Explanation - Lyndhurst First School

Report
Progression In Calculations at
Lyndhurst First School.
Addition and
Subtraction
Mathematical Calculations in School Today.
This document is designed to help you to understand the calculation methods
your child will be taught in school. When supporting your child at home
with Maths work it would be helpful if you could reinforce these methods
rather than teach them the way that you were taught. The methods are
levelled according to ability and you would need to speak to you child’s
teacher to find out which methods would currently be the most
appropriate for your child to practice at home.
Remember each child progresses at their own pace.
Understanding Addition. (EY/1C/1B)
Explanation
The physical act of counting out
a set number of objects, and combining two
groups, is an important step for children to
explore. This is best done in a practical play
based context as much as possible.
Use a Numicon shape and add on the 1 shape...
What number do you have now? Find the new
Numicon shape to cover over the top.
Understanding addition as combining two groups
Children need to experience counting out a set of
objects and combining them with another set of
objects to make a total amount. Initially this needs
to be adding 1 more.
Explore 1 more through simple songs and rhymes, for
example ‘1 man went to mo’ or ‘1, 2, 3, 4, 5, once I
caught a fish alive’.
Eg. 4 plus 1 makes 5.
Count out a set of 4 and another set of 1. Then
count them altogether to reach a total of 5
Key Questions/Vocabulary
More, more than, one more, after, add, plus, count, total, equals,
makes
What is the number after 6?
How will you find out how many there are in total?
Can you show me how you worked out 1 more than....?
Success criteria
•I can add one to a small group of
objects up to a total of 10 and explain
what I am doing.
•I can count out 1p coins to pay for 2
items totalling up to 10p.
Understanding Subtraction. (EY/1C/1B)
Explanation
The physical act of counting out
a set number of objects and taking some away
is an important step for children to explore.
This is best done in a practical play based
context as much as possible.
Count out a given number of objects and take
away 1 of them... How many do you have now?
Understanding subtraction as taking away
Children need to experience counting out a set
number of objects and then removing/taking away
a certain number from that group. Initially this
needs to be taking away 1 from a set.
Eg.
Explore 1 less through simple songs and rhymes, for
example ’10 green bottles’ or ‘5 little speckled frogs’.
7 take away 1 leaves 6
Count out 7 objects. Then remove 1 from that set
and count the objects that are left over.
Key Questions/Vocabulary
Less, less than, one less, before, take away, subtract, leaves,
equals
What is the number before 5?
How many different ways can you show me that 8 subtract 1 is
7?
Can you show me how you worked out 1 less than.....?
Success criteria
•I can use objects to take away 1 from
any number up to 10.
• I can work out how much I have left
from an amount up to 10p when I buy a
sweet costing 1p (using 1p coins to work
practically).
Using a Number Track for Addition. (1B/1A)
1
2
3
4
5
6
7
8
9
10
One more than four is five
Explanation
Number tracks can be
used for children to
locate a number, learn
the order of numbers,
and to begin to add one
and then more than one
to a given number.
Children need to be able to understand the order of numbers remains
the same and that as we count on the numbers get bigger by 1. They
need plenty of practise in counting objects and by rote... Count the
stairs as you go up to bed... Count your footsteps as you walk across a
room.... Write the numbers to 10 on separate pieces of paper and get
your child to put them into order, counting to check., then progress to
ordering numbers to 20.
Begin to recall all pairs of
numbers that total 10.
Key Questions/Vocabulary
Begin to know doubles up to
Order Numicon
double 5.
Count on, add, more, more than, equals, totals,
1 – 10 set, place a
makes
shape on top of
Success criteria
Find the number that is one more than...? 4
the next one,
• I can use a number track to
more than...?
noticing how
count on and find the answer to an
there is a
Count on 3 places from 15, where do you land?
addition sum up to 10 and then to
difference of 1.
How many is 5 more than 8?
20.
Simple Jottings/Mark Making for Addition. (1B/1A)
13
+
2
=
15
Explanation
Simple mark making is the first stage of children’s independent
jottings to help them solve additions. They draw or make the
appropriate number of marks under each number then count them up
to reach the total. It is not necessary to draw the number of marks
under the answer. Children can also use objects, such as counters,
sweets, beads, to create groups to combine to find the total of an
addition.
Key Questions/Vocabulary
Count, count on, more, add, plus, sum,
altogether, total, equals
How many altogether?
Find the number that is five more
than...?
Count on 6 more from 13, what number
do you get to?
Children need to begin to see that
addition produces the same
answer which ever way round it is
solved eg 8 + 2=10 and 2+8=10.
It is COMMUTATIVE. Lay the 8
and 2 Numicon shapes together
and place another 2 then 8 on top
to see it is the same. Encourage
children to see that it is easier
and quicker to count on from the
largest number.
Success criteria
• I can use simple jottings
to support the addition of
two numbers up to a total of
10, then 20.
• I can begin to select
appropriate apparatus to
support addition.
Using a Number Track for Subtraction. (1B/1A)
1
2
3
4
5
Explanation
Number tracks can be used for
children to locate a number, learn the
order of numbers, and to begin to
find out one less and then a few less
than a given number.
