Transcript Numeracy - Parent Workshop

Supporting Your Child
in Maths
March 2014 – J Cartwright
Areas of Maths
Maths is split into 4 main parts:
Ma 1 – Using and applying
Ma 2 – Number
Ma 3 – Shape, space and measure
Ma 4 – Handling data
Number makes up 50% of what the children need to know.
APP
(Assessing Pupils’ Progress)
• APP is used to collect evidence of what
skills and knowledge children
demonstrate in class.
• Provides an opportunity to collect
evidence during practical activities and
games.
• We use these grids to set individual
targets.
New Target Grids
We will now be using the following target
grids throughout the school. They will be
stuck into the front of the childrens’ maths
books. They are based on the APP grids
used by teachers to assess children and
the childrens’ individual targets will be
taken from these grids. (Note – they only
cover Number and not the other areas of
maths).
1c
1b
1a
2c
I am beginning to count
10 objects.
I can read most
numbers up to 10.
I am beginning to write
numbers up to 10.
I can count on in 1’s.
I can count back in 1’s.
I am beginning to
recognise and
sort coins and use
them in role play.
I am beginning to
record my work
using my own
mark making.
I
I
I
I
I
I can count and read numbers
from 0-20.
I can order numbers up to 20.
I am beginning to count
forwards and back in 2’s
and 10’s.
I am beginning to find ½ of an
even number of objects.
I can count on from the
smallest number to the
biggest.
I can find coins which make
10p.
I can jump in 1’s on a numbered
number line to help me
solve problems.
I can write addition and
subtraction sums using +
– and =
I am beginning to understand
place value.
I am beginning to recognise
odd and even numbers.
I can say what number comes
next.
I can say the number which is
10 more or 10 less.
I am beginning to count in 5’s.
I am beginning to use the
fraction ¼
I can count up to find the
difference between 2
numbers.
I am beginning to remember all
of the number bonds to
10.
I can use my number bonds to
add and subtract pairs of
numbers in my head.
I can double numbers up to 5.
I can choose coins to make
20p.
I can jump in 1’s and 10’s on a
numbered number line to
help me solve problems.
I
I
I
I
I
I
I
I
I
can
can
can
can
can
count 10 objects.
read numbers up to 10.
write numbers up to 10.
order numbers up to 10.
say the next number and what
number is one more or one less.
can count back from 10 to 0.
am beginning to find 1/2 of shapes.
am beginning to add by counting on.
am beginning to know some addition
facts.
can subtract numbers of objects to
10.
can solve addition and subtraction
problems up to 10 objects
(practically).
can solve problems involving 1p and
£1.
can record my work with objects and
pictures.
am beginning to write addition sums
using + and =
2c
2b
2a
3c
I am beginning to
understand place
value.
I am beginning to recognise
odd and even
numbers.
I can say what number
comes next.
I can say the number which
is 10 more or 10 less.
I am beginning to count in
5’s.
I am beginning to use the
fraction ¼
I can count up to find the
difference between 2
numbers.
I am beginning to
remember all of the
number bonds to 10.
I can use my number bonds
to add and subtract
pairs of numbers in
my head.
I can double numbers up to
5.
I can choose coins to make
20p.
I can jump in 1’s and 10’s on
a numbered number
line to help me solve
problems.
I can order numbers to at least
100.
I can recognise sequences of
numbers including odd and
even.
I can continue a number
sequence going up or down.
I can count in 2’s, 5’s and 10’s.
I can halve and quarter amounts
of objects.
I can colour ½ or ¼ of a shape.
I know that subtraction is the
inverse of addition.
I can write the matching
subtraction sum for an
addition sum.
I am beginning to use a number
line to find the difference
between 2 numbers.
I know my number bonds to 10.
I can solve simple problems
using addition and
subtraction (involving
money and measure)./
I can double and halve numbers
up to 20.
I can choose coins which make
50p
I can count, read, write and
order numbers to 100.
I know the value of each digit
in 2 digit in any 2 digit
number.
I am beginning to find 1/3 of
shapes.
I can multiply using repeated
addition.
I can use a number line to
multiply.
I am beginning to divide using
repeated subtraction.
I can add multiple of 10.
I can add a multiple of 10 to a
2 digit number in my
head.
I can subtract a multiple of
10 from a 2 digit
number in my head.
I can decide if to add or
subtract when solving
problems.
I can choose coins to make £1
I can use the X and ÷ signs
when writing sums.
I can use the £ sign.
I can use £ and p
I know the value of each digit in a
3 digit number.
I can order numbers to 1000.
I can multiply numbers by 10.
I can count on or back in 10’s or
100’s.
I can find fractions of shapes and
numbers.
