Transcript KS1 Maths Information Presentation

Maths Information Evening
Foundation & Key Stage 1
Wednesday
th
24
April 2013
What is the Maths Framework?
• The Maths Framework follows on from the
success of the Numeracy Strategy
• It is structured to enable children to spend
more time on a particular area and to
make links in their learning
• The Maths Framework incorporates seven
strands of learning that are organised into
blocks
Using and applying mathematics [including problem solving]
Knowing and using number facts
Calculating
The seven
Counting
andmathematics
understanding strands
number of objectives - 1
Handling data
Understanding shape
Measuring
Block A
Counting,
partitioning
and calculating
Using and applying mathematics
Block B
Securing number
facts, understanding
shape
Using and applying mathematics
Block C
Handling
data and measures
Counting and understanding number
Calculating
Knowing and using number facts
Understanding shape
Using and applying mathematics
Measuring
Handling data
Block D
Calculating, measuring
and
understanding shape
Using and applying mathematics
Calculating
Block E
Securing number
facts, relationships
and calculating
Using and applying mathematics
Measuring
Understanding shape
Counting and understanding number
Knowing and using number facts
Calculating
Block A
Counting,
partitioning
and
calculating
Block B
Securing
number
facts,
understanding
shape
Block C
Handling data
and measures
Block D
Calculating,
measuring and
understanding
shape
Block A
Unit 1
Block B
Unit 1
Block C
Unit 1
Block D
Unit 1
Block E
Unit 1
Block A
Unit 2
Block B
Unit 2
Block C
Unit 2
Block D
Unit 2
Block E
Unit 2
Block A
Unit 3
Block B
Unit 3
Block C
Unit 3
Block D
Unit 3
Block E
Unit 3
Term 1
Block E
Securing
number
facts,
relationships
and calculating
Term 2
Term
3
Block B
Securing
number
facts,
understanding
shape
Block C
Handling data
and measures
Block D
Calculating,
Measuring and
Understanding
shape
Block A
Unit 1
Block C
Unit 1
Block B
Unit 1
Block D
Unit 1
Block E
Unit 1
Block A
Unit 2
Block B
Unit 2
Block D
Unit 2
Block C
Unit 2
Block E
Unit 2
Block A
Unit 3
Block B
Unit 3
Block C
Unit 3
Block D
Unit 3
Block E
Unit 3
Block A
Counting,
partitioning
and
calculating
Block E
Securing
number
facts,
relationships
and calculating
The Teaching and Learning
Cycle
Review – Teach – Practise – Apply –
Review
The cycle constitutes four teaching and learning foci:
• Focus A: Review prior learning and introduce new
learning
• Focus B: Practice and Consolidate learning
• Focus C: Apply, secure and extend learning
• Focus D: Review and evaluate progress in learning
Examples of teaching sequences over a Unit
(10 lessons)
Focus A
Focus B
Focus C
Focus D
Review prior
learning/
introduce new
learning
Practise and
Consolidate
Apply, secure
and extend
learning
Review and
evaluate
progress in
learning
(3
Lessons)
(1 Lesson)
(2 lessons)
(2
Lessons)
Foci B, C
Focus D
Review and
evaluate
progress in
learning
(1 Lesson)
(1 Lesson)
or
Focus A
Focus B
Focus C
Focus B
Focus C
Focus D
Review prior
learning/
introduce new
learning
Practise and
Consolidate
Apply, secure and
extend learning
Practise and
Consolidate
Apply, secure and
extend learning
Review and
evaluate progress
in learning
(1 lesson)
(4 Lessons)
(2 Lessons)
(1 Lesson)
(1 Lesson)
(1 Lesson)
Developing an understanding of number
• When children arrive in Reception we work to
develop their knowledge of numbers 1-10
(before moving on to numbers to 20) by:
- singing number songs and nursery rhymes (e.g.
10 green bottles, 5 currant buns)
- reading number stories (e.g. The Three Pigs,
Goldilocks)
- playing number games when matching numerals
and objects in practical situations in class and
the outside area.
Experience, Language, Pictures, Symbols (ELPS)
(Liebeck, 1984)
Firstly the children are first exposed to learning
to add, subtract, double and halve through
experiences with objects which is when they
begin to develop some mathematical language.
