multiples of 10, 100 etc, it can be
more efficient to count on.
The number line should still show 0 so children can
cross out the section from 0 to the smallest number.
They then associate this method with ‘taking away’.
82 – 47 =
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- 1 -1 -1 -10
0
82-47 =35
47 48 49 50
-10
60
-10 -1 -1
70
80 81 82
Stage 3
Partitioning and Decomposing:
89 =
- 57
89
80 + 9
- 50 + 7
30 + 2 = 32
–
80 – 50
57 =
9–7
30 + 2 = 32
Your Turn!
Have a look at the subtraction picture sums.
Which one represents this number sentence?
7–5=2
It should look like this:
Use the number line and count back to find the
answer to this sum:
18 – 7 = ?
Can you do it by counting up to find the difference?
Draw a blank number line.
Count back in tens and units to find the
answer to this sum:
63 – 12 = ?
Can you count the units in one jump?
Can you count the tens in one jump and the
units in one jump?
Draw another blank number line.
Can you bridge through the ten to find the
answer to this sum?
72 – 18 = ?
Can you partition and recombine these 2-digit
numbers to subtract them?
99 – 51 = ?
90 + 9
50 + 1
- + =
Calculation in Key Stage 1
Multiplication – Stage 1
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Experience through play:
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
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
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
Stage 3 – Repeated Addition
4 times 6 can be written as:
6 + 6 + 6 + 6 = 24,
4 lots of 6, or
6x4
 Using a blank number line for repeated addition:
+6
0
+6
6
+6
12
+6
18
24
Your Turn!
Can you write the repeated addition to show
these multiplication sums?
1)4 lots of 5 =
2)6 lots of 2 =
3)7 lots of 10 =
4)2 lots of 5 =
5)3 lots of 2 =
Can you show one of these repeated
addition sums on a number line?
Which multiplication sums does this array
show in the columns?
In the rows?
Calculation in Key Stage 1
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
Stage 2
Using an empty number line:
24 ÷ 4 = 6
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-4
0
-4
-4
4
-4
8
-4
12
16
-4
20
Calculations involving remainders:
13 ÷ 4 = 3 r 1
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-4
0
1
-4
5
-4
9
13
24
Your Turn!
Use the objects on your table.
Can you share them equally
between you and your partner?
Can you share them with the whole
group?
Are there any remainders?
Can you show the repeated
subtraction on a number line?
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.
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.