I am beginning to recognise simple
fractions which are the same
as each other.
I know that ÷ is the inverse of X.
I am beginning to divide where
there are remainders.
I know my number bonds to 20.
I can add or subtract a near
multiple of 10 from a 2 digit
number in my head.
I can do simple X and ÷ sums in my
head.
I can solve 1 step problems
involving + - X and ÷
I can use written methods to add
and subtract 2 digit
numbers.
3c
3b
3a
4c
I can use £ and p
I know the value of each digit in a 3
digit number.
I can order numbers to 1000.
I can multiply whole numbers by 10.
I can count on or back in 10’s or
100’s.
I can find fractions of shapes and
numbers.
I am beginning to recognise simple
fractions which are the same
as each other.
I know that ÷ is the inverse of X.
I am beginning to divide where
there are remainders.
I know my number bonds to 20.
I can add or subtract a near
multiple of 10 from a 2 digit
number in my head.
I can do simple X and ÷ sums in my
head.
I can solve 1 step problems involving
+ - X and ÷
I can use written methods to add
and subtract 2 digit numbers.
I can read and write numbers to at least 1000 and put
them on a number line.
I can divide whole numbers by 10.
I can add or subtract 1, 10 or 100 to any number.
I can recognise sequences of multiples of 2, 5 and 10.
I can recognise negative numbers.
I can count back past 0.
I can use decimals to one decimal place.
I know the matching fractions and decimals for ½ and
1/10.
I am beginning to relate fractions to division.
I can find ½, ¼, 1/3, 1/5 and 1/10 of shapes and sets
of objects.
I am beginning to use = for balancing sums.
I know my 2, 3, 4, 5 and 10 X tables.
I can solve problems involving X and ÷ including those
with remainders.
I can solve 2 step problems involving – and +
I can use written methods to + and – 3 digit numbers
including bridging through 10 and 100.
I can use the grid method to X 2 digit numbers by 2,
3, 4, 5 or 10.
I can ÷ 2 digit numbers by 2, 3, 4, 5 or 10 including
those with remainders.
I can X and ÷ whole
numbers by 10 or
100.
I can round numbers to
the nearest 10 or
100.
I can use decimals to 2
decimal places.
I can position decimal
numbers on a
number line.
I can recognise
equivalent
fractions.
I can find fractions of
numbers and
shapes.
I am beginning to know
my 6, 7, 8 and 9 X
tables.
I can round up or down
after dividing.
I can choose the correct
operation and the
best method to
solve 1 and 2 step
problems.
I can convert pounds to
pence.
I am beginning to use the
written method
for ÷
I can X and ÷ whole
numbers by 10
and 100
including those
with decimal
answers.
I can read write and
order decimal
numbers and
know the value
of each digit.
I can recognise
multiples of 6,
7, 8 and 9.
I can convert mixed
numbers to
improper
fractions and
vice versa.
I can recognise simple
equivalent
fractions,
decimals and
percentages.
I can + and – 2 and 3
digit numbers in
my head.
I can estimate and
check by
rounding.
I can + and – 4 digit
numbers.
I am beginning to know
when to use a
calculator.
4c
4b
4a
Level 5
I can X and ÷ whole numbers by
10 and 100 including those
with decimal answers.
I can read write and order
decimal numbers and know
the value of each digit.
I can recognise multiples of 6, 7,
8 and 9.
I can convert mixed numbers to
improper fractions and
vice versa.
I can recognise simple equivalent
fractions, decimals and
percentages.
I can + and – 2 and 3 digit
numbers in my head.
I can estimate and check by
rounding.
I can + and – 4 digit numbers.
I am beginning to know when to
use a calculator.
I can identify square numbers.
I can find pairs of factors for
any number to 100.
I can order negative numbers.
I can recognise and describe
number patterns.
I can + and – decimal numbers to
2 decimal places.
I can use inverse operations to
find a missing numbers.
I can give the matching ÷ fact
for any X fact up to 10 X
10.
I know all the X facts to 10 X 10.
I can do simple sums involving
negative numbers.
I can X and ÷ 3 digit numbers by
a 1 digit number.
I can round any number to the
nearest 10, 100 or 1000.
I can round decimal numbers.
I can recognise and describe
number relationships
including multiple, factor and
square.
I can order decimal numbers to 3
decimal places.
I am beginning to understand simple
ratio.
I can match fractions and decimals.
I am beginning to understand
percentages.
I can use brackets in simple sums.
I can solve problems involving
converting money and finding
simple percentages.
I am beginning to use simple
formulae expressed in words.
I can X decimal numbers.
I can multiply and divide whole and
decimal numbers by 10, 100
and 1000.
