Transcript Maths KS1 - Claverley Primary School

Maths Evening For Parents.
March 2015
Key Stage 1
Addition
• When children first begin to add we begin with pictorial
recording
Jane had 3 bears. She was given 2 more.
How many does she have now?
3+2 = 5
We then encourage the children to think about which number to start withCounting3 on from the larger number : 3 + 5 a child chooses the larger number, even when it is not
the first number, and counts on from there: 'six, seven, eight'
As well as children using their fingers to add on small amounts, a number line will be introduced.
It is more efficient to count on from the larger number because you have less to work out. It also
shows children that addition can be done in any order ; it doesn’t matter which number you add first,
you get the same answer.
The second stage in addition
Children then begin to use numbered lines to support their own calculations using a numbered line to count
on in ones.
8 + 5 = 13
+1 +1 +1 +1 +1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Year 2 Add with 2-digit numbers.
Developing mental fluency with addition and place value involving
2-digit numbers, then establish more formal methods.
Add 2-digit numbers and tens:
27+30=
Partitioning is important here: knowing that 23 =
10 + 10 +1 +1 +1
Add 2-digit numbers and
units:
16+7=
16+4=20 +3=27
Add pairs of 2-digit numbers, moving to the partitioned column
method when secure adding tens and units:
•
STEP 1:Only provide examples that do NOT cross the tens boundary until
they are secure with the method itself.
STEP 2: Once children can add a multiple of ten to a 2-digit
number mentally (e.g. 80+11), they are ready for adding pairs of
2-digit numbers that DO cross the tens boundary (e.g. 58 + 43).
Subtraction
Counting back – taking away
There were five frogs. Two jumped into the pond. How many were left?
1 less than 10
Subtract by taking away
Count back in ones on a
numbered number line to
take away, with numbers up
to 20:
Find the ‘difference between’
This will be introduced
practically with the language ‘find the
difference between‘ and ‘how many
more?’ in a range of familiar contexts.
‘Seven is 3 more than four’
‘I am 2 years older than my sister’
Make up some difference questions
with the answer 5
Mental subtraction
• Children should start recalling addition and subtraction facts up to and within 10
and 20, and should be able to subtract zero.
• At this stage we also help the children to make links between addition and
subtraction…
Eg if 3+4 =7 then 7-3 must=?
A difference can be found by counting up from the smaller number to the larger
number.
E.g. 24 – 19 = 5.
Count up from 19 to 24 and the difference is 5.
A number line may be used for this.
If my friend is 14 and his sister is 11, how much older is my friend?
Subtract with 2-digit numbers
47 - 23 = 24 Partition the second
number and subtract it in tens and
units, as below:
Move towards more
efficient jumps back,
as below:
Teaching children to bridge through ten
can help them to become more efficient, for example 42—25:
Multiplication
Multiply with concrete objects and
pictorial representations.
The first stage in written multiplication
Children will experience equal groups of objects and will begin to count in 2s, 10s and 5s. They will
work on practical problem solving activities involving equal sets or groups.
How many legs will 3 teddies have?
2
+
2
+
2
There are 3 sweets in
one bag.
How many sweets are in
5 bags altogether?
= 6
3+3+3+3+3
= 15
Multiply using repeated addition
(using at least 2s, 5s and 10s)
Use repeated addition on a number line:
Starting from zero, make equal jumps up on a number line to work out multiplication facts and write
multiplication statements using x and = signs.
Use practical apparatus:
Multiply using arrays
(using at least 2s, 5s and 10s)
• Use arrays to help teach children to understand the commutative
law of
• multiplication, and give examples such as 3 x = 6.
Use arrays:
5 x 3 = 3 + 3 + 3 + 3 = 15
3 x 5 = 5 + 5 + 5 = 15
Use mental recall:
Children should begin to recall multiplication facts for 2, 3 ,
5 and 10 times tables through practice in counting and
understanding of the operation.
Division
The first stage in division.
Children will understand equal groups and share items out in
play and problem solving. They will count in 2s and 10s and
later in 5s.
Group and share small quantities
Using objects, diagrams and pictorial representations to solve problems involving
both grouping and sharing.
Grouping:
How many groups of 4 can be
made with 12 stars? = 3
Sharing:
12 shared between 3 people
is ? 4
Children need to be taught to understand
the difference between ‘grouping’
objects
(How many groups of 2 can you make?)
And ‘sharing’ (Share these sweets
between 2 people)
Grouping or repeated subtraction
There are 6 sweets, how many people can have 2 sweets each?
Repeated subtraction using a number line or bead bar
12 ÷ 3 = 4
0
3
1
2 3
4 5 6
3
7 8
3
9 10 11 12
3
Grouping using a number line:
Group from zero in equal jumps of the divisor to find out ‘how many groups of _ in _ ?’.
Pupils could and use a bead string or practical apparatus to work out problems like ‘A book costs £3. How many books can I buy
with £12?’
This is an important method to develop understanding of division as grouping.
Arrays:
This represents 12 ÷ 3, posed as
how many groups of 3 are in 12?
Pupils should also show that the same array can represent 12 ÷ 4 =
3 if grouped horizontally.
Key number skills needed for multiplication and division at
Y2:
•
•
•
•
•
•
Count in steps of 2, 3, and 5 from 0
Recall and use multiplication and division facts for the 2,3, 5 and 10 multiplication tables, including
recognising odd and even numbers.
Calculate mathematical statements for multiplication and division within the multiplication tables
and write them using the x, ÷ and = signs.
Show that multiplication of two numbers can be done in any order (commutative) and division of
one number by another cannot.
Solve problems involving multiplication and division, using materials, arrays, repeated addition,
mental methods, and multiplication and division facts, including problems in contexts.
Recognise and use the inverse relationship between multiplication and division