They are then gradually encouraged to record
their working out. Initially this is by mark
making, drawing pictures, or moving images on
the interactive white board. They then write
numbers and eventually symbols (number
sentences, for example 3+2=5).
An example of addition using ELPS in the
context of toy cars
1) Experience and Language:
The children are encouraged to develop mathematical vocabulary such as
‘altogether’, ‘more’, ‘makes’ and ‘adding’ in practical contexts when counting
objects in 2 or more groups.
Example:
Whilst the children are playing with various amounts of cars each. An adult
asks the children ‘How many cars have you got each / altogether? Who has
got the most? How many more do you have than ‘Child A’?’
2) Pictures:
Once a child has started to develop their understanding of counting objects.
An adult would encourage them to record their working out either by;
mark making, tally charting or drawings of cars or shapes. They would also be
encouraged to work with images on the interactive white board or paper
instead of counting objects.
Once a child has developed recognition of number they are also introduced to
number lines when counting objects to help with the concept of ‘counting on’.
3) Symbols:
A child would then be encouraged to record how many cars there are by
matching numeral cards to objects / writing numerals. At a later
developmental stage the child would record their working out using a number
sentence e.g. Child A has 2 cars and Child B has 3, so Child A writes 2+3=5.
An example of subtraction using ELPS in the
context of money.
1) Experience and language:
Similar to addition, the children are encouraged to develop mathematical
vocabulary such as ‘take away’, ‘less’ ‘left’ and ‘fewer’ in practical contexts when
subtracting one or more from a group.
Example:
Child B is pretending to be a shopkeeper who has pretend price tagged fruit.
Child A is pretending to be a customer, he/she has counted ten penny coins into
her bag:
Child A: ‘I would like an apple please.’
Child B: ‘That’s 3p please.’ (Child A counts out / subtracts 3p from her 10p and
passes it to Child B)
Adult intervenes: ‘Child A, how much money do you have left now? Can you buy
anything else from Child B?’
2) Pictures:
Once a child has started to develop their understanding of taking away
objects, similar to addition an adult would ask a child to move / take away
images on the interactive white board or on paper.
Example:
A child has images of 10 pennies on the interactive white board / paper.
When asked to pay for a 3p apple, he/she subtracts 3p by crossing off 3
images of coins and counting how many coins are left.
Once a child has developed recognition of number they are also
introduced to number lines when subtracting objects to help with the
concept of ‘counting back’.
3) Symbols:
The child is then encouraged to record how many coins they have by writing
numerals / selecting numeral cards. At a later developmental stage they
would record their working out using a number sentence e.g. 10p - 3p = 7p.
Multiplication
• The children learn to count in 2s and 10s
by singing songs and counting with
actions.
• They also learn about doubling. This is
introduced as ‘adding on the same amount
again’. The children use the following
mathematical language: ‘add’, ‘double’,
‘more’, ‘and’, ‘altogether’, ‘same amount’.
An example of doubling using ELPS in the
context of plastic bears
1) Experience and language:
Discussion about doubling objects:
Adult: Can you make double 3 by counting out these bears? (child makes two
groups of 3 bears).
Adult: How much is double three? / How many bears are there altogether?
(Child counts all of the bears in two groups)
2) Pictures:
Once a child is familiar with doubling objects, they double pictures on the
interactive white board and double numbers on the number line by circling the
number they are doubling and counting on.
3) Symbols:
The child would then record double of a number by writing number sentences
e.g. 3+3=6 (In Year 2 they start to write the symbol for division when writing
number sentences).
Division
• The children’s first introduction to division
is through being taught sharing and
halving. This is introduced as ‘sharing in to
two or more equal groups / parts’. They
halve an object as an introduction to
halving number.
• The children use the following
mathematical language: ‘take away’,
‘halve’, ‘share’, ‘equal’, ‘fair’.
An example of halving using ELPS in the
context of an apple and buttons
1) Experience and language:
Discussion about halving an object:
Adult: How can I cut this apple in half?
Child: You can cut it down the middle.
Adult: How do I know that the apple is in half now?
Child: Because it is in two equal bits.
Then a child would develop an understanding of sharing an amount of buttons
in half between themselves and another child.
2) Pictures:
On the interactive white board the child would then share out images of
buttons
into two equal groups.