Key Questions/Vocabulary
Count back, take away, subtract, less than, leaves,
equals
Find the number that is one less than ....? Five less
than....?
Count back 4 places from 8, where do you land?
How many is 5 less than 9?
6
7
8
9
10
One less than nine is eight
Children need to be able to understand the order of
numbers remains the same and that when counting
back the numbers get smaller by 1. They need lots of
practice in counting backwards... Count back as you go
down the stairs.... Do a countdown from 10 or 20
before you leave the house....Write the numbers to 10
on separate pieces of paper and get your child to
order them in reverse, then try from 20.
Order Numicon
1 – 10 set, note
the difference
between two
shapes next to
each other is 1.
Success criteria
• I can use a number track to
count back and find the answer
to a given question starting from
numbers up to 10, then up to 20.
Simple Jottings/Mark Making for Subtraction (1B/1A)
12
-
3
=
9
Explanation
Simple mark making is the first stage of children’s
independent jottings to help them solve subtractions.
They draw the initial number of objects and then
cross off the number it says to take away and
count the ones left over. Children can also use
objects, such as counters, sweets, beads, to create
the initial group and then physically take away the
right number to find the answer to the subtraction.
Key Question/Vocabulary
Count, count back, subtract, take away, cross off
Difference between, leaves, equals
How many are left over?
Find the number that is 6 less than...?
Count back 5 from 16, what number do you get to?
At this level,
children need to
see that when
doing subtraction
the biggest number
needs to be first
and you take away
the smaller
number.
Success criteria
• I can use simple jottings
to support the subtraction
of two numbers starting
from numbers up to 10, then
20.
• I can begin to select
appropriate apparatus to
support subtraction.
Using a Blank Number Line for Addition. (1A/2C)
Explanation
Blank number lines are used to enable children to count on and back with more than one jump. Children
are taught to draw their own number line and start with the biggest number. There is no need to write
+1 in each jump. Children learn to use ones jumps, adding single digit numbers and working within a range
up to about 20. It is only necessary to record where they start and where they end up after adding on.
They can then progress to using this method of single jumps when adding ‘teen’ numbers and working
within numbers to about 30. Remember to jump on from the biggest number!
15 + 3 = 18
15
4 + 17 = 21
18
17
Rapidly recall all pairs of numbers that have a total of 10.
Know doubles to double 5 and begin to know doubles up to double 10.
Key Questions/Vocabulary
Count on, count on in ones, add, plus, more than, total,
equals, makes
Which number are you going to start your line with?
How many ones jumps do you need to do?
What number have you reached?
Children can use
Deines (one
blocks) to place
in the jumps and
support the
visual image of
how many they
need to add on.
21
Success criteria
• I can use number lines to
support the addition of two
numbers starting from
numbers up to 20, then 30.
• I can use a number line to
help me solve addition
problems involving money ,
up to 30p, and measures, up
to a similar amount.
Using a Blank Number Line for Subtraction. (1A/2C)
Explanation
Blank number lines are used to enable children to count on and back with more than one jump. Children
are taught to draw their own blank number lines, enabling them to do calculations within any range of
numbers. There is no need to write -1 in each jump. Children learn to use ones jumps, subtracting single
digit numbers and working within a range up to about 20, then 30. Their recording methods should be
the same as for addition, except that with subtraction they start at the right hand end of the line and
jump back.
9–4= 5
5
14 – 6 = 8
9
Key Questions/Vocabulary
Count back, count back in ones, less than, take away,
Subtract, leaves, equals
Where are you going to start your number line?
Which number are you starting with?
How many jumps back do you need to do?
What number have you reached?
8
Children can use
Deines (one
blocks) to place in
the jumps and
support the visual
image of how
many they need to
count back.
14
Success criteria
• I can use number lines to
support the subtraction of
two numbers starting from
numbers up to 20, then 30.
• I can use a number line to
help me solve subtraction
problems involving money ,
up to 30p, and measures, up
to a similar amount.
Developing use of Number Lines, Adding Tens and Ones. (2B)
Children need to understand the place value of each digit in order to partition
2-digit numbers into tens and ones.
26p + 12p = 38p
Recall all + and –
facts for each
number to at least
10.
Know doubles up to
double 10 and
their corresponding
halves.
+10
26p
36p
38p
33 + 21 = 54
+10
33
Key Questions/Vocabulary
Addition, add, plus, more, more than,
ten more, count in tens, one more, count in
ones, total, equals, altogether
How many tens jumps do you need to do?
How many ones jumps?
Inverse (children need to know at this
stage that addition and subtraction are
inverse operations, they undo each other)
+10
43
Explanation
When children understand that 15
is made up of one ten and five ones,
they can learn a more efficient
method of using a number line than
just doing 15 single jumps. When
confident adding on ‘teen’ numbers,
progress to adding numbers with
more than one ten.
53
54
Success criteria
• I can use number
lines more efficiently
to add on 2-digit
numbers by adding on
the tens and then the
ones.
Developing use of Number Lines, Subtracting Tens and Ones. (2B)
Children need to understand the place value of each digit in order to partition
2-digit numbers into tens and ones.