I can round decimals to the nearest
decimal place.
I can recognise and use number
patterns and relationships,
I can reduce a fraction to its
simplest form.
I can order fractions and decimals.
I understand simple ratio.
I can find a simple fraction or
percentage of a number or
amount.
I can + and – negative numbers.
+ and – decimal numbers which do
not have the same number of
decimal places.
I can solve simple problems involving
ratio and direct proportion.
I can understand and use simple
expressions using symbols.
I can use and interpret coordinates
in all 4 quadrants.
Addition
Begin with place value – children must know the value of each digit.
At level 2 we use the expanded version of the addition method:
e.g. 54
+27
11
70
81
54 + 27 = 81
Then we move on to the compact version of the addition method:
e.g.
67
+24
91
1
67 + 24 = 91
At level 3 we use the addition method to add 3 digit numbers.
We also begin to add decimals (where bridging is not required)
146 + 128 =
1.32 + 1.25 =
e.g. 146
+128
274
e.g. 1.32
+1.25
2.57
1
At level 4 children would be expected to use the addition
method to add decimals which DO require bridging.
Subtraction
We teach children different methods and allow them to choose
their preferred methods when solving problems.
We find the difference between 2 numbers using a number line:
81 – 57 =
+20
+3
57
+1
60
20 + 3 + 1 = 24
80
81
We also teach the subtraction method:
4
1
156
- 39
117
156 – 39 = 117
Multiplication
At level 2 we use repeated addition to
solve multiplication sums or problems.
e.g.
8X4=
8+8+8+8=
At level 3 we need to be able to multiply a 2digit number by 2, 3, 4, 5 or 10.
To do this we use the multiplication method:
23 X 4 =
e.g.
X 20
3
4 80
12
80
+12
92
At level 4 we also need to be able to multiply a simple
decimal by a single digit:
8 X 3.8 =
X
3.0
0.8
8
24.0
6.4
24.0
+ 6.4
30.4
Division
At level 2 we use repeated addition to solve
division sums and problems:
e.g.
16 ÷ 4 =
0
4
8
12
16
At level 3 we divide 2-digit numbers by 2, 3,
4, 5 and 10.
To do this we teach 2 different methods and
allow children to choose their preferred
method when solving problems:
172 ÷ 5 =
3 4 r2
5 172
10 X 5
50
122
10 X 5
50
72
10 X 5
50
22
4X5
20
2
10
10
10
+ 4
34 r2
Or: 172 ÷ 5 =
3 4
5
2
1 7 2
r2
When teaching division we always teach it as
how many equal parts can fit into that
number.
e.g. 45 ÷ 5 = how many 5’s go into 45?
count in 5’s until we reach 45.
the answer is 9.
Basics
•
•
•
•
•
•
Number bonds to 10
Number bonds to 100
Number bonds to 20
X tables
Doubling
Halving
X tables
Children can never do too much X tables practise!
If they have been set a X tables to learn as a target
this includes not only counting in that number but also
answering quick fire questions in random order.
Effective ways of learning include clapping and
counting, quick fire questions, singing songs and
playing games such as Multiple Madness (Maths Zone),
pennies in a jar, jumping multiples.
At level 2 we focus on 2’s, 5’s and 10’s.
At level 3 we also need to know 3’s and 4’s.
At levels 3 and 4 we move on to 6’s, 8’s, 9’s and 7’s.
Doubling and halving
If children can not double or halve a 2-digit
number in their heads, we encourage them to
use arrows:
3 4
60
8
4 4
60+8 =68
20
2 20+2=22
Problem Solving
Huge importance in children being able to
apply the skills they have learnt.
1 step problems
e.g. Amy had 3 boxes of eggs with 6
eggs in each box. How many eggs
altogether
Children need to recognise what operation to use (multiplication or
repeated addition), then decide what numbers to multiply, then
work out the answer.
6 X 3 = 18
or
6 + 6 + 6 = 18
2 Step problems:
e.g.
Amy has 3 boxes of eggs with 6 eggs
in each. She eats 4 of the eggs, how
many does she have left?
Step 1: 3 X 6 = 18
Step 2: 18 – 4 = 14
Useful Websites
www.educationcity.com
www.mathszone.co.uk
www.woodlandsjunior.co.uk
www.coxhoeprimary.co.uk
www.ictgames.co.uk
www.oxfordowl.co.uk (Maths and Literacy)
www.beam.co.uk
Areas which are always useful to
practise:
X tables (check targets!)
Number bonds
Written methods
Word problems
Using money in real life
Telling the time
Extras
Work books to complete at home (order from Miss Cartwright)
Education City tests (available to use on the website)
Parent Voice (use the link on our school website to leave comments).