3) Symbols:
The child would then record their groupings by writing numbers. (In Year 2
they
start to write the symbol for multiplication when writing number sentences.)
Shape, Space and Measures
• We talk about, recognise and recreate simple
patterns
• We use language such as ‘greater’, ‘smaller’,
‘heavier’ or lighter to compare quantities
• We use language such as ‘circle’ or ‘bigger’ to
describe the shape and size of solids and flat
shapes
• We use developing mathematical ideas and
methods to solve practical problems
Theory into Practise
Year 1
Counting and Understanding Number
Most children:
• Read, count and write numerals from 0-20
(then beyond)
• Use knowledge of place value to order
numbers
• Say the number that is one more and one
less than a given number
Knowing and Using Number Facts
•
•
•
•
Number bonds to 5 and 10
Simple addition to at least five
Count on and back in 1, 2, 5, and 10’s
Know doubles of all numbers to at least 10
Calculating
Most children learn to:
• Use the vocabulary related to addition and
subtraction and the symbols to describe and
record
• Relate addition to counting on and understand
that addition can be done in any order
• Understand as take away and find the difference
by counting up
• Apply these skills solving practical problems
Understanding Shape
Most children learn to:
• Name common 2D shapes and 3D solids
and describe their features
• Use them to make patterns, pictures and
models
• Use everyday language to describe
position, direction and distance
Measure and Data Handling
Most children learn to:
• Estimate, measure weigh and compare
objects, choosing and using suitable
uniform non-standard units and measuring
instruments
• Answer a question by recording
information in lists, tables, pictograms and
graphs
Writing number stories and number sentences
Writing and solving word problems
Number line
100 square
Counting in 2s 5s and 10s to understand
values of coins
Repeated subtraction as division
Theory into Practise
Y2
Counting and Understanding Number
Most children learn to:
• Count up to 100 objects by grouping them
and counting in tens, fives and two’s
(aerobics)
• Explain what each digit in a two digit
number represents, including numbers
where 0 is a place holder (partitioning)
• Add two digit numbers using the
partitioning strategy
Knowing and Using Number Facts
Most children learn to:
• Derive and recall all addition and subtraction
facts for each number to at least ten (number
bonds)
• Understand that halving is the inverse of
doubling, derive and recall doubles of all
numbers to 20 and the corresponding halves
• Derive and recall multiplication facts for the 2, 5,
and 10 times tables and the related division
facts
Calculating
Most children learn to:
• Add or subtract mentally a one digit number or a
multiple of ten from a two digit number
• Use practical and informal written methods to
add and subtract two digit numbers
• Repeated addition and arrays as multiplication
and sharing and grouping as division
Understanding Shape
Most children learn to:
• Name common 2D and 3D solid shapes,
sort make and describe shapes referring
to their properties
• Identify reflective symmetry in patterns
and 2D shapes and draw lines of
symmetry in shapes
• Follow and give instructions involving
position, direction and movement
Measuring and Handling Data
Most children learn to:
• Estimate compare and measure length, weights
and capacity using standard units
(m,cm,kg,litre)
• Use units of time (seconds, minutes, hours and
days) and know the relationship between them
• To read the time to the quarter hour, half past
and on the hour
• Answer a question by collecting and recording
the data
• Use ICT to organise and present data
Addition- Partitioning method
24 + 35 =
T: 20 + 30 = 50
U: 4 + 5 = 9
50 + 9 = 59
Some children might prefer to use a number line
or a 100 square to support them with each step
of the addition. Most will be able to add a single
digit to a multiple of 10 mentally.
Subtraction- Number line
36 – 14 =
-1
22
-1
23
-1
24
-1
25 26
-10
36
Multiplication- Repeated addition
Division- Repeated subtraction
Homework and Top Tips
• The homework set is to reinforce the learning that has
taken place during the week
• It will not contain any new strategies or concepts
• You can help by working on the 2, 5, 10 and 3 times
tables beyond that they will learn the 4 and 6’s
• Research shows that children learn best through
practical experiences that they can relate to the world
around them
• So let your children buy the newspaper or ask them to
work out how many apples you will need for pack
lunches next week
• If you are feeling really adventurous get cooking with
them and let your child weigh and measure the
ingredients