48g – 13g = 35g
-10
35g
38g
48g
116 – 24 = 92
-10
92
Key Questions/Vocabulary
Subtract, take away, minus, less than,
ten less, count back in tens, one less,
count back in ones, leaves, equals,
Difference between (we find the
difference between when the numbers
are close together and it is easier and
quicker to count up than back.
Eg 53 – 47, it is easier to count on from
47 to find the difference between the
two numbers than count back 47 places.)
96
-10
106
Explanation
Subtracting tens and ones is the same as for
addition. Jottings are set out as shown, with a
record of where you have reached kept under
the line and the jumps done recorded over the
line. There is no need to write +1 or -1 in the
small jumps, this would be inefficient. When
confident adding on ‘teen’ numbers, progress to
adding numbers with more than one ten.
116
Success criteria
• I can use
number lines more
efficiently to
subtract a 2-digit
number by
counting back the
tens jumps and
then the ones
jumps.
Add or subtract 9 or 11 by Compensation (2B/2A)
To subtract 9, -10 and then +1
To add 9, + 10 then -1
25 + 9 = 34
146 – 9 = 137
+10
25
-10
34 35
136 137
To subtract 11, -10 then - 1
To add 11, + 10 then + 1
85 – 11 = 74
117 + 11 = 128
-10
+10
117
146
127 128
74 75
Practical exploration with money,
using 10p and 1p coins can help to
Explanation
support the understanding of
When adding or taking away 9, children
which way to compensate.
are taught that it as quicker to add
Key Questions/Vocabulary
/subtract ten and then adjust by one
Add, plus, more than, sum
accordingly. This is why it is important
Subtract, take away,
that children recognise number
minus, less than
patterns to count on and back in tens
Equals, leaves, totals
from any number.
adjust
85
Success Criteria
• I can quickly add or subtract 9
from any 2 or 3 digit number by
adding or subtracting 10 first
and then adjusting by 1.
• I can quickly add or subtract 11
from any 2 or 3 digit number by
adding or subtracting 10 first
and then adjusting by 1.
Partition and Recombine. (2B/2A)
To add 23 and 35....First add the number of tens,
so 20 + 30 = 50
23
+
35
Then add the number of ones, so 3 + 5 = 8
Finally combine the answers to give the total,
so 50 + 8 = 58
50
+
8
= 58
Explanation
Some children find this strategy a quick and easy method for addition, that
they soon are able to do it mentally. Initially it is important to give
calculations where the ones digits do not total more than 10, (we say they
don’t cross the tens boundary). Once they are confident in this method
they can progress to partition and recombining 2-digit numbers where the
ones do cross the tens boundary,
eg 37 + 26. So 30+20=50, 7+6=13 Then 50 +13=63
Key Questions/Vocabulary
Tens digit, ones digit, units
Partition, split, recombine
How many tens? How many ones?
How many altogether?
Confidently recall + and – facts to 10
then 20 (eg, 9 + 6, 13 – 7, 15 + 4)
Know all + and – facts for multiples of
10 to 100 (eg, 30 + 50, 90 – 20)
Success Criteria
• I can do addition
more efficiently by
partitioning numbers
into tens and ones
and then recombining
them.
Develop Efficient Use of Number Lines. (3C/3B)
74 + 43 = 117
+40
+3
74
114
152 – 68 = 96
-60
-6
84
117
90
-2
150
152
Explanation
Once children are confident and accurate in the use of tens and ones jumps, they can progress to using
multiple of tens jumps. Encourage children to use their knowledge of number bonds to bridge to the nearest
multiple of 10 to make counting easier (as in the second eg). Make sure they keep a record in their jumps of
what they are doing so that they can check they have + or – the correct number.
Key Questions/Vocabulary
Addition, add, plus, more, more than
Subtract, take away, minus, less than
Ten more, ten less, count in tens
One more, one less, count in ones
Difference between, inverse
Equals, leaves, altogether
Use mental recall of + and –
facts to 20 and apply to
problems.
Know all the + and –facts for
multiples of 5 to 100 (eg 35 +
45, 80 – 55).
Derive rapidly all number pairs
that total 100 (eg 61 + 39,
22 + 78)
Success Criteria
• I can add and subtract
chunks of tens and ones to
make my calculations more
efficient.
• I can bridge through the
nearest multiple of ten.
Partition and Recombine. (3C/3B)
346
+
38
300 + 70 + 14
300 + 80 + 4 = 384
Key Questions/Vocabulary
Hundreds digit, tens digit, ones
digit, Partition, split, recombine
How many hundreds? tens? ones?
How many altogether?
137
+
400 + 110
389
+
500 + 20 +
Explanation
At this phase. Children can
partition and recombine
numbers that may cross the
tens or hundreds boundary.
They will also be able to use this
method with 3-digit numbers.
16
6
Deines can be used to
create a clear visual image
of the place value of each
digit and supports the
understanding when the
tens or hundreds
boundaries are crossed.
= 526
Success Criteria
• I can add 3 digit
numbers by partitioning
them into hundreds, tens
and ones, adding them and
then recombining to reach
the total.

similar documents